Supersymmetric gauge theory with space-time-dependent couplings

• Published in: Progress of theoretical and experimental physics Vol. 2018; no. 1
• Main Authors: Choi, Jaewang, Fernández-Melgarejo, José J, Sugimoto, Shigeki
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.01.2018
• Subjects: Physics; Spacetime; String theory; Symmetry; B10; B16
• ISSN: 2050-3911; 2050-3911
• DOI: 10.1093/ptep/ptx181

Abstract We study deformations of ${\cal N}=4$ 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 in which $ISO(1,1)$ is enhanced to $ISO(1,2)$, it reproduces the supersymmetric Janus configuration found by Gaiotto and Witten [J. High Energy Phys. 06, 097 (2010)]. 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 have also found the general solution of the supersymmetry conditions for the cases with $ISO(1,1)\times SO(2)\times SO(4)$ symmetry. Cases with time-dependent couplings and/or masses are also considered.