1. Dynamical SUSY Breaking and Meta-Stable Vacua Ken Intriligator, UCSD Annual Theory Meeting, Durham, Dec 19, 2006 Based on work with Nathan Seiberg, and David Shih

2. Susy field theories are interesting Theory playground: can obtain exact results about strong coupling. Explore QFT, develop ideas and intuitions. Interconnections with string theory and properties of gravity, e.g. AdS/CFT May exist in Nature, and be discovered in the near future, perhaps at the LHC.

3. A SUSY motivation: hierarchy problem Highly sensitive to UV physics, top loops + etc. But sums up to SUSY: all perturbative contributions cancel.

4. A complete SUSY model must include SUSY breaking. Attractive scenario: Dynamical Supersymmetry Breaking

5. Dynamical Supersymmetry Breaking: No explicit breaking: Vacuum spontaneously breaks SUSY. SUSY breaking related to some dynamical scale (non-perturbative in coupling) Can naturally get hierarchies (Witten).

6. Dynamical Supersymmetry Breaking V eff fields Aside: with gravity, a susy preserving, negative contribution can be added to V. So (Susy does not make a wrong prediction here.)

7. Susy breaking, and mediation MSSM SUSY (gauge or gravity) Interested in finding nice (simple?) models of DSB. Old intuition: DSB = hard. Requires complicated theories. It is non-generic in space of theories. Our recent result (KI, Seiberg, Shih, '06): meta- stable DSB = easy. Can be generic.

8. Perhaps we're in a long-lived false vacuum You are here. (?) V fields maybe unbroken SUSY elsewhere An old idea (with renewed prominence in string theory and cosmology). Accepting the possibility, we find much simpler models of DSB. E.g. good, old SQCD! Suggests meta-stable DSB is generic.

9. Review the Basics of SUSY Superpotential: quantum corrections constrained by holomorphy: exact results Kahler potential: quantum corrections not constrained by susy. Susy vacua:. Equivalent to if the sigma model metric is non-singular. (Singularities in sigma model metric can occur. If so, there are new light d.o.f. there, which should be included in the low-energy effective theory. This removes the singularities.)

10. Basics of SUSY, cont. Example: has zeros = susy vacua. X V

11. Basics of SUSY & breaking cont. “susy broken” but too trivially (free, susy spect.) susy unbroken at origin. Lesson: need to know both W, and also something about K, to know whether or not susy is broken. O’Raifeartaigh model, breaks susy at tree level.

12. O’Raifeartaigh model, cont. V X Pseudo-modulus X, typical of tree-level breaking (it's fermion component is massless goldstino). X massless at tree level, gets mass at 1-loop. Susy broken at tree-level, not dynamically. Not DSB.

13. Roadmap to DSB, circa 1984 fields Affleck, Dine, and Seiberg can have DSB. But often no. weak coupling

14. DSB looks very non-generic Witten index: All SUSY gauge theories with massive, vector-like matter have SUSY vacua (1982). So for broken SUSY, need a chiral* gauge theory. SUSY breaking is related to breaking global symmetries (Affleck, Dine and Seiberg '85). SUSY breaking requires an R-symmetry (or non-generic W) (Nelson and Seiberg '93). And must lift all classical flat directions.** *Some vector-like exceptions, with massless matter (KI and S. Thomas '96; Izawa and Yanagida '96).

15. DSB is hard to analyze Most of our techniques to analyze SUSY theories are based on holomorphy/chirality/BPS. But for a detailed analysis of SUSY breaking we need to know the Kahler potential, which is hard to analyze and control. Since the vacuum is not SUSY, dependence on parameters might not be smooth – can be phase transitions.

16. “Simplest” example of calculable DSB (Affleck, Dine, Seiberg ‘84) ensures large vevs (weak coupling). Therefore the theory is calculable: gauge theory with matter: and superpotential squark vevs

17. Mediating susy breaking Additional structure, complicates the models. Sometimes leads to unwanted vacua, with susy unbroken (Dine, Nelson & co. '93-'95)... MSSM SUSY (gauge or gravity)

18. Reexamine, 10 years later Existing models of DSB are all so complicated. None are very compelling. Soon we'll have data from the LHC. Find susy? Would be good to have more & better models. Discovery of dark energy! Positive vacuum energy. Perhaps our vacuum is only one of several (or even perhaps very, very many) possibilities. Perhaps it's time for a new approach to DSB...

