Deconstructing graviphoton from mass-deformed ABJM

TL;DR

This paper explores the structure of mass-deformed ABJM theory, constructs fuzzy sphere solutions, and deconstructs the graviphoton term to connect D4 and M5 brane theories, fixing normalization and coupling constants.

Contribution

It constructs TGRVV matrices using Schwinger oscillators and deconstructs the graviphoton term, establishing a link between D4 and M5 brane theories with fixed normalization.

Findings

Constructed fuzzy sphere solutions with TGRVV matrices.

Fixed the U(1) gauge field normalization via topological arguments.

Showed agreement of zero mode contributions in D4 and M5 brane partition functions.

Abstract

Mass-deformed ABJM theory has a maximally supersymmetric fuzzy two-sphere vacuum solution where the scalar fields are proportional to the TGRVV matrices. We construct these matrices using Schwinger oscillators. This shows that the ABJM gauge group that corresponds to the fuzzy two-sphere geometry is $U(N)\times U(N-1)$. We deconstruct the graviphoton term in the D4 brane theory. The normalization of this term is fixed by topological reasons. This gives us the correct normalization of the deconstructed U(1) gauge field and fixes the Yang -Mills coupling constant to the value which corresponds to M5 brane compactified on $\mb{R}^ {1,2} \times S^3/{\mb{Z}_k}$. The graviphoton term also enable us to show that the zero mode contributions to the partition functions for the D4 and the M5 brane agree.