Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Supersymmetric vacua of mass-deformed M2-brane theory

Hee-Cheol Kim, Seok Kim

TL;DR

The paper addresses counting supersymmetric vacua of the mass-deformed N=6 U(N)_k×U(N)_{-k} Chern-Simons-matter theory by computing the Witten index. It introduces a Yang-Mills–Chern-Simons deformation and compactifies on a small T^2 to reduce to a quantum-mechanical index, enabling a tractable count of vacua around each classical configuration. It derives a closed form for the generating function I_k(q) that reduces to the gravity-predicted partitions for k=1 and generalizes to higher k with explicit expressions such as I_2(q); the results illuminate the relationship between field theory vacua and M2-brane gravity duals, suggest possible Z_k modding in the gravity side, and discuss non-relativistic holography implications. The work thereby provides a microscopic, field-theoretic verification of vacuum degeneracies and connects them to geometric droplet pictures in the dual gravity description.

Abstract

We count the supersymmetric vacua of mass-deformed N=6 U(N)xU(N) Chern-Simons-matter theory by calculating the Witten index. When the Chern-Simons level k is 1, our result perfectly agrees with that from the gravity dual, given by partitions of N. For general k, our index generalizes partitions of N, including additional degrees. We also comment on non-relativistic superconformal theories constructed from this model.

Supersymmetric vacua of mass-deformed M2-brane theory

TL;DR

The paper addresses counting supersymmetric vacua of the mass-deformed N=6 U(N)_k×U(N)_{-k} Chern-Simons-matter theory by computing the Witten index. It introduces a Yang-Mills–Chern-Simons deformation and compactifies on a small T^2 to reduce to a quantum-mechanical index, enabling a tractable count of vacua around each classical configuration. It derives a closed form for the generating function I_k(q) that reduces to the gravity-predicted partitions for k=1 and generalizes to higher k with explicit expressions such as I_2(q); the results illuminate the relationship between field theory vacua and M2-brane gravity duals, suggest possible Z_k modding in the gravity side, and discuss non-relativistic holography implications. The work thereby provides a microscopic, field-theoretic verification of vacuum degeneracies and connects them to geometric droplet pictures in the dual gravity description.

Abstract

We count the supersymmetric vacua of mass-deformed N=6 U(N)xU(N) Chern-Simons-matter theory by calculating the Witten index. When the Chern-Simons level k is 1, our result perfectly agrees with that from the gravity dual, given by partitions of N. For general k, our index generalizes partitions of N, including additional degrees. We also comment on non-relativistic superconformal theories constructed from this model.

Paper Structure

This paper contains 3 sections, 45 equations, 1 figure.

Table of Contents

  1. Introduction and discussions
  2. The theory and classical vacua
  3. The index

Figures (1)

  • Figure 1: An example of our parametrization for $N\!=\!11$, with $N_1\!=\!3$, $\hat{N}_1\!=\!2$, $N_3\!=\!2$. Grey boxes with longer horizontal/vertical edges denote insertions of irreducible blocks of first/second type, respectively. Unbroken gauge group is $U(3)^2\times U(2)^2$ in this case.