Mass-deformed Brane Tilings

TL;DR

This paper investigates renormalization group flows in N=1 superconformal field theories realized on D3-branes at toric Calabi-Yau singularities, interpreting flows as complex deformations that preserve the toric structure, supported by string amplitude calculations.

Contribution

It introduces a geometric interpretation of mass-induced RG flows as complex deformations of toric Calabi-Yau singularities, extending known constructions like Klebanov-Witten.

Findings

Flows correspond to complex deformations preserving toric conditions

String amplitude computations support the geometric interpretation

Volume of the Sasaki-Einstein base increases along the flow

Abstract

We study renormalization group flows among N=1 SCFTs realized on the worldvolume of D3-branes probing toric Calabi-Yau singularities, thus admitting a brane tiling description. The flows are triggered by masses for adjoint or vector-like pairs of bifundamentals and are generalizations of the Klebanov-Witten construction of the N=1 theory for the conifold starting from the N=2 theory for the C^2/Z_2 orbifold. In order to preserve the toric condition pairs of masses with opposite signs have to be switched on. We offer a geometric interpretation of the flows as complex deformations of the Calabi-Yau singularity preserving the toric condition. For orbifolds, we support this interpretation by an explicit string amplitude computation of the gauge invariant mass terms generated by imaginary self-dual 3-form fluxes in the twisted sector. In agreement with the holographic a-theorem, the volume of the Sasaki-Einstein 5-base of the Calabi-Yau cone always increases along the flow.