Interface Yang-Mills, Supersymmetry, and Janus
Eric D'Hoker, John Estes, Michael Gutperle
TL;DR
This work classifies the possible interface supersymmetries of ${ m N}=4$ super Yang–Mills across a planar 2+1D interface with a smoothly varying gauge coupling, by constructing a general interface Lagrangian and deriving SUSY-compatibility conditions. Using ${ m SU}(4)$ covariance, the authors solve a set of algebraic matrix equations to obtain explicit Lagrangians for theories with ${ m N}=4$ interface SUSY, ${ m N}=2$ interface SUSY, and ${ m N}=1$ interface SUSY, including their conformal limits and residual internal symmetries. They identify a maximal case with ${ m N}=4$ interface SUSY and ${ m SU}(2) imes{ m SU}(2)$ R-symmetry, show how to remove interface-proportional $( abla_ pi g)^2$ terms to achieve a conformal limit, and discuss holographic interpretations via dual supergravity multiplets. The results provide a systematic framework for constructing supersymmetric Janus-like interface theories and illuminate prospects for AdS/CFT duals, including potential relations to D3–D5 brane configurations.
Abstract
We consider theories consisting of a planar interface with $\N=4$ super-Yang-Mills 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 $SU(2) \times SU(2)$, $SO(2) \times SU(2)$ internal symmetry. The Lagrangians for these theories are explicitly constructe d. 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.