Dynamical Supersymmetry Breaking from D-branes at Singularities - PowerPoint PPT Presentation

Dynamical Supersymmetry Breaking from D-branes at Singularities Angel M. Uranga TH Division, CERN and IFT-UAM/CSIC, Madrid S.Franco, A.U, hep-th/0604136 I. Garc ´ ıa-Etxebarria, F. Saad, A. U, hep-th/0605166 GGI, Florence, June 2006

Motivation • Gauge dynamics from D-branes at singularities Relation between properties of the gauge theory and properties of the singularity. Both in conformal and non-conformal cases: - Confinement vs. geometric transitions [Vafa; Klebanov, Strassler] - Removal of SUSY vacuum for D-branes at obstructed singularities [Berenstein, Herzog, Ouyang, Pinansky; Franco, Hanany, Saad, A.U; Bertolini, Bigazzi, Cotrone] Realization of Dynamical Supersymmetry Breaking with D-branes? • Recent discussion of local SUSY breaking metastable minima in very simple system [Intriligator, Seiberg, Shih] - N = 1 SYM with massive flavours m ≪ Λ Parametrically low decay rate to far-away supersymmetric vacua. Realization in string theory? • Application of local configurations of D-branes with DSB to string model building - Towards gauge mediated supersymmetry breaking [Diaconescu, Florea, Kachru, Svrcek]

D3-branes at singularities • Systems of D3-branes at singular points in the transverse CY space lead to intricate N = 1 gauge theories, whose structure is nicely encoded in dimer diagrams - Periodic tiling of the plane, with faces giving gauge factors, edges giving chiral bi-fundamentals, and nodes giving superpotential couplings [Hanany, Kennaway; Franco, Hanany, Kennaway, Vegh, Wecht] 2 a) b) 1 1 3 3 2 2 1 2 1 • Dimer techniques allow to obtain the gauge theory on D3-branes at any toric singularity • Fractional branes: Anomaly free assignments of ranks on gauge factors (faces) → Non-conformal theories

DSB fractional branes • Consider the theory on the volume of M fractional D3-branes at the dP 1 singularity 2M a) b) M 3M 0 M 3M 0 2M 2M 2M M M • We have U (3 M ) × U (2 M ) × U (1) with W = X 23 X 31 Y 12 − X 23 Y 31 X 12 • The U (1)’s have Green-Schwarz anomaly cancellation and disappear; their FI terms are dynamical vevs of closed Kahler moduli. → Effectively neither U (1) vector multiplet, nor D-term constraint.

DSB branes: No SUSY vacuum • In the regime where the SU (3 M ) dominates, we have an Affleck-Dine-Seiberg superpotential M 21 = X 23 X 31 , M ′ 21 = X 23 Y 31 � Λ 7 M � 1 M W = ( M 21 Y 12 − M ′ M = ( M 21 ; M ′ 21 X 12 ) + M 3 ; 21 ) det M • No SUSY vacuum F X 12 , F Y 12 send M 21 , M ′ 21 → 0, and then F M 21 , F M ′ 21 send X 12 , Y 12 → ∞ . [Berenstein, Herzog, Ouyang, Pinansky; Franco, Hanany, Saad, A.U; Bertolini, Bigazzi, Cotrone] • Assuming canonical Kahler potential, scalar potential has runaway behaviour [Franco, Hanany, Saad, A.U; Intriligator, Seiberg] • Runaway can be stopped if e.g. Kahler moduli are fixed, so FI terms are effectively no longer dynamical, and U (1) D-terms reappear. • All similar to SU (5) with 10 + 5 in [Lykken, Poppitz, Trivedi]

The ISS model [Intriligator, Seiberg, Shih] • Consider SU ( N c ) SYM with N f massive flavors, with m ≪ Λ SQCD and N c + 1 ≤ N f ≤ 3 2 N c , → Seiberg dual is infrared free → Canonical Kahler potential. • Dual is SU ( N ) SYM with N = N f − N c , with N f flavors q , ˜ q , q − hµ 2 Tr Φ and mesons Φ, with W = h Tr q Φ˜ → SUSY breaking at tree level: q i q j − µ 2 δ i F Φ = ˜ j � = 0 since rk ( 1 N f ) = N f > rk (˜ qq ) = N • Classical moduli space with V min = ( N f − N ) | h 2 µ 4 | � � � � � � 0 0 ˜ ϕ 0 ϕ 0 q T = ϕ 0 ϕ 0 = µ 2 1 N Φ = ; q = ; ˜ , with ˜ 0 Φ 0 0 0 One-loop Coleman-Weinberg potential leads to a minimum at Φ 0 = 0 , ϕ 0 = ˜ ϕ 0 = µ 1 N

The ISS model [Intriligator, Seiberg, Shih] • Include the SU ( N ) gauge interactions For generic Φ, flavors q , ˜ q are integrated out, leaving SU ( N ) SYM with scale Λ ′ Λ ′ 3 N = h N f det Φ Λ − ( N f − 3 N ) with Λ the Landau pole scale of the IR free theory. → Complete superpotential W = N ( h N f Λ − ( N f − 3 N ) det Φ ) 1 /N − hµ 2 Tr Φ → There are N f − N supersymmetric minima Nf − 3 N − Nf − N 1 N f where ǫ ≡ µ � h Φ 0 � = µǫ Λ • For ǫ ≪ 1, local SUSY breaking minimum is parametrically long-lived V 4( Nf − 3 N ) − Φ 0 S ≃ | ǫ | ≫ 1 Nf − N

