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

Büşra Dedeoğlu, Mehmet Ozkan, Özgür Sarıoğlu

TL;DR

This work addresses constructing a CS‑like, third‑way consistent family of 3D massive gravity models extending MMG and analyzes the simplest non‑trivial case (N=2). Using a torsionful CS‑like Lagrangian with an auxiliary hierarchy, they solve the field equations, obtain AdS$_3$ backgrounds, and compute the central charges $c^{3}$; linearization reveals two massless and three massive modes governed by a cubic mass polynomial. Along the chiral line a rank‑2 Jordan block appears, signaling logarithmic CFT behavior, while at a degenerate point a rank‑3 Jordan form yields two logarithmic partners and an ultra‑logarithmic boundary sector. The results show that unitary, tachyon‑free regimes compete with ghost or tachyonic modes in this class and motivate extending the analysis to higher‑$N$ and to supersymmetric or higher‑spin generalizations.

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.

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

TL;DR

This work addresses constructing a CS‑like, third‑way consistent family of 3D massive gravity models extending MMG and analyzes the simplest non‑trivial case (N=2). Using a torsionful CS‑like Lagrangian with an auxiliary hierarchy, they solve the field equations, obtain AdS backgrounds, and compute the central charges ; linearization reveals two massless and three massive modes governed by a cubic mass polynomial. Along the chiral line a rank‑2 Jordan block appears, signaling logarithmic CFT behavior, while at a degenerate point a rank‑3 Jordan form yields two logarithmic partners and an ultra‑logarithmic boundary sector. The results show that unitary, tachyon‑free regimes compete with ghost or tachyonic modes in this class and motivate extending the analysis to higher‑ and to supersymmetric or higher‑spin generalizations.

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.
Paper Structure (11 sections, 84 equations, 1 figure)

This paper contains 11 sections, 84 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Chern-Simons-like formulation of MMG-like models
  3. Lg MMG-like models
  4. Models with three distinct massive states
  5. Chiral case
  6. Models with degenerate massive states
  7. Chiral case
  8. Conclusions
  9. Jordan form and similarity matrix in section \ref{['chiralsection']}
  10. Jordan form and similarity matrix in section \ref{['degMassStates']}
  11. Jordan form and similarity matrix in subsection \ref{['ultrachiral']}

Figures (1)

  • Figure 1: Shaded regions in the $(\rho,\gamma)$ plane: light gray strip shows $\rho\ge5$ which is the common region for $\rho$ satisfied by $e_1(r)$ and $e_2(r)$ in \ref{['no-tachyon']}; the lightly hatched outer wedge shows $4\gamma^2-9(1+\rho)^2\ge0$; the dashed inner wedge corresponds to $9(\rho-1)^2-4\gamma^2>0$. The dashed lines correspond to the chiral case, which is discussed in section \ref{['chiralsection']}. The point $(5,6)$ is a special point discussed in subsection \ref{['ultrachiral']}. No points satisfy all conditions \ref{['unitarity']} and \ref{['no-tachyon']} simultaneously.