PoS(CORFU2019)133 milar present https://pos.sissa.it/ s an example. , basically just run several (dual) strings on the string. The remarkable NOT interact rn[1]. Our "objects" (essentially the on with tary Particle Physics and Gravity" s" do y hadrons with their partons all having Physics Sciences, Ritsumeikan y, Kyoto 606-0105, Japan light cone variables in our formalism. e Commons al License (CC BY-NC-ND 4.0). , by means of a constituent / a strings from objects picture si 0, and thus infinitely many constituents. The p-adic string i ∗ Scattering is a fake = x string field theory [email protected] [email protected] This opens also up for hoping for generalizations inspired b Bjorken variable Speaker. We have constructed a new formalism for describing a situati at a time, a to, but importantly different from the “bits” by Charles Tho feature and simplicity of ouror formalism sit is, trivially that fixed. the "object bits) represent rather a making a lattice in the ∗ Copyright owned by the author(s) under the terms of the Creativ c Corfu Summer Institute 2019 "School and(CORFU2019) Workshops on Elemen 31 August - 25 September 2019 Corfu, Greece

university E-mail: and Yuji Sugawara Lab., Science and Engineering , Department of Holger Bech Nielsen Niels Bohr Institute, Copenhagen University E-mail: Masao Ninomiya Yukawa Institute for Theoretical Physics , Kyoto Universit Instructive Review of Novel SFT with Non-interacting consituents “objects”, and attempt Generalization to p-adic theory Attribution-NonCommercial-NoDerivatives 4.0 Internation PoS(CORFU2019)133 ; and the variable, σ one tanding of the the other of the alled “objects” ( possibility of de- eld theories as a uch “objects” by: of the bits) as con- Holger Bech Nielsen make discretization . The crucial differ- y have only a trivial g of the fields on the scattering amplitudes nd we want to extend nd them in this article , we basically got rid σ thin structure. Indeed τ we ey should probably then g to the splitting into bits , which we called a Novel , if Replaced by a Quan- the string parametrized by d string from bits reformu- different way from ordinary BY RENOMALIZATION FINITE NUMBERS FROM theory gives 1 is split into string-bits by discretizing the parameter become non-divergent STRING σ ONLY for the left and the right moving components respectively. σ − τ and . In this light it should not be so surprising that a main characteristic of our σ σ . So while he has to have some time development with + respectively, whereas say Thorn still has both the discretized variable τ − τ - Veneziano models. τ σ In Thorn’s the bit (= constituents) do interact, but in quite − or = Quantum field theories τ σ or + quantum field theory particles. Thorn The most important gain of (super)string theory over ordinary quantum fi Here when then also alluded to our formalism may bring hopefully some unders The Wonderful Finiteeness of (Super)String-theory gets Spoiled We can announce this feature, while thinking of our “objects” (analogous We have worked since long on a formalism for a string field theory[2] with the QFT The real crux of the matter is that we for each of the two “movers” only need τ σ • . I.e. each string bit corresponds to a very small interval in the parameter + relation of the usual string theory tonot the be p-adic string called theories[5, string 4]. theories, Well, because th analogous although to Veneziano the models, p-adic they formalism are leads accordingprecisely to to of the attempt a to different understa kindthey of rather share structure the than clumpy the structure true of the string: p-adic being numbers. 1.1 a long Major Achievement Anti-suggests putting it into objects: situents of the strings;Novel the SFT strings being with thenadic Non-interacting thought String consituents upon Generalization as “objects”, composed p- of s scribing an arbitrary number of strings, inSFT.