U(N) Gauged N=2 Supergravity and Partial Breaking of Local N=2 Supersymmetry

We study a minimal model of U(N) gauged N=2 supergravity with one hypermultiplet parametrizing SO(4,1)/SO(4) quaternionic manifold. Local N=2 supersymmetry is known to be spontaneously broken to N=1 in the Higgs phase of U(1)_{graviphoton} \times U(1). Several properties are obtained of this model in the vacuum of unbroken SU(N) gauge group. In particular, we derive mass spectrum analogous to the rigid counterpart and put the entire effective potential on this vacuum in the standard superpotential form of N=1 supergravity.Comment: 22 pages, a version to appear Int. J. Mod. Phys.

Low Energy Processes Associated with Spontaneously Broken N=2 Supersymmetry

We consider low energy processes described by the N=2 supercurrent on its partially (to N=1) and spontaneously broken vacuum and the attendant Nambu-Goldstone fermion (NGF), which the presence of the electric and magnetic Fayet-Iliopoulos (FI) terms is responsible for. We show suppressions of amplitudes decaying into the NGF as its momentum becomes small. In the lagrangian realization (namely, the model of arXiv:hep-th/0409060) of the conserved supercurrent, the NGF resides in the overall U(1), which is nonetheless not decoupled, and interacts with the SU(N) sector through nonderivative as well as derivative couplings. The low energy suppression is instead accomplished by a cancellation between the annihilation diagram from the Yukawa couplings and the contact four-Fermi terms. We give a complete form of the supercurrent and the model is recast in more transparent notation.Comment: 20 pages, 6 figure

Deformation of Dijkgraaf-Vafa Relation via Spontaneously Broken N=2 Supersymmetry

It is known that the fermionic shift symmetry of the N=1, U(N) gauge model with a superpotential of an adjoint chiral superfield is replaced by the second (spontaneously broken) supersymmetry in the N=2, U(N) gauge model with a prepotential and Fayet-Iliopoulos parameters. Based on a diagrammatic analysis, we demonstrate how the well-known form of the effective superpotential in the former model is modified in the latter. A set of two equations on the one-point functions stating the Konishi anomaly is modified accordingly.Comment: 12 pages, 1 figure; v2: typos corrected and a footnote added; v3: minor corrections adde

Instantons on ALE spaces and Super Liouville Conformal Field Theories

We provide evidence that the conformal blocks of N=1 super Liouville conformal field theory are described in terms of the SU(2) Nekrasov partition function on the ALE space O_{P^1}(-2).Comment: 10 page

N=2 Quiver Gauge Model and Partial Supersymmetry Breaking

We construct an action of N=2 affine $A_n$ quiver gauge model having non-canonical kinetic terms and equipped with electric and magnetic FI terms. N=2 supersymmetry is shown to be broken to N=1 spontaneously and N=1 multiplets realized on the vacua are given. We also mention the models with different gauge groups. It is argued that the affine $A_1$ quiver gauge model provides a dynamical realization to approach the Klebanov-Witten N=1 fixed point.Comment: 19 page

Quiver Gauge Theory and Extended Electric-magnetic Duality

We construct N=1 A-D-E quiver gauge theory with the gauge kinetic term which depends on the adjoint chiral superfields, as a low energy effective theory on D5-branes wrapped on 2-cycles of Calabi-Yau 3-fold in IIB string theory. The field-dependent gauge kinetic term can be engineered by introducing B-field which holomorphically varies on the base space (complex plane) of Calabi-Yau. We consider Weyl reflection on A-D-E node, which acts non-trivially on the gauge kinetic term. It is known that Weyl reflection is related to N=1 electric-magnetic duality. Therefore, the non-trivial action implies an extension of the electric-magnetic duality to the case with the field-dependent gauge kinetic term. We show that this extended duality is consistent from the field theoretical point of view. We also consider the duality map of the operators.Comment: 24 pages; v2: references added, typos correcte

Penner Type Matrix Model and Seiberg-Witten Theory

We discuss the Penner type matrix model recently proposed by Dijkgraaf and Vafa for a possible explanation of the relation between four-dimensional gauge theory and Liouville theory by making use of the connection of the matrix model to two-dimensional CFT. We first consider the relation of gauge couplings defined in UV and IR regimes of N_f = 4, N = 2 supersymmetric gauge theory being related as $q_{{\rm UV}}={\vartheta_2(q_{{\rm IR}})^4/\vartheta_3(q_{{\rm IR}})^4}$. We then use this relation to discuss the action of modular transformation on the matrix model and determine its spectral curve. We also discuss the decoupling of massive flavors from the N_f = 4 matrix model and derive matrix models describing asymptotically free N = 2 gauge theories. We find that the Penner type matrix theory reproduces correctly the standard results of N = 2 supersymmetric gauge theories.Comment: 22 pages; v2: references added, typos corrected; v3: a version to appear in JHE

A New 2d/4d Duality via Integrability

We prove a duality, recently conjectured in arXiv:1103.5726, which relates the F-terms of supersymmetric gauge theories defined in two and four dimensions respectively. The proof proceeds by a saddle point analysis of the four-dimensional partition function in the Nekrasov-Shatashvili limit. At special quantized values of the Coulomb branch moduli, the saddle point condition becomes the Bethe Ansatz Equation of the SL(2) Heisenberg spin chain which coincides with the F-term equation of the dual two-dimensional theory. The on-shell values of the superpotential in the two theories are shown to coincide in corresponding vacua. We also identify two-dimensional duals for a large set of quiver gauge theories in four dimensions and generalize our proof to these cases.Comment: 19 pages, 2 figures, minor corrections and references adde

BPS Monopole Equation in Omega-background

We study deformed supersymmetries in N=2 super Yang-Mills theory in the Omega-backgrounds characterized by two complex parameters $\epsilon_1, \epsilon_2$. When one of the $\epsilon$-parameters vanishes, the theory has extended supersymmetries. We compute the central charge of the algebra and obtain the deformed BPS monopole equation. We examine supersymmetries preserved by the equation.Comment: 14 pages, typos corrected, published version in JHE

N=2 Generalized Superconformal Quiver Gauge Theory

Four dimensional N=2 generalized superconformal field theory can be defined by compactifying six dimensional (0,2) theory on a Riemann surface with regular punctures. In previous studies, gauge coupling constant space is identified with the moduli space of punctured Riemann surface M_{g,n}. We show that the weakly coupled gauge group description corresponds to a stable nodal curve, and the coupling space is actually the Deligne-Mumford compactification \bar{M}_{g,n}. We also give an algorithm to determine the weakly coupled gauge group and matter content in any duality frame.Comment: v2, reorganizing the materials, discussions on 2d CFT is remove