Color decorations of Jackiw-Teitelboim gravity

TL;DR

This paper extends Jackiw-Teitelboim gravity to a colored version with matrix-valued fields, formulated via BF action with $su(N,N)$ gauge algebra, introducing new non-Abelian and matrix-valued fields and interactions.

Contribution

The paper introduces a colored JT gravity model with matrix-valued fields, formulated through a BF action with $su(N,N)$ gauge algebra, embedding standard JT gravity as a special case.

Findings

Formulation of colored JT gravity via BF action with $su(N,N)$ algebra.

Inclusion of $su(N)$ non-Abelian fields and matrix-valued metric and dilaton.

Interactions governed by minimal couplings and cubic/quartic potential terms.

Abstract

We introduce the colored version of Jackiw-Teitelboim (JT) gravity which is the two-dimensional dilaton gravity model with matrix-valued fields. It is straightforwardly formulated in terms of BF action with $su(N,N)$ gauge algebra so that the standard JT gravity is embedded as $su(1,1) \subset su(N,N)$ subsector. We also elaborate on the respective metric formulation which is shown to involve the JT fields plus $su(N)$ non-Abelian fields as well as $su(N)$-matrix valued metric and dilaton fields. Their interactions are governed by minimal couplings and potential terms of cubic and quartic orders involving derivatives.