[3] other Our words “Novel a string SFT” field has theory samelation spirit of as string the theory before by ours Charlesthe developpe parameter Thorn along [1]. the In string usually Charles called Thorn’s theory ence between our string and thatconsider the of wellknown Charles conformal Thorn gauge is choice that formalismstring and we into use before right the goin splittin mover and left mover components. Then the point is that of the “time”, since wetwo only need the variable, which we discretize, i.e. one or while the (even made a string fieldTHE theory) START of the variable formalism is that the time-development forwhich our is string-bits, good which to distinguish we them sincedevelopment as from long time Charles c goes Thorn’s on. “string bits”) Thisand feature that generalize is the that then feature a as very being interesting of feature interest a in itself. τ σ Generalizing Novel SFT 1. Introduction theory of everything is: tum Field Theory of “bits” (unless the bits are not normal particles) “time” variable PoS(CORFU2019)133 or example g the more rresponding type and one ”, which first f a string, which tate in which we in the pair, and a Holger Bech Nielsen lly speaking circle. mbine such a pair and type” and “left-mover- ory. alar particle. (For a string shall now be identified by (which is the name we use for our of time at first). That is to say that , so we basically think of two types of “objects” 2 at one moement do not interact sum of the objects in the pair . So the perturbation with the usual divergencies does not come up. In ours it turns out that the are the ones that like Chreles Thorns ( “objects” string bit do NOT interact bits) Nielsen-Ninomiya : Now we assume that the objects sit in what we call “cyclically ordered chains This mathematically constructed The reader should get in mind that the connection from our “objects” to gettin Now the rather new idea is that one shall now imagine selecting one right-mover At first have in mind that the state of the whole universe - i.e. the structure co • of all means that they are organized as sitting very closely along a topologica essentially a corresponding to such a pair wethen can has - its sometimes connection - attache toequal an to the “infinitesimal” the “object” bit sum formalism o of of the “objects” ours in by the having pair. the momentum f free particles in this description of the analogon of the second quantizedleft the mover type of these particles,construct which from we that call a “objects”. position,momentum Then which which we is is can the the co sum sum of the of momenta the of positions the of two objects the in objects the pair. 1.2 Overview Ignoring Tecnical Details: Generalizing Novel SFT to the usual secondhave quantized “objects” state each in object e.g. havingtheory degrees with closed of usual strings freedom quantum there shall like field betype”). that two theory types of These of - a “objects” is “right-mover sc a s physically understandable string is of a new type and needs explanation: PoS(CORFU2019)133 al- (see (1.1) ) τ , σ ( ts - a right- µ t that would L of “objects” - X nown formula rom consisting lically ordered of the string(s). as you like) but e very long that for the “objects” et by combining e at quite differ- anti-intuitive for yclically ordered t µ of the string is R e information for a Holger Bech Nielsen , and . or pairs X ) ent moments of time, e left mover one gets g as time develops! σ τ τ red chain” visitng one , and σ cts is basically nothing. ( µ L µ R time track X X -dimensional sheet. This two- . ) but only in σ two . One could say this with the words σ + τ − time-development ( τ µ L X )+ the objects of the two object momenta and positions. σ − 3 τ respectively is supposed to lead to ambiguities, so are not periodic: sum ( even when strings scatter on each other as they do µ µ R L σ string theory, is more new and more is achieved by our X X not periodic in − ) τ σ and ) = τ − µ R , and solving τ X σ ( σ ( R µ X + X τ the formalism in terms of functions of built into that looking at these right mover and left mover variables Think of Right- and Left mover as distinct degrees of freedom...? global basically as Declair Notice two objects to EachThis bit “TWO of OBJECTS String at in each Charles point Thorn of Sense the string” is to correspond to the wellk The truly remarkable observation is that A little Problem that say This is very remarkable since it means that the whole This means that these “objects” sit in a one-dimesnional structure, the “cyc Technical problem, because This means that the objects, if they are considered to be anywhere at all, ar We have to either: But now when you attache the string bits - the small pieces of string - to • the objects do not interact even in the (string-)scattering situation! in string theory, you can claim that what goes on in terms of the obje (1.1)). However, we think that this “object” formulation, when you apply this formulationchains to and a also situation