Generalization: Adding massless flavours [Franco, A.U.] • SQCD Consider SU ( N c ) with N f, 0 massless and N f, 1 massive flavours To have rank SUSY breaking in dual theory, need N f, 1 > N i.e. N f, 1 > N f, 1 + N f, 0 − N c → N f, 0 < N c Repeat ISS-like analysis: - Almost local minimum: Φ 00 (= ˜ Q 0 Q 0 ) remains flat at one loop - At large fields, Φ 00 is a runaway direction (as without ISS flavours) → Suggests no local minimum, but saddle point and runaway • SSQCD Add field Σ 0 , with W = Q 0 Σ 0 ˜ Q 0 to render Φ 00 massive Repeat ISS-like analysis; → Local minimum for all fields! → At large fields, Σ 0 is a runaway direction (as without ISS flavours) V Σ 0 • The condition N f, 0 < N c , and the cubic coupling to Σ 0 are present in gauge theories of D-branes at obstructed geometries

Flavoured dP 1 [Franco, A.U.] • Add massive flavours to the theory of fractional branes at dP 1 Q 3i 2M 3M j i i M Q k3 M k 3M Q i2 k Q 1k 0 2M M 2M 2M Q 2j Q j1 M j = λ ( X 23 X 31 Y 12 − X 23 Y 31 X 12 ) W λ ′ ( Q 3 i ˜ Q i 2 X 23 + Q 2 j ˜ Q j 1 X 12 + Q 1 k ˜ = Q k 3 X 31 ) W flav. m 3 Q 3 i ˜ Q k 3 δ ik + m 2 Q 2 j ˜ Q i 2 δ ji + m 1 Q 1 k ˜ = W m Q j 1 δ kj • For SU (3 M ), N f, 0 < N c , hence the dual is IR free Q i 3 Q 3 k − hµ 2 tr Φ + hµ 0 ( M 21 Y 12 − M ′ h Φ ki ˜ W = 21 X 12 ) + h ( M 21 X 13 X 32 + M ′ 21 Y 13 X 32 + N ′ + k 1 Y 13 Q 3 k ) + λ ′ Q 2 j ˜ Q j 1 X 12 − h 1 ˜ Q k 1 X 13 Q 3 k − h 2 Q 2 i ˜ + Q i 3 X 32 • Repeating ISS-like analysis: One-loop potential for classical moduli → Local minimum separated by a large barrier from runaway at infinity

String theory realization • Consider D3-branes at a singularity, and add D7-branes passing through it → D7-branes wrap non-compact supersymmetric 4-cycles in toric singu → Flavours arise from D3-D7 open strings → Flavour masses from D7-D7’ field vevs (due to 73-37-77’ couplings): D7-branes recombine and move away from D3-branes • Dimer diagrams efficiently describe these properties for general toric singularities (and dP 1 in particular). [Franco, A.U.] • Geometric picture D7 D7 D7 D3 D3

Local models of GMSB [Garc ´ ıa-Etxebarria, Saad, A.U.] • Consider local CY’s with two singular points, with D-branes → Two chiral gauge sectors decoupled at massless level • For suitable singularities, and D-brane systems at them, → MSSM-like sector e.g. D3/D7’s at C 3 / Z 3 [Aldazabal, Ib´ a˜ nez, Quevedo, A.U.] → Gauge sector with DSB e.g. D3/D7’s at dP 1 singularity D7 D7 MSSM D3 DSB D3 • Models of Gauge mediation in string theory → Similar in spirit to [Diaconescu, Florea, Kachru, Svrcek] → Local model, enough for substringy separation: UV insensitivity → Separation related to Kahler or complex modulus → Spectrum and interactions of massive messengers is computable

A simple example • For sub-stringy separtion, better described as small blow-up of gauge theory of D-branes at the singularity in the coincident limit • A simple example: Partial resolution of X 3 , 1 singu to C 3 / Z 3 and dP 1 a) b) c) A A C C G E G E D B D B b) U(3M) a) U(2M) U(3) U(2M) U(3+M) U(1+2M) U(1+2M) U(M) U(1) U(1) U(1) 0 0 U U(1) ( 2 U + ( M 1 + ) 3 M U(3M) U(2) ) U(2M) U(2M) U(2+2M) U(2+2M) U(2) U(3) U(3+3M) dP0 dP1 • General framework, flexible enough to implement many other models

Conclusions • D-branes at singularities can be used to engineer gauge theories with interesting infrared dynamics • We have studied differents aspects of dynamical SUSY breaking in systems of D-branes at singularities Important role of fractional D-branes at obstructed geometries (DSB branes), like dP 1 theory → Runaway for systems of just D3-branes → Local SUSY-breaking minimum for D3/D7’s • Many applications come to mind → String models of GMSB → Supergravity dual of DSB gauge theories (subtle...) • Need to improve techniques to carry out gauge theory analysis → Insight from dimer diagrams? • We expect interesting progress in these directions