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

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

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).

Dynamical Supersymmetry Breaking

Veff

fieldsAside: with gravity, can add an extra negativecontribution, so . Will ignore gravity.

susy orderparameter

Susy breaking, and mediation

MSSMSUSY

(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.

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 theoryand cosmology). Accepting the possibility, we findmuch simpler models of DSB. E.g. good, old SQCD! Suggests meta-stable DSB is generic.

Review basics of SUSY

Example:

has zeros = susy vacua.

X

V

breaks susy, but a trivial, free theory.

Simplest interacting model of SUSY breaking: O’Raifeartaigh model

Three fields, with canonical Kahler potential and

V

X

Tree-level susynot DSB. (Can be“retrofitted” into amodel of DSB: Dine,Feng, Silverstein.)

Roadmap to DSB, circa 1984

fields

Affleck, Dine, and Seiberg

can have DSB. But often no.

weak coupling

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).

“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

squarkvevs

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.

Metastable DSB in N=1 SQCD

KI, N. Seiberg, D. Shih ‘06

Give masses:

M

V

?* susy vacua *:

There are

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 theoryis IR free and known. Dual fields have canonical Kahler potential at the origin. Find susy breaking. *

*

Using the dual, we find the potential

V

Nc SUSY vacua

cutoffnon-perturbative effect

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

DSB vacua! No tachyons!

wide

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:

New topic: SUSY and U(1)R symmetry

SUSY requires an R-symmetry (or non-genericsuperpotential). (Nelson and Seiberg ‘93):

k equations for k variables, generically a sol’nso susy is unbroken. With a U(1)R symm, it’sinstead k equations for k-1 variables, so thengenerically there is no solution, susy is broken.

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.

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 susybreaking vacua.

The R-symmetry problem and metastable vacua

Susy breaking U(1)R symmetry

Gaugino masses U(1)R broken

Explicitly, spontaneously, or both? If justspont., get massless R-axion, exp. ruled out.Assuming low-energy scenarios (where gravitycan be decoupled) requires explicit breaking.Then we must live in a metastable state!

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 withR(X)=2, unbroken invacuum.

Modified O'R: explicit U(1)R breaking

Breaks U(1)R . Susy breaking vacuum near X=0is only slightly altered (it’s pushed to ). New susy vacua at . Vacua near origin now metastable. (A similar toy model, withwas already discussed by Dine, Feng, Silverstein.)

Details depend on . As long as y isn't too close to 1, the metastable vacuum doesnot have a tachyon.

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-energyeffective field theory of some UV theory, makingthe breaking dynamical.) Typical picture of V:

V

X

e.g. goldstinosuperfld. R(X)=2

The R-symmetry isnot spontaneouslybroken here.

Mention a recent work of David Shih

• For generalized O’R models without gauge interactions, and with all fields having R charges 0or 2 (as is the case for most models studied to date), then always has minimum at theorigin. 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 breakingvacuum turns out to be only metastable.)

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 givenby the anomalous dimension of X:

Witten’s inverse hierarchy

Taking get

Veff

X

Runaway? Stabilized by higher loop correctionsonly if g/h is not too big.

We instead look for examples where

Veff

X

Compute here via(leading log insufficient)

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).

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). Moredetailed phase diagram (alignment / misalignment).

a small window, e.g.:

Comment on alignment / misalignment

"Suppose a theory has a global symmetry G, that'sspontaneously broken to H G . Now gauge FG. 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.

Example of alignment / misalignment

Global SO(N) symmetry, unbroken if y<1 or brokento SO(N-1) for y>1. Gauging SO(n), the remainingglobal symmetry is SO(N-n). Superpotential termsnow need only respect SO(n) x SO(N-n). Dependingon 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 theorigin (in these models). An involved phase diagram,with U(1)R spontaneously broken only in a corner of the parameter space.

Summary of spont. U(1)R breaking

• Only if G broken. A small window of g/h - (inour 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...

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.