several with strings several c resulting from combining objects in pairs. rather one gets the shape andtoo. momentum density That say is of to the say stringclosed that at string by all we having differ have the not twointo only cyclically pairs the ordered of information chains “objects” of carrying in the different th combinations string also at the one behavior moment of but the g strin This means that the positionmover and and momentum a left of mover the object string-bit - sitting is at given as a the pair of objec ent places from theconstituents. string itself, or the points they correspond to. Completely Generalizing Novel SFT That means you can imagine goingobject arround after such the a other circle one / and a finally “cyclically return orde to the staring one again. for single string dynamics in the conformal gauge: That is to say that whenof we one combine “object” to in make the stringnot right-mover- bits only cyclically all all ordered the the chain pairs bits and we arround one can a from form closed th f string at one moment of time (think of then one easily sees thatdimensional the sheet pairs is will now meant correspondingly in form our a picutre to be identified with the ready that we have solved thebe string giving time development the by “object” writting formulationthe it string too into dynamics much the is honor, solvable “objects”. by because writting Bu it it into is right wellknow and sinc left mover chain”. PoS(CORFU2019)133 Holger Bech Nielsen 4 Fig. 4. Fig. 3. Generalizing Novel SFT PoS(CORFU2019)133 ed on smaller , so that we have ) ) σ Holger Bech Nielsen 2 2 / / + ∆ ∆ τ anonically conjugate) − − or ) ) I I σ ( ( ′′ ′′ , i.e. − σ σ µ τ R X − − τ τ “ “ . ( ( and )) µ µ R L )) I µ L I X X ( ( X ′′ ′′ − − σ σ ) ) 2 2 − − / / τ have in string theory a derivative of delta func- τ ∆ ∆ . “ .... “ ( 2 µ ( R 5 µ , R ˙ µ X )+ )+ L ˙ 1 X ˙ I I Fig. 5 , X ( ( ∗ 0 ′′ ′′ ∗ , and ∆ 1 σ σ ∆ distance µ ′′ L − ≈ − − ˙ ≈ , X ) τ τ 2 ) I “ “ I ( in these variables. Then ( ( − ( µ R µ µ µ L ∆ R L J ob ject J “ X X ..., = = I ) = ) = ∆ I I ( ( is the “lattice constant” for the variables µ µ R L ∆ J J and Here only piecewise functions. we identify only the derivatives or difference of Or that we only care forintervals. local functions in the sense of only letting them be defin More detailed: The But have in mind: The right and left mover variables We then want to Arrange: Each “object” a Full Physical System (a set of variables and their c • Generalizing Novel SFT an “object” for each step of length PoS(CORFU2019)133 the (1.2) ∆ an other enly Num- ith one vari- objects with e can and shall ). We call Objects have full R Holger Bech Nielsen and the canonically ) I ( only the even numbered h an odd number. jects be described just by µ R les for the even neighbors. J is modulo the discretization = = instead of ) ) ) odd) even); ∆ ∆ L 2 in to 2 R ) ) I I R L τ I I R τ τ ( ( ( ˙ X R µ µ R R ˙ − − X (for (for ˙ ˙ X X 1 1 L R τ τ ( ( . ′ ′ ) ) = ) ) δ δ I I )) = 2 2 or from ( ( 1 / / R σ σ µν µν µ R R 1 1 ˙ − X J X ig ig − + I − − ( τ τ − − I I µ R ( ( 6 R R = = = = Π τ τ ( ( form.   L R − ) ) µ µ ′ τ τ R R ) 2 2 even) object a variable set δ X X L 1 R I τ τ ( ( − − ( + where ν ν ) ) L I R ˙ ˙ ( 2 2 X X µ / / R , , of the ) ) 1 1 Π ) 1 1 I ( L R + + ( τ τ ∗ I I R ( ( ( ( ˙ ∆ µ X µ L The kept right objects carry all the right mover information; and the R R R ˙ ˙ π τ τ X X ( (   − µ µ R R discretizes to a function only non-zero in two neightboring points to even numbered X X ) = = R τ (here leaving out a quite analogous left set with ( ′ ) δ I ( , then modify them somehow to achieve: µ R ) I Π Different objects commute. ( L X But the odd ones are essentially the conjugate of the even ones. In fact w and Those objects, which we end upable keeping also in be the associated with formalism, its shall canonically if conjugate associated one w together with it. All variables associated with oneobject. object shall commute with those associated with left carry the left mover information. sets of degrees of freedom. in the “kept” “objects”. We select a subset of objects still so that all information in We found a way to achieve the following wishes before identifying (half) the Because the The Commutator of the Wishes about to construct Object-degrees of freedom: So we shall seek to put in all information from We achieve the wishes by theWe following ansatz: define for each So one object would