Comments on domain walls in holographic duals of mass deformed conformal field theories

TL;DR

This paper analyzes M-theory backgrounds dual to mass deformed superconformal field theories in 2+1 dimensions, focusing on domain walls created by wrapped M5-branes and their charge quantization, with detailed examples and comparisons to field theory.

Contribution

It provides a detailed examination of domain walls in specific M-theory backgrounds, including flux quantization, charge shifts, and a novel M2/anti M2 configuration, enhancing understanding of holographic duals.

Findings

Charge shifts are consistent with flux quantization.

Wrapped M5-branes create domain walls with predictable charge effects.

M2/anti M2 pairs behave as domain walls matching field theory expectations.

Abstract

We consider M-theory backgrounds which are gravity duals of mass deformed superconformal field theories in 2+1 dimensions. The specific examples we consider are the B_8, Stenzel, and the Lin-Lunin-Maldacena geometries. These geometries contain compact 4-cycles on which one can wrap an M5-brane to create an object which behaves effectively like a domain wall in 2+1 dimensions. We review the quantization of flux and charges of these M-theory backgrounds, and confirm that the back reaction of the domain wall shifts the charges in a manner consistent with these quantization conditions, paying particular attention to various subtle half integer shifts of the charge lattice which arise as a part of the complete story. We also describe a configuration of a stationary, merging M2/anti M2 pair in the Lin-Lunin-Maldacena background, which can also be interpreted as a domain wall, and compare its basic properties with the expectations from its field theory description.