Three-Dimensional Tricritical Gravity

TL;DR

This paper explores a special three-dimensional gravity theory with six derivatives, revealing a tricritical point where the theory's solutions exhibit logarithmic behaviors and proposing a duality with a rank-3 Logarithmic Conformal Field Theory.

Contribution

It introduces a novel tricritical point in six-derivative 3D gravity theories and analyzes its dual LCFT, including boundary conditions and conserved charges.

Findings

At the tricritical point, two massive gravitons become massless.

The dual LCFT has calculable boundary stress tensor and anomalies.

Conserved charges vanish for certain boundary conditions at the tricritical point.

Abstract

We consider a class of parity even, six-derivative gravity theories in three dimensions. After linearizing around anti-de Sitter space, the theories have one massless and two massive graviton solutions for generic values of the parameters. At a special, so-called tricritical, point in parameter space the two massive graviton solutions become massless and they are replaced by two solutions with logarithmic and logarithmic-squared boundary behavior. The theory at this point is conjectured to be dual to a rank-3 Logarithmic Conformal Field Theory (LCFT) whose boundary stress tensor, central charges and new anomaly we calculate. We also calculate the conserved Abbott-Deser-Tekin charges. At the tricritical point, these vanish for excitations that obey Brown-Henneaux and logarithmic boundary conditions, while they are generically non-zero for excitations that show logarithmic-squared boundary behavior. This suggests that a truncation of the tricritical gravity theory and its corresponding dual LCFT can be realized either via boundary conditions on the allowed gravitational excitations, or via restriction to a zero charge sub-sector. We comment on the structure of the truncated theory.