Almost 50 Years with String Theory:
A framework to formulate from the Planck length to the Hubble radius
M.M. Sheikh-Jabbari
Iranian Physics Society, Annual meeting on particle physics and fields Isfahan, Bahman 1394
1 • In 1968, string theory was born through a paper by G. Veneziano On Dual Resonance Model, as an effective theory for hadrons.
• Since then, in almost 50 years, string theory has undergone many ups and downs, commonly known as string theory revolutions.
• Despite these “revolutions,” a satisfactory understanding of string theory is still missing.
• This talk is devoted to presenting the current status of string theory from a historical viewpoint.
2 On the timeline of string theory, and its revolutions
• Late 1960’s, birth of string theory and “dual resonance models.”
• 1974-5, first revolution: String theory contains massless spin two particles, string theory as a theory of gravity.
• 1984-5, second revolution, cancellation of anomalies in superstring theories, string theory as a theory of quantum gravity.
• 1994-95, third revolution, dualities, birth of M-theory, D-branes.
• 1997-98, fourth revolution, AdS/CFT presented and formulated.
• 2000’s, fifth revolution/revelation: String Theory landscape.
• Current status and future expected revolutions/breakthroughs.
3 On the birth of string theory:
• By early 1960’s hadron physics was in full bloom, there was a zoo of hadronic particles, resonances, found in (deep) inelastic scattering experiments.
• Gell-Mann’s quark model, was nicely accommodating these parti- cles, mesons and baryons. Nonetheless, it did not contain dynam- ics, the cross-sections and decay rates.
• “Strong interactions” was thought not to be described by a quan- tum field theory.
• This led people to think outside the field theory models of the time. The S-matrix theory developed in this atmosphere.
4 • The “sum rules” and phenomenological formulas describing “res- onance”, their mass and width, was very common.
• In 1968, Veneziano wrote a “dual resonance model,” which was compatible with the mass to spin ratio predicted by Regge.
• Veneziano’s model predicted infinitely many hadrons and their scat- tering amplitude as a function of their mass and spin.
• In 1969-70, Nambu, Nielsen, and Susskind realized independently, through a study of poles of the Veneziano amplitude (as pointed out by Hagedorn in 60’s), that these poles coincides with energy levels in vibrating modes of a string.
• However, the course of dual models was in decline....
5 • In 1972-73, ’t Hooft and Veltman showed renormalizability of Yang- Mills theories and, soon after Gross, Wilczek and Politzer estab- lished asymptotic freedom.
• In 1973-74, the quantum field theory model for strong interaction, Quantum Chromo Dynamics, was proposed.
• During 1973-76, some people tried to dismiss QCD or the “dual resonance model” in favor of the other and some tried to reconcile them.
• The experimental evidence (deep inelastic scattering) was piling up in favor of the quark model and the QCD, and implicitly against the dual model.
6 First revolution: String theory is a theory of gravity.
• In 1974, J. Schwarz and J. Scherk, and independently T. Yoneya, noted that the spectrum of “dual resonance model” contained massless spin two particles.
• But, this theory had its own issues, it had tachyons in its spectrum.
• In 1976, S. Deser, B. Zumino, and independently L. Brink, P. Di Vecchia, P. Howe, wrote the string worldsheet action.
• In 1981, A. Polyakov quantized the worldsheet action.
7 • In the rest of 1970’ and early 1980’s, it was noted that
– there are open strings as well as closed strings. The latter have massless spin two, while the former a massless vector boson.
– the theory of bosonic strings is well-defined in 26 dimensions.
– Interaction of strings (via joining and splitting of the endpoints) was formulated in the light-cone gauge.
– Strings had tachyon in their spectrum.
– “Bosonic String” theory has no fermions in its spectrum.
– Most of string computations were done in light-cone gauge and it was not clear whether these results are gauge-independent and whether light-cone gauge captures the whole theory.