at firstWe not move commute with the its Information neighbors. on Oddly Numbered Objects to Neighboring Ev ) • • • I ( R particles in a second quantized fieldX theory. Think of at first having the ob objects. zero, we could achieve full commutation by leaving out all objects wit choose the odd objects to be written as differences of the conjugate variab bered Ones to make up Conjugate Variable to say Generalizing Novel SFT tion commutation rule with themselves: discretization step: conjugate set PoS(CORFU2019)133 )) I ( µ R Π , ) I ( µ R equations of J ( Holger Bech Nielsen ith their , of cyclically ordered “even L and R . EVEN I 7 Fig. 7 Fig. 6 here for ) I ( closed string by two sets, µ R J one and ) I ( . µ R ) Π ,... 4 , 2 , 0 , 2 − , 4 − ..., Summary: We can describe Note: We only use We got a way to put the information of a free closed string solution of = I ( Generalizing Novel SFT numbered objects”. motion into that two sets of (infinite) numbers of “even objects” w PoS(CORFU2019)133 reclassify , meaning eld theory closed ones rings in the e(s). I.e. you fake and the canon- ) s a I ( in which you have Holger Bech Nielsen µ R J n. , namely by just putting more couples quantum field theory look nice in “objects”. 0 ≈ 8 ′ , and then we have a formal scattering, although in Fig. 8 X several strings · ˙ X One open string and 0 ≈ do anything during the scattering, but we/the physicists (= second quantized string theory like Kaku and Kikkawa[2] or 2 ) ′ not X string you let it correspond to a +( 2 one - for each of the 25+1 dimensions. (modulo some troubles with gauge ˙ X one ) I ( for free! µ R Π new cyclically ordered chains . L “string field theory” and First describing the two cyclically ordered chains(with massless of non-interacting “objects” spin (= zero particles)). the particles in the quantumThis gives fi the obvious idea to describe Witten[2]...) of cyclically ordered chains upgot in a the same quantum field theory Hilbert spac R Main Point: We Second Quantize the Objects; and There can be Many St The Constraints In String Theories with Open Strings Only One type of “Objects”; while only Each “object” has in the bosonic string theory one degree of freedom - a • • Same Quantum Field Theory ically conjugate choosing ...) the physics of our model for non-interacting “objects” nothing can happe that the objects themselves do 1.3 Scattering of Strings is a Fake. We managed - though with some technical difficulties - to obtain string scattering a Generalizing Novel SFT have the objects into PoS(CORFU2019)133 0 ≈ ′ X · continue ˙ X s, there is no scribed as par- 0 and tinuing being true ot be used to keep Holger Bech Nielsen tates of the ≈ ins would be to just 2 tarted forming such a ) ′ that there is any allusion X +( 2 ˙ X considered 0 0 (1.3) ≈ ≈ should be “weakly” 0 take a nice form in the 2 2 ′

X µ µ R L · ˙ ˙ 9 X X ˙ in 25+1 dimensions: X Fig 9 µ = = X closed (c), closed (a), and 2 2 L R ˙ ˙ 2 X X ) ′ open and closed (b) X String in terms of objects: +( 2 ˙ X and open and closed (d) respectively. The string of It is only by the (initial) states of the objects to denote the “weak” equality. ≈ “Objects” Stringiness (one-dimensionaly touching of objects) is put in via the S In that model, a quantum field theory of just non-interacting massless particle Our “String Field Theory” model is basically the second quantized theory de Since we have no interaction between the “objects” such an interaction cann The usual constraints that stringiness at all! ticles (best in a timeless universe), and then with the constraints imposed. variables used for our “objects”: or make the objects sittingto in “sit”( a or chaine. better run) Sincechain. as they In forming only this a move sense the trivially continuous onlyassume though chain, way it they provided to as will they assume an inittial have the condition, objects s forever being to (from true form the - continuous trivial say cha development). in the beginning - and thus con 1.3.1 Generalizing Novel SFT Here we used PoS(CORFU2019)133 of Ob- gives a String. t the state of the rete it as corre- lic chains extract ], then it is crucial olicaly show in fig Holger Bech Nielsen ted. These cyclically points in common. By ted continuity behavior tion of these objects the red to two other strings! in the final state - the out t least different from the rdered chains open strings Cyclically ordered chain of “even Indeed wecan first interpret it as a