Supersymmetric Gauge Theory with Space-time Dependent Couplings

Abstract

We study deformations of $\mathcal{N}=4$ supersymmetric Yang-Mills theory with couplings and masses depending on space-time. The conditions to preserve part of the supersymmetry are derived and a lot of solutions of these conditions are found. The main example is the case with $ISO(1,1)\times SO(3)\times SO(3)$ symmetry, in which couplings, as well as masses and the theta parameter, can depend on two spatial coordinates. In the case $ISO(1,1)$ is enhanced to $ISO(1,2)$, it reproduces the supersymmetric Janus configuration found by Gaiotto and Witten. When $SO(3)\times SO(3)$ is enhanced to $SO(6)$, it agrees with the world-volume theory of D3-branes embedded in F-theory (a background with 7-branes in type IIB string theory). We also find the general solution of the supersymmetry conditions for the cases with $ISO(1,1)\times SO(2)\times SO(4)$ symmetry. The cases with time dependent couplings and/or masses are also considered.

48 pages, v2: minor corrections

References in corpus (7)

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Cited by in corpus (7)

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• Yang-Baxter deformations and generalized supergravity -- A short summary
• Deformation of $\mathcal{N}=4$ SYM with varying couplings via fluxes and intersecting branes
• Baryons under Strong Magnetic Fields or in Theories with Space-dependent $\theta$-term
• (1,0) gauge theories on the six-sphere
• Extended Gauge Theory Deformations From~Flux~Backgrounds
• Properties of multiple D0-brane system: 11D origin, equations of motion and their solutions