8 Other relevant technical developments of the era:
• Supersymmetry was proposed in 1971-72 (several people are at- tributed to it).
• In 1974 Wess and Zumino showed the first example of non-renormalization properties of supersymmetric field theories.
• Supersymmetry proved a very useful technical tool in taming loop effects and runnings. The era of SUSY-gauge theories had began.
• In the 1975 and 1976 theories with local supersymmetry, super- gravity, were introduced by Arnowitt, Nath and Ferrara, Freedman, Van Nieuwenhuizen.
9 Other relevant technical developments of the era, cont’d:
• SUGRA was continued in many different ways (Abdus Salam was one of its main advocates) and is still an active field of research.
• From the early days in 1971, supersymmetry and string theory (of Schwarz, Ramond and Neveu) had intimate relations.
• K. Settle in 1976 (see also his 1978 paper) wrote a very influential paper on renormalizability of higher derivative gravity theories.
• Blavin-Polyakov-Zamolodchikov in 1984 developed the 2d confor- mal field theory which was extensively used for further development of string worldsheet theory.
• Alvarez-Gaume and Witten in 1983 analyzed chiral anomaly in su- pergraivty theories.
10 Second revolution: String theory is a theory of quantum gravity.
• Superstring theory was formulated in early 1980’s. Two ways to add SUSY:
– Via supersymmetry on the worldsheet (Ramond-Neveu-Schwarz) + Gliozzi-Scherk-Olive (GSO) projection, or
– through imposing superymmetry both on the worldsheet and on target space (Green-Schwarz formulation).
• Superstring theory is consistently formulated in 10dim (critical string theories).
• By 1984 three 10dim. superstring theories were known: type IIA, type IIB and type I. The first two were closed string theories and type I includes both open and closed strings. 12 • In 1984 M. Green and J. Schwarz proved that type IIB and type I theories are anomaly free.
• In 1985 two more superstring theories found (Gross-Harvey-Martinec and Rohm): Het SO(32) and Het E8 × E8:
• There are FIVE 10d superstring theories which are anomaly free.
• We only knew how to formulate them perturbatively using world- sheet 2d CFT techniques.
• It was shown that superstring theory is one-loop renormalizable.
13 String compactifications, infinitly many string theories.
• Although it was portrayed as a unifying theory, because in 10d. it has only one parameter gs a scale ℓs it.
• But usual physics is in 4d. Four dimensional theories can be ob- tained via Kaluza-Klein reduction or compactification.
4 • For R × M6 background, there are infinitely many choices for M6.
• Geometric properties of M6 appear as physical parameters of 4d theory. So, there are potentially infinitely many 4d string theories.
• Specific requirements about 4d theory can restrict M6, but as it has become very clear now, in no ways fixes it.
14 Third revolution: Dualities as the unifying theme; Discovery of D-branes.
• This unfortunate feature motivated string theorist to accept in- finitely many theories as a feature and cure the problem in an ingenuous way: All these theories are equivalent, they are dual to each other.
• Idea of dualities was known in the context of QFT’s and string theory: – S-duality, like Electric-Magentic duality. 2 – T-duality, string theories on circles with radius R and ℓs /R are equal.
• A good part of 1990’s was devoted to developing web of dualities.
15 • Dualities opened the way to discuss beyond perturbative, weakly coupled theories.
• Exploring dualities was very fruitful:
– Dualities were essential to considerably reduce the number of independent lower dimensional string theories.
– A more fundamental M-theory was proposed. Low energy ef- fective theory of M-theory is the 11d SUGRA.
– T plus S duality led to discovery of D-branes (Polchinski, 1995).
– The important property of D-branes is that there is a U(N) gauge theory structure associated with N coincident D-branes. (Witten, 1995).
16 D-branes on their own turn were the key to all post-1995 developments in string theory:
• D-branes were used to propose the M(atrix) model formulation for M-theory (Banks-Fishler-Shenker-Susskind, 1996).