couple of Something that at the end leads to the stringy one 10 Fig. 10 objects”: If the two cyclically ordered chains cross in two places, we can interp Now Add One more Open String described also as a Cyclically Oredered Chain The string is in the initial -(When and we also derive final our conditions Veneziano we model need amplitudes - from conditions our only! Novel SFT[3 The Rest of the Objects also form a Cyclically ordered chain menaning it Without Anything happening except in Phantasy two strings scatte jects. hanging together. to the hanging together to one-dimensional chains. Generalizing Novel SFT sponding to two open strings in different ways. cyclically ordered chains in Minkowsky space in two ways: Indeed we symb 11 (b) two cyclically orderedusing chains, just a the black points, and objects, a onetwo can brown combinations see say, of that having objects we two extract shown from onordered the Fig chains combina 12 fig (a) 12(a) and and figtwo 12 12 illustrated (b) (b) in can are fig be each 11 extrac ofquite (b). them differnt Thus along ones. one some can But piecewith out now a different of there shape two correspond and in time to two development. different points cyclically crossing o cyc for reaching the Veneziano model, that also thegoing ansatz strings states - for are the chains strings with thehaving same at Gaussian least wave function some and stringiness associa future, in namely it. a certain Thus stringiness.) we assume basically something abou 1.3.2 A single Open String is described by just PoS(CORFU2019)133 lly ordered nt of time we all the averages of Holger Bech Nielsen of the objects to get such a pair of point- of a factor 2. So you is gotten by aseries of 11 (a) (a) (b) (b) Fig 12 (a) and (b) Fig 11-(a) and (b) On (b) cyclically ordered chains of objects for two open strings. The reader may keep in mind the way one obtains the open string from a cylcica chain of objects. In factthat it of is a so space-time that point sumcoordinates for the or a space-time we point positions take on of the the anycould average pair (open) then of say string. theem the events Whether is through we ofpairs which sum course the of the only points string a on passes convention the iscan the cyclically claim collection ordered as of chain. drawn in Thinking the of figure the to situation give at in least a the mome crude idea that the string Generalizing Novel SFT PoS(CORFU2019)133 that corresponds cyclically ordered Holger Bech Nielsen it is true. ts and on the midle of n expect that in some rallel lines. The string e appropriate moment: essentially from locality We take part of the chain corre- change in a true scattering of dual strings. not in a new way! 12 Fig. 13 To argue that our string theory really is correct, one would first see that If one has couple of double crossing cyclically ordered chains, one ca sponding to the first of theto two the initial second strings and string. combine it with a part of the one 2. Achievements 2.1 In principle we rewrote String Theory, but still would like toone check can if see that indeed the system of “objects” will pairs of objects - paired with each other by a series of locally approximate pa goes through the midle points of all the pairing pieces of lines. Generalizing Novel SFT Lorentz frame you can find the piecethat connection of line line piece connecting will the be two the crossingThe crossing poin idea point of of “faked the scattering” open now stringschains for is into th that a we split couple the of combined cyclically sets ordered of chains the two PoS(CORFU2019)133 remain the L the Veneziano / µ R ut got only one ˙ X - like in Nambu- ”. Then the image Holger Bech Nielsen neziano model from Calculation[3]: having no stringiness 13 Fig 14. By locality one argued the image of the will only change on a nullset. µ R ˙ X out of three terms in the infinite momentum frameIncluding gauge the choise. possibility of negativeBethe-Salpeter[8] energies equation for - the we constituents(objects) at leastamplitude. glimps a way to get all three terms of Spectrum of a string using our Novel String FieldThe Theory (“faked”) Model.