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).