• D-branes were used to model certain BPS black holes within string theory and propose black hole microstate counting. (Strominger and Vafa, 1996.)
• Brane configurations were essential for modelling supersymmetric gauge theories within string theory setup and giving a simple, geo- metric picture for non-perturbative analysis of SUSY gauge theories (Mainly due to Witten, 1996-97.)
• Most importantly, D-branes led to AdS/CFT (Maldacena, 1997).
17 Fourth revolution: The AdS/CFT
• D-branes may be described by their low energy effective theory, a U(N) SUSY gauge theory, or by viewing them as sources for energy momentum tensor, solutions to SUGRA.
• This dual description led J. Maldacena to the AdS/CFT proposal:
Maximally SUSY d- dimensional gauge theories at their conformal × D−d−1 fixed line (point) is dual to string theory on AdSd+1 S back- ground.
• This duality was given a very precise meaning and formulation by Gubser-Klebanov-Polyakov and independently by Witten in early 1998.
18 • This duality has been extended to gauge theories with almost ar- bitrary gauge group and matter content.
• This duality has been a key player of the developments of string theory and HEP-TH in general.
• A more relaxed, less robust, but very useful statement of AdS/CFT is gauge/gravity correspondence:
Einstein gravity on a weakly curved background describes strongly coupled gauge theories at large N.
• Gauge/gravity correspondence has been used as a very powerful tool to address regimes in QFT where usual perturbative tools fail.
19 The AdS/CFT duality or gauge/gravity correspondence
• have changed our understanding of QFT (beyond the Wilsonian formulation).
• has changed how we think about gravity.
• provides a different handle on string theory.
• is a powerful framework for (rough) modelling of many observa- tionally relevant physical phenomena.
The AdS/CFT is now at a stage which seems deeper and more fundamental than its parent theory (string theory).
20 Fifth revelation: String theory landscape
• Starting from some handful of theories in 10 or 11 dim. which are related to dualities, the number of options increases very rapidly as we come to lower dimensional theories.
• All geometric parameters of the compactification manifold appear as dynamical (quantum) fields in the lower dimensional theory.
• Number of such fields is very large for a generic given (Calabi-Yau) compactification.
• Most of these fields are massless scalars, the moduli.
21 • Existence of the moduli causes both theoretical and observations problems.
• The moduli problem can be tackled through moduli fixing.
• Many efforts has been devoted to resolution of this problem in the last 20 years.
• We do not have a single satisfactory (stable) moduli fixed com- pactification which allows for formulation of physics in a world like ours, e.g. with a tiny positive cosmological constant.
• However, there are many moduli fixed compactifications which are meta-stable and are moduli fixed.
22 • Although we are very far from a full classification of consistent compactifications. The emerging picture is that these many pos- sibilities are then allowing for the string theory landscape of vacua:
The low energy theory of a moduli-fixed compactifiction of string theory is described by a complicated potential with a large number of fields. This potential have huge number of local minima. String theory expanded around each minimum desribes a world, which in some aspects is potentially similar to ours.
• BUT, string theory itself does not provide us with a principle on how to choose among these huge number, from within string theory they are as good:
String theory in itself does not have the means to leads us to a universe in this landscape.
23 • If this is true (yet to be 100% established), string theory faces a very big issue, the landscape or multiverse problem:
Real world models based on string theory fail to produce falsifiable predictions. We can not expect string theory to have any prediction on the value of the parameters of the low energy theory, like mass and couplings and the cosmological constant.
• String moduli problem if settled as where it is suspected now, calls for a drastic change in the way we are doing physics, its philosophical framework, something that we are not prepared for.
24 We seem to be standing in a decisive moment for the future of string theory, if not the whole physics or empirical sciences.
Awaiting for revolutionary, reliefing ideas for string theory,
may be from you,
Thank You For Your Attention
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