1. SUSY breaking, R-symmetry breaking, and Metastable Vacua Ken Intriligator, UCSD UCI SCSS, May 5, 2007 Based on works with Nathan Seiberg, and David Shih

2. Outline Introduction to SUSY and SUSY breaking (Not needed here!) Dynamical SUSY breaking in metastable vacua. KI, N. Seiberg, D. Shih, ‘06 Supersymmetry breaking, R-symmetry breaking, and metastable vacua. KI, N. Seiberg, D. Shih, ‘07

3. 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).

4. Dynamical Supersymmetry Breaking V eff fields Aside: with gravity, can add an extra negative contribution, so. Will ignore gravity. susy order parameter

5. 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. KI, Seiberg, Shih, '06: meta-stable DSB = easy. Can be generic.

6. 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.

7. Review basics of SUSY Example: has zeros = susy vacua. X V breaks susy, but a trivial, free theory.

8. Simplest interacting model of SUSY breaking: O’Raifeartaigh model Three fields, with canonical Kahler potential and V X Tree-level susy not DSB. (Can be “retrofitted” into a model of DSB: Dine, Feng, Silverstein.)

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

10. 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 requires an R-symmetry (or non-generic W) (Nelson and Seiberg '93). (And must lift all classical flat directions**.) *Some vector-like exceptions (KI and S. Thomas '96; Izawa and Yanagida '96). ** Some exceptions (KI, ST. ‘96).

11. “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

12. Hard to avoid susy vacua...so don’t DSB is non-generic, so models are complicated. None seem compelling. Susy vacua will anyway crop up in full models of gauge mediation (e.g. Dine, Nelson, Nir, Shirman). Discover of dark energy. Perhaps we do not live in the true vacuum. Perhaps ours is only one of many. Metastable DSB is easy! E.g. SQCD. Generic. R-symmetry problem and metastable susy breaking.

13. Metastable DSB in N=1 SQCD KI, N. Seiberg, D. Shih ‘06 Give masses: M V ? * susy vacua * : There are

14. Near origin: use Seiberg duality For the theory in IR is IR free in a dual set of fields: Electric Magnetic A key point: below cutoff the low-energy theory is IR free and known. Dual fields have canonical Kahler potential at the origin. Find susy breaking. * *

15. Using the dual, we find the potential V N c SUSY vacua cutoff non-perturbative effect DSB vacua! No tachyons! wide

16. Lifetime of metastable DSB vacua False vacua decay via nucleating a bubble of true vacuum. Only expands if it’s big enough. Decay probability ( Langer,Coleman ) The potential barrier is not high, but it can be made arbitrarily wide. Leads to arbitrarily long lifetime of metastable DSB vacua:

17. New topic: SUSY and U(1) R symmetry SUSY requires an R-symmetry (or non-generic superpotential). (Nelson and Seiberg ‘93): k equations for k variables, generically a sol’n so susy is unbroken. With a U(1) R symm, it’s instead k equations for k-1 variables, so then generically there is no solution, susy is broken.

18. Extend to relate metastable susy breaking and approximate R-symmetry Suppose a small R-symmetry breaking parameter : there is an R-symmetry, and broken susy. (Assume a compact space of vacua.) : the R-symmetry is broken. Susy breaking vacua only slightly deformed if. But also get vacua with unbroken susy, at field vevs ~ inverse power of. Susy breaking vacua are metastable. Long lived for since is large.

19. DSB in SQCD is an example of this SQCD with massive flavors has no U(1) R symmetry, so susy vacua. For there is an accidental and approximate U(1) R symmetry, seen in IR free dual. So there are metastable susy breaking vacua.

20. The R-symmetry problem and metastable vacua Susy breaking U(1) R symmetry Gaugino masses U(1) R broken Explicitly, spontaneously, or both? If just spont., get massless R-axion, exp. ruled out. Assuming low-energy scenarios (where gravity can be decoupled) requires explicit breaking. Then we must live in a metastable state!

21. Explicit and spontaneous U(1) R breaking in toy models KI, N. Seiberg, D. Shih ‘07 V X Recall O'R: U(1) R symmetry with R(X)=2, unbroken in vacuum.

22. Modified O'R: explicit U(1) R breaking Breaks U(1) R. Susy breaking vacuum near X=0 is only slightly altered (it’s pushed to ). New susy vacua at. Vacua near origin now metastable. (A similar toy model, with was already discussed by Dine, Feng, Silverstein.) Details depend on. As long as y isn't too close to 1, the metastable vacuum does not have a tachyon.

23. Spontaneous U(1) R breaking in generalized O’R models Consider a generalized O’R type model of tree- level SUSY breaking. (This could be a low-energy effective field theory of some UV theory, making the breaking dynamical.) Typical picture of V: V X e.g. goldstino superfld. R(X)=2 The R-symmetry is not spontaneously broken here.

24. Mention a recent work of David Shih For generalized O’R models without gauge interactions, and with all fields having R charges 0 or 2 (as is the case for most models studied to date), then always has minimum at the origin. So the U(1) R is not spontaneously broken. Surprisingly, there are models without gauge interactions, with other R charge assignments, where can have a minimum for breaking U(1) R. (In these cases the susy breaking vacuum turns out to be only metastable.)

25. Old intuition of inverse hierarchy Witten ‘81 “Superpotential interactions push X to the origin, gauge interactions push it away from the origin.” Indeed, for large X, the effective potential is given by the anomalous dimension of X:

26. Witten’s inverse hierarchy Taking get V eff X Runaway? Stabilized by higher loop corrections only if g/h is not too big.

27. We instead look for examples where V eff X Compute here via (leading log insufficient)

28. Spontaneous U(1) R breaking via generalized O'R models Take to be reps of a symmetry group G. Vacuum depends on. : G is not spontaneously broken. : G is spontaneously broken to some H. Gauge the group G. In y > 1 case (only), we can get if g/h lies in a certain window (which is small in our examples).

29. Example of spont. U(1) R breaking (Overlap w/ Dine + Mason) in N of SO(N), with gauge coupling g. only if ~0.47 ~0.5 We also consider gauging a subgroup SO(n). More detailed phase diagram (alignment / misalignment). a small window, e.g.:

30. Comment on alignment / misalignment "Suppose a theory has a global symmetry G, that's spontaneously broken to H G. Now gauge F G. Does F dynamically align with (within) H?" The question is not applicable if there are any rel. tree-level interactions. If there are, since they can not be restricted to respect G, how F aligns is entirely determined by these tree-level couplings. In our context, we only get spontaneous U(1) R breaking if F is broken (not aligned inside H). That depends on the tree-level couplings.

31. Example of alignment / misalignment Global SO(N) symmetry, unbroken if y<1 or broken to SO(N-1) for y>1. Gauging SO(n), the remaining global symmetry is SO(N-n). Superpotential terms now need only respect SO(n) x SO(N-n). Depending on these couplings, either SO(n) breaks, or SO(N-n) breaks, or neither breaks. only depends on g if SO(n) breaks. Only then can the pseudomodulus be stabilized away from the origin (in these models). An involved phase diagram, with U(1) R spontaneously broken only in a corner of the parameter space.

32. Summary of spont. U(1) R breaking Only if G broken. A small window of g/h - (in our models) - otherwise get X=0 (or runaway). Massless R-axion, so might want to include explicit breaking anyway. Can apply to ISS-type models to break their accidental, approximate R-symmetry. E.g. Csaki, Shirman, Terning; Kitano, Ooguri, Ookouchi; Murayama and Nomura, etc...

33. 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. Cosmology and thermal effects turn out to be promising. Susy breaking vacua favored. Many new avenues for model building.