[3, scattering 6, amplitude, 10] expecting to get the Veneziano model; b Think say of a couple of strings scattering classically by “exchange of tails • • • of the In spite of the fact that our modelproper being in only itself, a but quantum field only theory in formalism our initial model and quickly final goes state into input, the the track derivation of of string the theory: Ve 2.2 The Veneziano Model Derivation Quickly comes to Technical String same ( mod. nullset) In fact we calculated: Generalizing Novel SFT PoS(CORFU2019)133 Holger Bech Nielsen 14 Fig 15 (a) and (b) Two open strings hit in a point, and exchange tails. Generalizing Novel SFT PoS(CORFU2019)133 µ J nal states ome cycli- for a single ) le that can be 2 ns in terms of tional integral really we may − . µ N tionally integrate J only particle sec- , Holger Bech Nielsen 4 − µ N J ,..., one can create particles (free µ 2 J , regions from the various imagi- H µ 0 ) J ( σ with an in the limit infinite number -values (26-vectors) as taken on by , Ψ µ τ J ( H , where we can think of the 26-vector ) µ J ( † a 15 Fig 16 associated with a series ) µ J ( † a . H Next we must take thecally overlap ordered between chains the - inital and state the - final state. of some stringsThis giving leads s to gluing together the space-time or rather We begin the calculation by“objects” representing being the derived from external a string functional by integral wave through functio an imaginar time of creation operators The string states are created by acting on this space our type “objects” and weighted with a wave function nary time developments. The glued together regions for definitionleads of the to functios complex over which surfaces toregions which func in usual becomes string theory. just like the correspondingThe func counting of the various waysleads to to identify precise the integration systems measures for of the objects Veneziano in model initial integrals. and fi On this ordinary free particle second quantized Hilbert space Formulation of Second quantized “strings” The basic second quantized Hilbert space for our string field theory is • • • • • • and massless) with creation operators denoted ond quantized space only need 24 components increated infinite in our momentum basic frame) model for Fig the 2. free massless partic (which is the main variable for one of our objects/bits) as say the 26-momentum ( Generalizing Novel SFT 2.3 The “usual surfaces” in string theory. PoS(CORFU2019)133 ) µ J ( (2.1) (2.2) † a m used e rough e operators rators tingly enough for the scattering red “objects”: Holger Bech Nielsen FT) for the scattering >. ′′ gy to the back ground state vac . )) “ ) | 2 u ′ ) ( > − 2 α µ N ′′ α − / J µ N 1 − ( J , † vac t ( ) a “ † t ∗ ∗ ) | ( )= a ′ 4 ′ † n ) ∗ ) 2 α − α 4 ) α µ − 2 N − / − µ J N ( µ − 1 N ( J )+ µ J N B † , string − ( 0 J 4 a ∗ ( ( † , − 4 a ··· α − C µ N 16 − ··· † 2 J in the mentioned calculation. µ ) N = ··· ∗ J µ 2 ) > C ∗ µ J ) = ) = ) = µ 2 ,..., t ( J n u 0 µ J ( † = µ , ( string 2 ,..., ( J = t a D † 1 J † α µ , 2 > α ) , a D s Ψ J ,..., µ 0 µ ) Z ( 0 , Ψ 2 J J µ 0 µ Z , A 0 ( ( and J J 1 ··· † should be Rough ( | string ( a Ψ ··· † ∗ string Z ∗ > a Ψ string = is a priori the empty state, meaning without any of the scalar free ∗ ∗ | Z ′′ = where e. g. = H vac “ | ∈ > : ′′ > : our objects). ′′ ) vac “ u | ∼ , Crux: We can make many string states trivially: vac t , “ | s . This problem is supposed to be cured by a more complicated vacuum state (th ( A > used. ′′ > string described as consisting of a cyclically ordered chain of even numbe particles ( The state vac ′′ A single string creation operator in our scheme in terms of object-creation ope With that we can simply make a several string state by acting with several of thes We ran into troubles of only obtaining one out of three Euler Beta-functions When we used infinite momentum frame (for gauge choice) we got, but interes “ | vac “ Dirac sea for Boson [7]),| so that one can both add and subtract ener We did not determine the overall coefficient has the form amplitude by using infinite momentumfor naturally combined with such a no particle vacuu Generalizing Novel SFT 2.4 Really the vacuum only quite right for 25+1amplitude dimensions, (for our bosonic string constituent S on a vacuum 2.5 Got Veneziano model from Fake scattering! PoS(CORFU2019)133 ) in our correc- rapidly in terms non-zero artificial “A solution ∼ eory. ’s one. transverse p is rather easily to y Holger Bech Nielsen be achieved, because seperately), we could momentum compared situents. L wave function construction on a free and carries no signal of ms of objects as being a X with our non-interacting l convergent loop in the “incoming” state , that one has a hopefully - comes