Dynamical SUSY Breaking in Meta-Stable Vacua

1. Dynamical SUSY Breaking in Meta-Stable Vacua Ken Intriligator, UCSD DPF 2006, 10/31/2006 KI, Nathan Seiberg, and David Shih hep-th/0602239

2. Dynamical Supersymmetry Breaking: • No explicitbreaking: • Vacuum spontaneously breaks SUSY. • SUSY breaking related to some dynamical scale Can naturally get hierarchies (Witten).

3. Dynamical SUSY breaking is hard • Witten index: All SUSY gauge theories with massive, vector-like matter have SUSY vacua.So DSB seems to require a chiral gauge theory. (Some exceptions, with massless, vector-like matter.) DSB looks non-generic. • Most of our techniques to analyze SUSY theories are based on holomorphy/chirality/BPS. SUSY breaking depends on the Kahler potential which is hard to control. Perhaps we should try a new approach...

4. Perhaps we're in a long-lived false vacuum You are here. (?) V maybe unbroken SUSY elsewhere fields 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.

5. Review of N=1 SQCD When all the quarks are massive, there are SUSY vacua. For with and the susy vacua are at where coupling is strong. Analyze near origin in dual variables (i.e. in the low energy effective field theory)... V ? M

6. The IR dual theory (Seiberg '94) Electric Focus on where the Seiberg dual theory is IR free. Magnetic UV cutoff of this IR free theory is .

7. Rank condition SUSY breaking. Key point: the Kahler potential for the IR free fields is smooth near the origin, so there it's of the form: SUSY broken at tree level! (rank Nf ) (rank Nf -Nc )

8. Dual theory yields the potential expected susy vacua, via non-pert effects wait... V M Susy broken at tree level at origin.: Up to here was known 12 years ago.

9. DSB vacua near the origin, via dual Classical vacua (up to global symmetries) with broken SUSY: Pseudo-moduli: Arbitrary and matrices DSB: Pseudo-flat directions are lifted in the quantum theory (typical of tree-level breaking).

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

11. 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: Vacua (meta) stable (we'll discuss tunneling soon). Vacua mysterious in electric description. Not semi-classical, very quantum mechanical.

12. Effects from the microscopic theory There are (uncalculable) contributions to from high energy modes ( ), e.g. loops of SUSY split massive particles. Is this a problem? No. All such effects can be summarized by corrections to the Kahler potential and lead to effects which are real analytic in . Our calculated is not real analytic in , because it arises from integrating out modes which are massless as . Corrections from UV modes are thus negligible for

13. Dynamical SUSY restoration SUSY vacua, in magnetic theory via: Non-perturbatively restores SUSY in the magnetic theory. In free magnetic range, , this term is , so insignificant for the DSB vacua near the origin. For , can reliably analyze effect of this term elsewhere, and find the SUSY vacua in the magnetic theory, staying below its cutoff:

14. Sketch of the full potential cutoff V Effect of (meta-)stable DSB Nc SUSY vacua

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

16. Lifetime of DSB vacua, cont. Decay probability Estimate classical, Euclidean action of bounce: (e.g. Langer,Coleman) Our meta-stable DSB vacuum isparametrically long-livedfor .

17. Compact moduli space of DSB vacua (SSB) DSB vacua: Large configuration space of vacua. Massless goldstone bosons and goldstino. vs Electric description: naively no massless fields, since quarks have masses and SYM has a mass gap. (True in susy vacua.)

18. Prospects for Model Building Longstanding model buildingchallenges: • Naturalness. • Direct gauge mediation leads to Landau poles. • R-symmetry problem. • They can be revisited. • The new DSB mechanisms offer new perspectives • on these issues and provide new avenues for • model building.

19. E.g. the 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)Rshould 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.

20. Comments on Cosmology Very gentle slope. Useful for inflation or quintessence? V . . . . . . susy Larger configuration space of DSB vacua. Can favor populating DSB vacua. Also,thermal Veff favors populating the DSB vacua.

21. Outlook • Accepting meta-stability leads to surprisingly simple models of DSB. • new avenues for model building. • Suggests meta-stable DSB is generic in N = 1SUSY field theory, and in the landscape of string vacua. • Extend to the landscape of string vacua. Relate to anti-D-branes in KS geometry? (note: baryonic). Counting vacua. • Cosmology.