1. What stringy people expect in Experiments Univ. of Tokyo, Komaba Koji Hashimoto 22 June 2007 @Hokkaido univ. Conference “SUSY in 2010’s” (a pure string theorist) Future of Superstring

2. Questions to string theorists : What do you think, about the possibility of finding SUSY at LHC? Answer (a) Of course, SUSY should be found there. We have been believing in SUSY more than 20 years. Answer (b) Even if SUSY is not found there, I am fine, because string theory can accommodate non-SUSY theories. Answer (∞) I don’t care.

3. Table of Contents Why do we need SUSY in string theory? What’s the problems of string theory without SUSY? What do stringy people (a)(b) expect in LHC/experiments? Section 1For the answer (a)(b) Section 2 For the answer (∞) Why do they say that they don’t care? But in reality …. they care about LHC in a different way! Then what is the path from strings to the real world? Section 3 Future of string theory

4. SUSY/non-SUSY in string theory Section 1

5. Popular path from string theories to phenomenology Start with superstring theory. Consistent only in 10 dimensions if in flat background. 10 dimensional SUGRA, 16 or 32 supercharges. Compactify it on a 6 dimensional Calabi-Yau manifold, to leave N=1 supersymmetric 4-dimensional theory. You can add D-branes and such, to have matter fields as you like. Supersymmetric Standard Model / GUT (with extra constraints / additional matters / gauge groups)

6. Benefit from string theory? If one follows this path, then low energy SUSY follows, and: (Gauge) hierarchy problem naturally solved. Gauge coupling unification naturally encoded. These are two major reasons why we need SUSY! Is SUSY a prediction of string theory? However, we have assumed that we start with superstring… Is only the “super”string a consistent starting point? NO. With our present analysis tools, SUSY is TECHNICALLY necessary, to project out TACHYONS perturbatively. Answer :

7. In the following, I will explain Tachyons in string theory, and the necessity of SUSY for projecting them out perturbatively You can see Why there are two answers in string theory : (a) SUSY and (b) non-SUSY or in other words, why stringy people call the theory as (a) “superstring theory” or (b) “string theory”

8. Tachyons in string theory String theory naturally includes tachyons:. 1) Bosonic string theory …….. Spectrum includes tachyons. 2) Superstring theory (worldsheet theory has supersymmetry) 2-1) spectrum is supersymmetric, no tachyon (type I, IIA, IIB, hetero) note: in the flat background only. 2-2) spectrum is not supersymmetric, w/ tachyon (type 0A, 0B) However, even in 2-1), D-brane - antiD-brane has tachyon. Supersymmetric D-brane configurations get rid of tachyon. No tachyon in perturbative spectra SUSY …….. tachyon – slide 1

9. Map describes string location Why does tachyon appear in string theory? String theory starts not from field theory action but from the action of a one-body problem Consistency on the worldsheet (ex. no anomaly in Lorentz symmetry) determines spacetime dimensions and spectrum! ・・・・ Tachyon, massless elemag fields, massive fields Open string : Closed string : tachyon, massless gravitons, massive fields First quantization of string theory tachyon – slide 2

10. Problems with the Tachyons in string theory Spectrum does not make sense in that form: Violation of causality and special relativity constraint. Divergence of one-loop diagrams. However, tachyon is familiar with us: it is a Higgs. Natural outcome of this theory : tachyon condensation We need information of finite fluctuation! tachyon – slide 3

11. Need of SUSY in string theory However, with the first quantization formalism, we cannot write the tachyon potential! Tools for analyzing the tachyon condensation is still missing in string theory. Technical difficulty in non-SUSY string theory Note 1: For open string tachyon, string field theory can help the analysis of the tachyon condensation. Note 2: Superstring theory is a lot easier to study. Strong coupling region can be analyzed by BPS nature of states, giving string dualities. Generic string theory does not predict SUSY! ? tachyon – slide 4

12. “String theory is under construction” What is not known in string theory: Stringy people are trying to solve these problems. (i)Second quantization of strings. String field theory. Fate of the tachyon condensation? (ii) Mechanism of spontaneous compactification. Dimensional quenching? (iii) Complete string duality web. Nowadays, even bosonic strings sits at a wing in it. M-theory? Non-perturbative definition of string theory? SUSY should play a role there…… tachyon – slide 5

13. Two answers : (a) SUSY or (b) non-SUSY We don’t know the full “landscape” of string theory, but, we can work in arenas which we know how to treat. Various results in string phenomenology We expect to find more generic features which are possibly common to string theories. Extra dimensions and Branes (TeV scale gravity, KK graviton, BH nucleation) Cosmic superstrings, Over-rotating blackholes Now, you can see the reasons why we have two answers. Standpoint of the answer (a) Standpoint of the answer (b)

14. Observation expected : Direct observation ： Gravitational Lensing by the cosmic strings. WMAP, LIGO, SKA, LOFAR, … Gravitational waves ： kinks on the Nambu-Goto strings travelling with the speed of light emit grav. waves. Constraint from observation : Cosmic strings = Macroscopic 1-dim. objects in cosmic space What are they made of ? Cosmic Superstrings Conventional ID : Vortex solitons in GUTs New ID : Superstrings or D-branes!

