Holographic Coulomb Branch Flows with N=1 Supersymmetry

TL;DR

This paper constructs a new class of N=1 supersymmetric holographic flow solutions with U(1)^3 symmetry, describing Coulomb branch flows with brane distributions and fluxes that break Calabi-Yau conditions.

Contribution

It introduces a novel set of almost Calabi-Yau solutions with specific fluxes and brane polarizations, expanding the landscape of holographic N=1 supersymmetric backgrounds.

Findings

Solutions exhibit U(1)^3 symmetry and Coulomb branch behavior.

The metric is hermitian but not Kahler, with a specific PDE characterizing the geometry.

Fluxes induce dielectric polarization of D3-branes into D5-branes.

Abstract

We obtain a large, new class of N=1 supersymmetric holographic flow backgrounds with U(1)^3 symmetry. These solutions correspond to flows toward the Coulomb branch of the non-trivial N=1 supersymmetric fixed point. The massless (complex) chiral fields are allowed to develop vevs that are independent of their two phase angles, and this corresponds to allowing the brane to spread with arbitrary, U(1)^2 invariant, radial distributions in each of these directions. Our solutions are "almost Calabi-Yau:" The metric is hermitian with respect to an integrable complex structure, but is not Kahler. The "modulus squared" of the holomorphic (3,0)-form is the volume form, and the complete solution is characterized by a function that must satisfy a single partial differential equation that is closely related to the Calabi-Yau condition. The deformation from a standard Calabi-Yau background is driven by a non-trivial, non-normalizable 3-form flux dual to a fermion mass that reduces the supersymmetry to N=1. This flux also induces dielectric polarization of the D3-branes into D5-branes.