On Exactly Marginal Deformations Dual to $B$-Field Moduli of IIB Theory on SE$_5$

TL;DR

This paper identifies the third exactly marginal deformation in quiver CFTs dual to IIB on $Y^{p,q}$, linking field theory couplings to the gravity modulus $ ext{int} B_2$, and provides an algorithm for finding such deformations in brane tiling models.

Contribution

The paper explicitly identifies the third exactly marginal direction dual to the $B$-field modulus and introduces a general algorithm for locating similar deformations in brane tiling CFTs.

Findings

Established the duality between the $B$-field modulus and a marginal deformation in the field theory.

Derived a relation between gauge couplings and the gravity modulus vev.

Demonstrated the algorithm on $L^{1,5,2}$ and Suspended Pinch Point models.

Abstract

The complex dimension of the space of exactly marginal deformations for quiver CFTs dual to IIB theory compactified on $Y^{p,q}$ is known to be generically three. Simple general formulas already exist for two of the exactly marginal directions in the space of couplings, one of which corresponds to the sum of the (inverse squared of) gauge couplings, and the other to the $\beta$-deformation. Here we identify the third exactly marginal direction, which is dual to the modulus $\int B_{2}$ on the gravity side. This identification leads to a relation between the field theory gauge couplings and the vacuum expectation value of the gravity modulus that we further support by a computation related to the chiral anomaly induced by added fractional branes. We also present a simple algorithm for finding similar exactly marginal directions in any CFT described by brane tiling, and demonstrate it for the quiver CFTs dual to IIB theory compactified on $L^{1,5,2}$ and the Suspended Pinch Point.