from the and we now know that the hadrons only R particles (hadrons). f would be preserved! X particles but ; , then there would be no energy for 0 = x by looking e.g. at hadrons with their . avoid divergences 17 Rather as if the strings are just a clever( momenta less strongly falling off under the scattering! It is divergence propblem “objects” to have large transverse momenta, but they do not the strings come in only via the objects being inserted in ∼ ! transverse ultraviolet chains exponentially they would in loops give rise to large no exponentially (as Gaussians). seek a theory that is finite fell off We have presented a “novel string field theory” or perhaps better to say and because of that emit fall off amplitude for partons they really Nothing happens to the objects construction in a fundamental world, most naturally interpreted as a particle th strings a priori in(quantum it. fluctuating) Rather overlap between the object statesof corresponding strings to and the in strings the “outgoing” one! The basic SFT Hilbert space is just that of free massless Our model is string-bit-theory deviating in important way from Charles Thorn If Generalization of non-interacting constituent idea Let us suppose we Object-picture from the wave function of the string in terms of con Since the main thing - to get soft cut off to Perspective: String theory may be considered as a mathematical But if all the partons had Bjorken variable[9] How the soft/exponential cut off of the Veneziano model comes in sa Conclusion The suppression of large transverse momenta in scattering in the faked way • • • tions and there would be falling off 4. Genralizations contain quantum field theory (for masslessconstituents spin (=objects= our zero string particles) bits) Remarkable string field theory model: formulation. Generalizing Novel SFT 3. Perspective wave function of the “string” in terms of our objects(=bits, but in replace the ‘string” by thought upon structure provided we take its interna of several-strings-string-theory”: the partons to scatter on each other and the exponential fall of understand, when one has assumed theGaussian wave falling function off of one. the “string” Then init the ter would large require momentum some faked constituents scatteringhave cannot that. Or rather it isto only the exponentially few ones objects with with small large momenta. transverse 5. Conclusion of the objects to PoS(CORFU2019)133 (then stituents quations tized parti- r cyclically trivial starting eories, such as ing high (trans- mber of strings. er and left mover mbered constituents/string- Holger Bech Nielsen ntial theories for all 10]. for all constituent zero! x . Bjorken scattering of string theory, in the sense that there is no 18 0 of course would need an infinite number of con- solution = x especially the fake stituents (since the Bjorken x’s must add up to unity. The string can with our objects be considered such an infinite nummber of con model. Could one generalize the stringordered sets to the another doubled pattern strings) ? for the constituents (than ou The p-adic string[4, 5] is the obvious candidate for such generalization[ The basic formalism is a massless quantum field theory without interactions. These particles are called “even objects” and arebits, identified when with one the first even discretize nu the stringd.o.f. after having divided it into right mov there would even be no enrgy for the partons to scatterA at all. model with only zero Bjorken verse) momenta should be avoided by making the By analogy with a hadronic bound state, we argued that the ultraviolet caus There is so little “string” incle, basic that formulation one only would being say: a Theformalism. massless string second is quan a mathematical construction from rather It is a string fieldBut theory it in is the very sense different in ofKaku the and describing spirit Kikkawa possibly or of an Wittens the arbitrary string formalism field nu from theories[2]. usual string field th Our formulation can be considered a more time development left in ourof object motion. formulation, meaning that we solved the e All the time development is Technical Resume Conclusion. Concerning the general looking for finite and therefore meaningfull pote • • • • • • • • • • • Conclusion on Generalization continued. of physics: Conclusion on Generalization to other Finite theories (hope) Generalizing Novel SFT PoS(CORFU2019)133 k as emeritus University, and oked upon as an les for which to Holger Bech Nielsen him very good hos- ld theories in higher or allowing him as a nce and Engeneering, e Corfu conference and to 191 (1987) ry - Liberating Right and Left nd the Standard Models”Bled July 574 -576 (1987) B 199 lving String Theory by Liberating arXiv 1112. 