Interface Yang–Mills, supersymmetry, and Janus

Abstract

We consider theories consisting of a planar interface with N = 4 super-YangMills on either side and varying gauge coupling across the interface. The interface does not carry any independent degrees of freedom, but is allowed to support local gauge invariant operators, included with independent interface couplings. In general, both conformal symmetry and supersymmetry will be broken, but for special arrangements of the interface couplings, these symmetries may be restored. We provide a systematic classification of all allowed interface supersymmetries. We find new theories preserving eight and four Poincaré supersymmetries, which get extended to sixteen and eight supersymmetries in the conformal limit, respectively with SU (2) × SU (2), SO(2) × SU (2) internal symmetry. The Lagrangians for these theories are explicitly constructed. We also recover the theory with two Poincaré supersymmetries and SU (3) internal symmetry proposed earlier as a candidate CFT dual to super Janus. Since our new interface theories have only operators from the supergravity multiplet turned on, dual supergravity solutions are expected to exist. We speculate on the possible relation between the interface theory with maximal supersymmetry and the near-horizon limit of the D3-D5 system.

Boundaries and defects of N = 4 $$ \mathcal{N}=4 $$ SYM with 4 supercharges. Part I: Boundary/junction conditions

“…Suppose X 9 obey Dirichlet, but not X 6 . Then we have c 2 = 0 from (A.52), and together with the previous results we have d 1 , c 1 = 0, c 2 = d 2 = 0, and the remaining equations are the Nahm equations for X 4,5,6 . Hence the equations reduce to the 1/2 BPS case.…”

“…Hence the equations reduce to the 1/2 BPS case. Similarly, if X 4 obey Dirichlet, but not X 7 , then we have d 1 , c 2 = 0, c 1 = d 2 = 0, and the remaining equations are the Nahm equations for X 5,6,7 . Again this is 1/2 BPS.…”

“…We also have F -terms from varying the Q fields which imply (3.31). For NS5-branes, the effective superpotential at the interface is 6) where ξ, ξ † are defined in (3.56). It is straightforward to check that the F -term equations from this superpotential reproduce the equations (3.60)-(3.65).…”

Janus and multifaced supersymmetric theories. II

“…There has been some interest in the Janus-type field theory where the coupling constants are dependent on space [1]. What is exciting about this subject is that some of supersymmetry of the original theory can be preserved even when the coupling constants are spatially dependent once some corrections are made on the Lagrangian and the supersymmetric transformation.…”

“…Starting from the 16 supersymmetric Yang-Mills theory, the various deformations of 2, 4, 8 supersymmetries have been found [1]. Especially, the 16 supersymmetric Janus geometries have been found [9,10], where both dilaton and axion fields vary along a spatial direction.…”