19. Perhaps we're in a long-lived false vacuum You are here. (?) V fields unbroken SUSY elsewhere Since it's so hard to avoid susy vacua, don't bother! Find simpler models of DSB. E.g. good, old SQCD! Suggests meta-stable DSB is generic.

20. Review of N=1 SQCD With massless flavors (Affleck, Dine and Seiberg) V M With massless flavors V M No static vacuum. Runaway. Quantum moduli space of vacua. Asymptotically free if N f < 3N c (IR free if not)

21. SQCD with massive flavors Study the limit in the region near the origin. (UV theory looks strongly coupled there; can find some surprises.) M V ? Give masses: E.g.. Get susy vacua * : There, we should use magnetic dual variables… * *

22. The magnetic theory (Seiberg ‘94) We will focus on where the theory is in a free magnetic phase; i.e. the magnetic theory is IR free. The IR effective field theory is with Electric Magnetic

23. Interpretation of Seiberg duality:. Electric. Same IR SCFT Interacting superconformal field theory. "Free Magnetic phase".. Magnetic theory is IR free. It is the low-energy effective field theory of the UV theory. Our case of interest here. Magnetic Electric Magnetic

24. The magnetic theory, cont. UV cutoff of this IR free theory is. where Key point: The leading Kahler potential is known, up to two dimensionless normalization constant factors. The Kahler potential for the IR free fields is smooth near the origin and can be taken to be canonical:

25. Rank condition SUSY breaking Quark masses are described in the magnetic dual by (rank N f ) (rank N f -N c ) (using the classical rank of.) This SUSY breaking is a check of the duality. Otherwise, would have had unexpected, extra SUSY vacua. SUSY broken at tree level! Quadratic mass term is now linear. "Confinement"

26. Elsewhere: SUSY dynamically restored For, magnetic q's massive ( ) so integrate them out. Then gaugino condensation in dual Non-perturbatively restores SUSY in the magnetic theory. Leads to the expected Tr(-1) F = N c susy vacua: a check (c. 1994) of Seiberg duality.

27. Summary: the potential with massive flavors M V To be uncovered soon! For M at the origin SUSY broken by rank condition in the magnetic description. Reliable in free magnetic range: SUSY vacua This ends our review of things from 12 years ago.

28. Non-SUSY vacua of the IR dual theory Classical vacua (up to global symmetries) with broken SUSY: Arbitrary and matrices Pseudo-flat directions are lifted in the quantum theory. Typical of tree-level breaking, like O'Raifearteigh model. Pseudo-moduli: DSB:

29. Pseudo-moduli get a potential at 1-loop in the magnetic theory Use 1-loop effective potential for pseudo-moduli: Higher loops (higher powers of small ) are smaller, because the magnetic theory is IR free. mass matrices are functions of the pseudo-moduli 1-loop vacuum energy

30. Effect of the one-loop potential for the pseudo-moduli The effective potential is minimized (up to symmetries): All pseudo-moduli get non-tachyonic masses at one-loop. SUSY broken: We have found (meta) stable DSB vacua in SQCD! Vacua mysterious in electric description. Not semi-classical, very quantum mechanical.

31. Dynamical SUSY restoration, revisited For, can reliably analyze effect of this term far out on the moduli space, and find the SUSY vacua in the magnetic theory, staying below its cutoff: In free magnetic range,, this term is, so it is irrelevant for the susy breaking vacua near the origin.

32. Sketch of the full potential V Effect of N c SUSY vacua (meta-)stable DSB by rank condition in free magnetic dual, cutoff

33. Effects from the microscopic theory? Contributions to the effective potential from modes above, e.g. from loops of SUSY split massive particles do not change our picture. Uncalculable. Unimportant. All such contributions can be summarized by corrections to the Kahler potential. Such effects are real analytic in. Our 1-loop potential is not, because it arises from integrating out modes that are massless as. This non-analyticity ensures that our DSB vacuum is robust. Corrections from UV modes are negligible for

34. Spaces of DSB vs SUSY vacua V N c isolated susy vacua. Mass gap. Compact moduli space of DSB vacua. Massless fermions and scalars: SSB of susy, and some global symmetries.......