542 [hep-th] y 2, Phys. Rev. D17 (1978) 1073 eory, in Proceedings of the 10th , Phys. Lett. 70B (1977) 85 71 ys. Rev. D52 (1995) 5980 5069 1 0011 Fukuoka Japan AIP conference , In Moscow 1991. Proceedings, etter y, Phys. Rev. D16 (1977) 366 hys. ysics Letters B 1992 (1987) theory for open string: 19 I. Volovich, “p-adic space-time and string theory”, Math. P P. Freund and E. Witten, “Adelic string Amplitudes”, Phys. L Tohwa International Symposium in String Theory,Proc July vol. 3-7, 607 2 p. 185-201; arXiv: hep-thH. 0111240.v1, B. Nov.200 Nielsen and M. Ninomiya,movers, An in idea Proceedings of of New the String 14th11-21, Field Workshop, 2011, “What Theo eds. Comes N. Beyo M. Borstnik, H.H. B. B. Nielsen Nielsen and and D. M. Luckman Ninomiya,Left “A and Novel Right String Movers’, Field JHEP_202P_05131.v2 Theory (2013) So ’ C. B. Thorn, Reformulating string theory with 1/N expansion O. Bergman, C. B. Thorn, String BitC. Model B. for Thorn, Superstring, Space Ph from String Bits, JHEP11 (2014) 110 M. Kaku and K. Kikkawa, Phys. Rev.D10(1974)110; M. Kaku and K. Kikkawa, Phys. Rev.M. D10(1974)1110; Kaku and K. Kikkawa, Phys- Rev.S. D10(1974) Mandelstam, 1823: Nucl. Phys. B64 (1973)205; E. Cremmer and Gervais, Nucl. Phys., B90Witten (1975) type 410 mid-point interaction of covariant stringE. field Witten, Nucl. Phys. B268 (1986) 253. C. B. Thorn, On the Derivation of Dual Models from Field Theor Sakharov Memorial Lecture in Physics, Vol 1* 447 hep-th/940 C.B. Thorn, On the Derivation of Dual Model from Field theory M. Ninomiya acknowledges Yukawa Institute of Theoretical Physics, Kyoto One of us (H.B.N.) acknowledges the Niels Bohr Institute for allowing him to wor [4] Peter Freund and M Olson, “Non-archimedian strings”, Ph [2] As for bosonc string field theory in the light-cone gauge: [3] H. B. Nielsen and M. Ninomiya, A New Type of String Field Th [1] R. Giles and C. B. Thorn, A lattice Aproach to String Theor also the Niels Bohr Institute andpitality Niels during Bohr his International stay. Academy M.N. for alsoDepartment giving acknowledges of at physics Yuji Sugawara sciences Lab. Ritsumeikanvisiting Scie Researcher. University, Kusatsu Campus f References and for partial economic support.Norma Also Mankoc thanks food Borstnik etc. for asking supportthan from for 4 th a dimensions. way The to thinking get onattempt hadronic meaningful to like quantum find bound fie states such could amake namely scheme the be convergent using lo theory. bound states as the theory behind the partic Generalizing Novel SFT Acknowledgement PoS(CORFU2019)133 Holger Bech Nielsen ˇ T Progress of Theoretical ˘ A U.), “Novel String Field theory with d Theory and Derivation of ea” â : - Study of the Naive Vacuum Theory ps://doi.org/10.1143/PTP.113.625 .) (2019) Contribution paper to 22nd sue 3, March 2005, Pages 603-624, . I: - Formulation of Negative Energy Sea o Amplitude”, JHEP 02(2018) 097, e-print: titute of Physics, P.O. Box 57, 11001 ”, Phys. Rev. 84, 1232 (1951) [4] 614 (1950) July-August. H. Bethe and E. 20 -Proton Scattering and the Structure of Nucleon, γ Physics, Volume 113, Issue 3, March 2005, Pages 625-643, htt Salpeter, “A relativistic Equation for bound state problem https://doi.org/10.1143/PTP.113.603 Holger B. Nielsen, Masao Ninomiya, “Dirac Sea for Bosons. II for Bosons” Progress of Theoretical Physics, Volume 113, Is for the Toy Model World Prior to Filling the Negative Energy S Veneziano Amplitude, published in Pos Corfu 2016 (2017) 134 1705.01739[hep-th] H. B. Nielsen and M. Ninomiya, “An Object Model of String Fiel Workshop on What comes Beyond the StandardH. Models B. p. Nielsen 232-236 ( Bohr Inst.)also and Negative M. Energy Ninomiya Constituents/Objects (Ocami, gives Osaka Venezian City Belgrade, SERBIA Phys.Rev.185 (1969) [8] Yichiiro Nambu for earlir work Prog.Theoretical Phys. 5 [9] J. Bjorken “Inelastic Electron-Proton and [7] Holger B. Nielsen, Masao Ninomiya, “Dirac Sea for Bosons [6] H. B. Nielsen (Bohr Inst.) and M. Ninomiya (Ritsumeikan U [5] “p-Adic, Adelic and Zeta Strings” Branko Dragovich, Ins [10] H.B. Nielsen and M. Ninomiya, paper to appear. Generalizing Novel SFT