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Citation Gutperle, Michael, and Andrew Strominger. 2002. “Spacelike Branes.” Journal of High Energy 2002 (4): 018–018. https:// doi.org/10.1088/1126-6708/2002/04/018.

Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:41417326

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The three-form g ψ t the mak go Charged The This This §∞ −∞ of ersed. string. the wish kwise terms v c the it e = = or where field z where z W 2.3 to where top the In tra as clo F compared implies alizations string. Explicitly JHEP04(2002)018 2 h is is es as to S tly An the the S2- en) has and and h that stop wire, 4 harge h (2.15) (2.13) (2.14) (2.12) whic this in (ev c the on arriv the solution whether oundary (suc ws. teraction time er the picture b dd Note ) ort whic v fields, the in o one on o should in the in 4 compared follo subsequen origin e F full t w 0, (2.9 v the ely ∗ = supp as electromagnetic flo whose example, = of ha will of the t D ecause large brane. t via The dimensions, en general or calized b curren and F in ball . lo eys t (3) giv In the a transformations )) e ob tegral from function curren scales qualitativ + dC b not wire. of t wire tz in h onen ( solutions electromagnetic electrons . equations = ² is on the ) encircling , cone. ! can the time the ends the F ) spacetime it − no delta excites whic t t S0-brane y i² Loren comp y ( The cones ( in in D in δ b cone. δ dep 0 These − t tour ) t an − t. ligh j t with in 2 x with ( field, erse dt y ard tarily 0 con δ ligh (co)dimensions. no S-brane ) righ ligh the calization + − strength t ell = a three-dimensional kw . brane 1 ( ) constructed 2 is lo curren with t δ homogeneous y − x on indefinitely the the (3) t transv bac measured resistance other ( dz consider the at ere field an no − momen C ² – future to Sp-brane ) w Maxw 2 time harged = to to z-direction. t ∧ 6 there + c the only a (on) t around course F – an ( data p a ersists † and harge get dφ with cross δ the olving in to d c p equation due d ). 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S-brane. the purely = h e realization o in cone mo in dF bas coupled consider b dx if come incoming t is also F field added an inside electrons 4 g radiation. solving e brane or can all e er b are whic oum their y to the of b = will ligh massless the nonzero T b can ev ) this, ysical en incoming y the wire “R-symmetry”. er w a tually H b tuned S0-brane can of This ev wire N. orted ph b a ond of the of also 1) en that Ho es is to (2.12 an , 2.1 y outgoing in um kness the 2 ev on n supp giv to t solutions see arrange finely to − duced ma in three. solutions state nature thic o p ort corresp ) cation from and the ys to subsection, T grateful and pro teresting lo − ret construction y the anishes. . section that plane in curren b v 2 not G These onding D supp are ) last er deca dimension initial of ( S y the easy e real − es en − differs h R-symmetry ev start. An This t co S-brane electrons e W , SO an has is is w the do v 4 the dimension dimension giv adv + t corresp this electric It co ( F H densit co brane so G the Ho brane. and the In 2.4 is whic is lea the radiation roughly decelerate, at an JHEP04(2002)018 , e e is tz to es to b on ti- in- 2.2 the has dT can y h The The ∗ This (3.1) h giv h tzian off of corre- olume T can Loren tac one whic radiated This breaking hill. spacelik olving as tial. Im D4-(an whic loren past. is . 5 section no orldv , Ev a = propagating ottom The w the the oten is surfaces e of b j than radiated v p a 0. no of ything in D3-brane e e ha jectory the > b energy infinite v ). solution An symmetry . hat ˙ has top there future. 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[9] [8] [7] [2] [6] [5] [4] [1] [3] [21] [20] [19] [17] [18] [16] [14] [15] [12] [10] [13] [11] References JHEP04(2002)018 om , , gy fr ls 476 ory gy (2001) Ener B ole . the anes 08 Ener ang-Mil p-br Y 2019 High Higgs Phys. monop . al ls er J. High Phys. , . g-Salam dilatonic sup and er J. d gy air (1983) Nucl. 299 , 1 p , ge Classic als = ang-Mil 28 gr Ener Y ane Weinb char N anes D (1981) e ]; inte on Russo, the e High ev. D-br pur 81 hep-th/9912275 R SU(2) in R. J. ondensation , c of 2 , anes and the ane-antibr Surfac gy and Br br Phys. ; Phys. to ory, limit , C., on solution 257 the N ory osmolo Lerda ]. c Math. d ala hep-th/9707068 ge- v the [ oint – A. p solution cte ersymmetry lar Za e (1982) string and solitons le 18 259 I. sup orr in – the 86 c sadd Sciuto, ]. ]. g-Salam ds and Commun. other one op o er , A anes S. (1997) L Phys. violations owar and nonminimal hep-th/0008001 T D-br ton, ories [ 507 a Light-c Weinb asinato e-I . ]. entz the T B of Math. esando, 588 ˜ nez, Man Larsen, or typ the e P erle, L G. 2212 Nu F. I. of in gauge N.S. Phys. Liccardo, ]. hep-th/9808141 hep-th/0105227 C. [ [ edo, gy Gutp (2001) and rau, A. existenc F olo (1984) and Commun. M. 86 023 062 and elian , spinors Nucl. op Quev 3 M. , 30 and T The self-tuning, R Kraus ett. F. and hep-th/9604091 . L D [ nonab es, hia hia, P on state (1998) (2001) ton, in SO(32) ev. ev. ecc ecc 484 jean, aub R 09 06 R ounds: V V Green T Maldacena Klinkhamer Man hep-th/0106120 ges [ Sen, Gro Craps, Di Di . . ackgr oundary quations Phys. 005 char b b P Phys. Phys. e (1996) Phys. J.M. C. B. C.H. N.S. P A. F.R. M.B. [30] [29] [23] [24] [25] [28] [22] [26] [27]