Maxwell-Chern-Simons-Matter in AdS${}_3$

Abstract

We study Maxwell-Chern-Simons theory on AdS${}_3$ coupled to $N$ complex scalars or Dirac fermions, including sextic and Gross-Neveu interactions, respectively. First, we derive the bulk Maxwell-Chern-Simons propagator, clarifying how Dirichlet boundary conditions fix the contributions of the massive and flat sectors. Upon coupling to the matter sector, we work at large $N$ with $\kappa =k/N$ and $\alpha =N{e}^2$ fixed, where $k$ is the Chern-Simons level. We determine the corresponding phase diagrams, and we resum matter insertions to obtain the photon propagator at leading order in large $N$, exactly in $\alpha$ and $\kappa$. Its poles determine the spin-one boundary spectrum, split into two helicity sectors by the Chern-Simons interaction. With Dirichlet boundary conditions, the unHiggsed scalar phase contains a protected chiral current, which is lifted by Higgsing. In the fermionic phases, the current persists for nonzero effective Chern-Simons level, with helicity determined by the induced level shift. At bulk conformal points, we extract large-$N$ BCFT data for the critical and tricritical scalar theories, as well as for the regular fermion and Gross-Neveu theories.

arXiv comment44+24 pages, 10 figures