Orientifold, geometric transition and large N duality for SO/Sp gauge theories

Abstract

We extend the large N duality of four dimensional N = 1 supersymmetric Yang-Mills theory with additional chiral fields and arbitrary superpotential recently proposed by Cachazo, Intriligator and Vafa to the case of SO/Sp gauge groups. By orientifolding the geometric transition, we investigate a large N duality between N = 1, SO/Sp supersymmetric theories with arbitrary superpotential and an Abelian N = 2 theory with supersymmetry broken to N = 1 by electric and magnetic Fayet-Iliopoulos terms.

Phases of SO(Nc) gauge theories with flavors

“…g 2s 2s TrΦ 2s (2.1) where the first two terms come from the N = 2 theory and the third term, W (Φ), can be described as a small perturbation of N = 2 SO(N c ) gauge theory [64,65,66,67,68,69,70,71,72,8,11] W (Φ) = where Φ ab is an adjoint scalar chiral superfield that plays the role of a deformation breaking N = 2 supersymmetry to N = 1 supersymmetry. Note that in [64] the coefficient for the mass term of quark in the tree superpotential is different from √ 2 used here, but it can be absorbed in the mass matrix and the only quadratic mass deformation for Φ with g 2 = µ (other parameters are vanishing) was considered in [64].…”

“…3) 8) where curve (3.7) is for U(N c ) at the non-baryonic branch and curve (3.8), for U(N c ) at the baryonic branch. Again, function H p (t) has a proper number of (t − m 2 ) to count the prefactor for various r-th branches.…”

“…These RR fluxes provide the effective superpotential which corresponds to one of four dimensional gauge theories on the D5-branes [5,6,7]. This equivalence has been tested for several different models in different contexts [8,9,10,11,12,13].…”

Mirror symmetry and aG2flop

“…In its mirror type IIB formulation this is closely related to the dualities considered in [10] [11]. Extensions of this duality to other geometric transitions has been considered in [12] (see also [13] [14]). …”

Comments on M theory dynamics onG2holonomy manifolds

“…Then it is easy to verify that 20) with k 2 = 0, 1, · · · , N 2 − 1. This can be rewritten in the form…”