35. Compact moduli space of DSB vacua vs SUSY vacua: Mysterious in electric description! Aside: SSB vs Vafa-Witten thm. OK: squarks, vacua meta-stable. DSB vacua have: exactly massless Goldstone bosons, and Goldstino. Also massless fermions (from pseudo-moduli). Electric description: naively no massless fields: quarks = massive, and SYM has a mass gap. True in susy vacua.

36. Lifetime of meta-stable DSB vacua Recall. Estimate height and width of potential: Barrier not high, but it's extremely wide.

37. Cartoon of the potential Recall. very gentle slope

38. Recall how false vacua decay By tunnelling, can nucleate a bubble of true vacuum. Like boiling. Bubble expands only if it is big enough (energetically favorable volume effect vs unfavorable surface effect). False vacuum true vac shrinks expands

39. Lifetime of DSB vacua cont. Decay probability ( Langer,Coleman) Estimate classical, Euclidean action of bounce: Our meta-stable DSB vacuum is parametrically long-lived for. Magnetic description: tunneling suppressed by large. Electric description: tunneling suppressed by small.

40. Aside: N f in the conformal window For the magnetic dual is not IR free. Magnetic gaugino condensation superpotential then cannot be neglected near the origin, SUSY vacua are then too close to ensure the longevity of the DSB vacua; DSB vacua then not meaningful. Long lived meta-stable DSB vacua only in free magnetic range of N f.

41. Prospects for Model Building Several longstanding challenges: Naturalness. Direct gauge mediation. Landau poles. R-symmetry problem. They can be reconsidered in the new context of meta-stable DSB vacua.

42. Naturalness Need small parameter:. We get Good. Perhaps better if all low-energy scales dynamically generated. Can consider similar models, with m replaced by a marginal or irrelevant coupling.

43. Direct gauge mediation and Landau poles. Direct mediation: longstanding goal to find a nice and simple model. SUSYSSM SM gauge fields SQCD has a large global flavor symmetry, can partly gauge and identify with SM or GUT groups meta-stable DSB Low-energy gauge fields partly electric and partly magnetic. Perhaps a scenario like this may help Landau pole problems. e.g.

44. R-symmetry problem DSB without SUSY vacua: non-generic superpotential or a U(1) R symmetry. (Affleck, Dine, Seiberg; Nelson, Seiberg). For nonzero Majorana gluino masses, U(1) R should be broken. To avoid a Goldstone boson, U(1) R should be explicitly broken, which might restore SUSY. (Gravity may help.) Our examples: no exact U(1) R. (Indeed, SUSY vacua.) Meta-stable DSB vacua have accidental approximate U(1) R. Perhaps it is better if that symmetry is also spontaneously broken. This can occur, once the flavor symmetry is gauged. More generally, with meta-stable DSB, don't need an exact R-symmetry (so susy vacua), just approx. one, in some limit.

45. Comments on Cosmology V...... susy Very gentle slope.. Much larger configuration space of DSB vacua. More light degrees of freedom here, so DSB vacua favored (c.f. moduli trapping of KLLMMS)

46. Thermal effects and cosmology Thermal effects favor populating the DSB vacua. Abel, Chu, Jaeckel, Khoze; Craig, Fox, Wacker; Fischler, Kaplunovsky, Krishnan, Mannelli, Torres Thermal effective potential favors fields near the origin, and DSB vacua are nearer. And favor DSB vacua because it has more light fields. Even if initially in susy vacuum, driven to DSB vacua. Even if reheat temp is above barrier height, transitions from DSB vacua to the SUSY vacua are suppressed. Excellent!

47. Conclude / Outlook Accepting meta-stability leads to surprisingly simple models of DSB. Suggests meta-stable DSB is generic in N = 1 SUSY field theory, and the landscape of string vacua. Many similar models, including realizations in string theory. (Moreover, could be holographic dual to other proposed string theory realizations of SUSY breaking, e.g. KKLT. Similarities.) Cosmology and thermal effects are promising. Many new avenues for model building.