Deformation of ${\cal N}=4$ SYM with varying couplings via fluxes and intersecting branes

TL;DR

This paper investigates how ${ m extbf{N}}=4$ supersymmetric Yang-Mills theory deforms with space-time dependent couplings by embedding D3-branes in supergravity backgrounds with fluxes, revealing explicit links to known supersymmetric Janus configurations.

Contribution

It provides a detailed analysis of the effective action on D3-branes in flux backgrounds, establishing a direct correspondence with supersymmetric Janus and intersecting D3-brane configurations.

Findings

Effective action maps deformation parameters to fluxes.

Reproduces supersymmetric Janus configurations.

Matches previous results on intersecting D3-brane backgrounds.

Abstract

We study deformations of ${\cal N}=4$ supersymmetric Yang-Mills theory with space-time dependent couplings by embedding probe D3-branes in supergravity backgrounds with non-trivial fluxes. The effective action on the world-volume of the D3-branes is analyzed and a map between the deformation parameters and the fluxes is obtained. As an explicit example, we consider D3-branes in a background corresponding to $(p,q)$ 5-branes intersecting them and show that the effective theory on the D3-branes precisely agrees with the supersymmetric Janus configuration found by Gaiotto and Witten in arXiv:0804.2907 . D3-branes in an intersecting D3-brane background is also analyzed and the D3-brane effective action reproduces one of the supersymmetric configurations with $ISO(1,1)\times SO(2)\times SO(4)$ symmetry found in our previous paper arXiv:1710.09792 .