15. How can superstrings be cosmic? Is the tension Okay? String scale is close to Planck scale, so the tension exceeds the obs. bound ? Okay, in warped compactifications. How were they created? D-brane inflation is a motion of D-branes in extra dimensions. Graceful exit is brane annihilation, where lots of cosmic superstrings are created. How to distinguish them from conventional GUT vortices? Difference of reconnection probability, and resultant number density of the cosmic strings. [Copeland-Myers-Polchinski]

16. You don ’ t care? Section 2 New standpoint of string theory

17. Why you don’t care? Possible reason: String theory itself is interesting enough, even without direct connection to reality. Connection to mathematics is more important. String theory is not mature enough, to relate itself to the reality. We have to resolve the issues of how to define the string theory itself, first. As a top-down flow, SM (and SUSY?) may follow. No “physics”! Then, what is the relation we can ask now, between the reality (LHC) and string theory?? In fact, some stringy people look at LHC very differently!

18. Protean applications: “theory of anything” ・ “Prediction” of QCD dynamics (“holographic QCD”) ・ Prediction of various solitons ・ New paradigm: “braneworld” for phenomenology/gravity ・ M-theory ・ SFT ・ Matrix model Recognizing importance of D-branes （ ’95 ） Progress toward “theory of everything” D-branes and New meaning of string theory After the second revolution of string theory (“D-brane”), string theory acquired a new standpoint/meaning. Development for non-perturbative definition of string theory String theory as a technology!

19. What is D-brane? What is AdS/CFT? D-brane closed open D-branes ＝ Hypersurface on which strings can end. [Dai,Leigh,Polchinski(89)] ・ Open strings (gauge fields) can live only on the D-branes. ・ Closed strings (gravity) live in the bulk. deform AdS/CFT correspondence D-branes = Source of closed strings = black hole Yang-Mills theory on the D-brane (open strings) can be analyzed by gravity with the black hole (closed strings) [Maldacena(98)]

20. Holographic QCD Application: analyze strong coupling QCD by supergravity! Meson spectrum, Baryon spectrum, Linear Regge behavior, Meson/baryon effective lagrangian (chiral lagrangian), Glueball spectrum, QCD at finite temperature, QCD at finite baryon density, Jet quenching, Quark drag force in QGP, Chiral symmetry restoration, Thermal deconfinement, Nuclear force, Glueball decay channel, etc etc.. Holographic QCD can explicitly give ---- Success of string theory : It produces a new technology for analyzing gauge theories AdS/CFT: “holographic” equivalence between strongly -coupled gauge theories and higher dim. classical gravity

21. What stringy people are looking at Stringy people are looking at LHC: not only ATLAS/CMS but also ALICE experiment! Stringy people take part in hadron physics, actually: They are with explicit predictions and useful tools.

22. Summary and Prospects Section 3 Future of string theory

23. Questions to string theorists : What do you think, about the possibility of finding SUSY at LHC? Three kinds of answers : (a) Of course, SUSY should be found there. We have been believing in SUSY more than 20 years. (b) Even if SUSY is not found there, I am fine, because string theory can accommodate non-SUSY theories. (∞) I don’t care. These two appeared, because SUSY is merely a technical necessity in the present form of the string theory. This pessimistic answer appeared because of immatureness of string theory.

24. Prospects Although there are three answers (a) (b) and (∞), stringy people expects closer relation to experiments, in various ways! The relation may not be really direct as suggested earlier, but certainly new possible paths have been created. More intimate interaction between stringy people and experiments/observation is necessary ! -- including cosmic superstrings and ALICE

25. Where are we going to? Although there are three answers, the ultimate goal of stringy people is just the non-perturbative definition. 1960’s ～ 70’s ： String theory was born from hadron physics Regge trajectory, s-t channel duality, ’tHooft large N 1970’s ～ 80’s ： String theory as quantum gravity and unification of all forces Superstrings, SUGRA, SM from compactification Late 1990’s ～： D-brane revolution 2010’s : Non-perturbative definition? String dualities, M-theory, Matrix theory, AdS/CFT

26. Reccurence time?! ？ 1960’s ～ 70’s ： String theory was born from hadron physics Regge trajectory, s-t channel duality, ’tHooft large N 1970’s ～ 80’s ： String theory as quantum gravity and unification of all forces Superstrings, SUGRA, SM from compactification Late 1990’s ～： D-brane revolution AdS/CFT = gauge/string duality Gauge/string duality : AdS/CFT duality is now upgraded, the AdS side is in fact a string theory itself on a curved b.g.! This duality may define string theory?! String theory is equivalent to nonAbelian gauge theory?!