Boundary Conditions and Unitarity: the Maxwell-Chern-Simons System in AdS_3/CFT_2

TL;DR

This paper explores the boundary conditions of the Maxwell-Chern-Simons system in AdS_3, revealing that most conditions lead to instabilities or ghosts, thus violating unitarity in the dual CFT_2.

Contribution

It systematically analyzes a broad class of boundary conditions in the MCS system and their implications for unitarity and stability in holography.

Findings

Most boundary conditions induce instabilities.

Almost all boundary conditions lead to ghost excitations.

Violations of unitarity bounds are consistent with these instabilities.

Abstract

We consider the holography of the Abelian Maxwell-Chern-Simons (MCS) system in Lorentzian three-dimensional asymptotically-AdS spacetimes, and discuss a broad class of boundary conditions consistent with conservation of the symplectic structure. As is well-known, the MCS theory contains a massive sector dual to a vector operator in the boundary theory, and a topological sector consisting of flat connections dual to U(1) chiral currents; the boundary conditions we examine include double-trace deformations in these two sectors, as well as a class of boundary conditions that mix the vector operators with the chiral currents. We carefully study the symplectic product of bulk modes and show that almost all such boundary conditions induce instabilities and/or ghost excitations, consistent with violations of unitarity bounds in the dual theory.