Supersymmetric gauge theory with space-time-dependent couplings

Abstract

We study deformations of 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) × SO(3) × SO(3) symmetry, in which couplings, as well as masses and the theta parameter, can depend on two spatial coordinates. In the case in which ISO(1, 1) is enhanced to ISO(1, 2), it reproduces the supersymmetric Janus configuration found by Gaiotto and Witten. When SO(3) × 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 have also found the general solution of the supersymmetry conditions for the cases with ISO(1, 1)×SO(2)×SO(4) symmetry. Cases with time dependent couplings and/or masses are also considered. *

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

“…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 [1]. 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) × SO(2) × SO(4) symmetry found in our previous paper [2]. …”

“…In the former example, we show that the effective action on the probe D3-branes precisely reproduces the action for the supersymmetric Janus configuration found in [1]. The latter example reproduces one of the supersymmetric solutions with ISO(1, 1) × SO(2) × SO(4) symmetry obtained in [2].…”

“…In our recent paper [2], we wrote down the conditions to preserve part of the supersymmetry in deformed N = 4 SYM with varying couplings and found various non-trivial solutions. 2 Though the motivation was in string theory, the analyses in [2] were purely field theoretical.…”

“…2 Though the motivation was in string theory, the analyses in [2] were purely field theoretical. In this paper, we try to realize such systems in string theory by putting probe D3-branes in supergravity backgrounds with fluxes and find a map between the couplings in the action of the deformed N = 4 SYM and the fluxes in the background.…”

“…In section 2, we review the deformations of N = 4 SYM with varying couplings that were studied in [2]. In particular, we summarize the SUSY conditions and a few explicit solutions that will be used in section 4.…”