Chern-Simons-like formulation of 3D MMG-like massive gravity models

TL;DR

This paper explores a Chern-Simons-like formulation of 3D MMG-like massive gravity models, analyzing their solutions, dual CFT properties, and the emergence of logarithmic modes at special points.

Contribution

It introduces a new class of MMG-like models with specific parity and auxiliary fields, providing exact solutions, dual CFT analysis, and revealing logarithmic structures in the spectrum.

Findings

AdS background solutions are explicitly constructed.

Central charges of the dual CFT are computed.

Logarithmic and ultra-logarithmic modes are identified at special points.

Abstract

We investigate the Chern-Simons-like formulation of 3D MMG-like massive gravity models that are "third-way consistent". Building on previous work on exotic massive gravities, we analyze a class of MMG-like theories characterized by a specific parity structure and an auxiliary field hierarchy. Focusing on the simplest non-trivial case, we solve the full set of field equations, determine the AdS background solutions, compute the central charges of the dual CFT, and perform a linearized analysis to obtain the mass spectrum. Along the chiral line, the linearized mass operator develops a rank-2 Jordan block, signaling logarithmic behavior of massive modes in the dual two-dimensional CFT. At a special degenerate point, this structure is enhanced to a rank-3 Jordan block, giving rise to two logarithmic partners and an ultra-logarithmic sector in the boundary theory.