Supersymmetry Breaking Vacua in Geometrically Realized Gauge Theories Yutaka Ookouchi (Caltech) Based on works in collaboration with Hirosi Ooguri

[Intriligator, Seiberg and Shih] Recently, it was found that simple field theories such massive SQCD have meta-stable vacua with broken supersymmetry [Intriligator, Seiberg and Shih] Idea and technique Long-live meta-stable vacua are phenomenologically viable This makes it easier to construct models that break supersymmetry Free magnetic dual description (Seiberg dual) is used to study IR physics

Quick Review of Seiberg duality 4D N=1 SUSY SU(Nc) with Nf quarks chiral multiplet Seiberg dual SU(Nf -Nc) with Nf dual quarks chiral multiplet and singlet Conformal Window Confining Free Magnetic Nc+1 3Nc/2 3Nc

SU(Nc) with adjoint field X and Nf quarks chiral multiplet Kutasov Dual SU(Nc) with adjoint field X and Nf quarks chiral multiplet [Kutasov, Kutasov-Shwimmer-Seiberg] Dual description SU(kNf-Nc) with Y and Nf dual quarks We use this dual in free magnetic range

Review of ISS meta-stable vacua Why free magnetic range? Kahler potential for the IR fields is smooth and can be taken to be canonical Add small mass term for all quarks

F-term condition for M can not be satisfied Rank Nf-Nc Rank Nf Note that in free magnetic range SUSY broken at tree level Veff decay process Broken vacua SUSY vacua q M

Motivation How generic are they? Is it possible to apply to another Seiberg dualities? Can we embed their construction in String theory? Geometric interpretation of meta-stable vacua Can we get a new insight into String Landscape?

N=1 Supersymmetric Quiver Gauge Theory [Cachazo, Fiol, Intriligator, Katz and Vafa] Type IIB string theory D5 brane probes wrapping cycles of Calabi-Yau three folds ALE w U(N1) U(Nk)

A2 Quiver Gauge Theory U(N1) U(N2) Assume U(N1) is much strong

Dual description Take magnetic dual description for first gauge group [ Kutasov, Schwimmer and Seiberg ] magnetic electric U(2N2-N1) U(N2)

Comments on dual description When N1 < N2 : N1=2N2-N1>N2 F-term condition can be solved vev of fields give mass-term and enforce Higgsing Type IIB string language Known as Duality cascade Weyl reflection symmetry of A2 Dynkin diagram What happens when N1 > N2 ?

× Does not happen in this range Instead, DSB occur Especially focus on Both U(N1) and U(N2) in electric description are asymptotically free Both U(2N2-N1) and U(N2) in dual description are IR free Suitable to study vacuum structure U(N1)×U(N2) Kutasov dual Duality Cascade U(2N2-N1)×U(N2) × Higgsing, integrate out massive Does not happen in this range Instead, DSB occur U(N2- N1)×U(N2)

Minimum of D and F-term potential Because of Rank condition, F-term equation can never be satisfied N1<N2 Minimum of D and F-term potential flat direction All the non-compact flat directions are lifted by the one-loop Coleman-Weinberg potential

R-symmetry All the moduli are locally stabilized There are [N2-N1/2] meta-stable vacua They are distinguished by unbroken gauge symmetry U(r1)×U(r2)×U(N1-N2) R-symmetry Tree level superpotential breaks U(1)R to Z4 ABJ anomaly breaks Z4 to Z2 R-symmetry is not restored on SUSY breaking vacua Gaugino can get masses from radiative corrections

Supersymmetric vacua SUSY vacua can also be found in the dual description Longevity of meta-stable vacua Higher order corrections to Kahler are negligible

IR The low energy structure of this model is rich UV U(N1)×U(N2) asymptotically free U(2N2-N1)×U(N2) IR free Supersymmetry breaking U(r1)×U(r2)×U(N1-N2) Low energy excitations are QCD glueballs IR

Generalization Veff SU(N1)×SU(N2) Degeneracy of meta-stable vacua are resolved by one-loop correction Y ADE Quiver Gauge Theories [Cachazo,Fiol, Intrilgator, Katz and Vafa] Under investigation Ak Dk E6,7,8

D-brane configuration for ISS meta-stable vacua We reproduce various features of meta-stable vacua in ISS NS’ NS’ (4,5) NS D6 NS D6 (7,8) 6 Nc Nf Nf-Nc < Nf electric massless magnetic NS’ NS’ D6 D6 NS Nf Nf-Nc Nc Nc NS massive

This configuration seems to describe features of SUSY breaking vacua Nf-Nc Vev of quarks and meson Project out of tachyon (stability of ISS) D6 project out tachyon on intersecting D4 Energy of SUSY breaking vacua Decay process to SUSY vacua Global symmetries including U(1)R Rotation symmetry in (78) decay process Nc NS D6 NS’ From above Nf-Nc Nf

Summary We identified brane configurations that correspond to the meta-stable SUSY breaking vacua in massive SQCD We found models that have landscape of inequivalent meta-stable vacua where supersymmetry is dynamically broken and all moduli are fixed It would be interesting to study properties of the meta-stable vacua from the geometric point of view of string theory