On 2D gauge theories in Jackiw-Teitelboim gravity

TL;DR

This work provides an exact quantization of Jackiw–Teitelboim gravity coupled to Yang–Mills theory for arbitrary gauge group $G$ and couplings, revealing that disk topology reduces to the Schwarzian theory coupled to a particle on $G$, while the full genus expansion is governed by a double-scaled matrix integral with matrix elements valued in the group algebra $\ olinebreak[0]\mathbb{C}[G]$ (and $\ olinebreak[0]\mathbb{R}[G]$ for unorientable manifolds). It establishes a precise boundary dual for the gravitational theory, both for Dirichlet and mixed gauge boundary conditions, and constructs a broad class of diffeomorphism-invariant observables, including generalized Wilson lines and quark worldline operators, with exact boundary descriptions. The analysis unifies JT gravity, 2D Yang–Mills, and matrix-model techniques to produce a coherent picture of the bulk-boundary correspondence in gravitational gauge theories and provides a platform for exploring near-horizon black-hole physics beyond the S-wave sector. The results offer insight into the holographic structure of low-energy black-hole dynamics and connect to disordered models with global symmetries via the Schwarzian+group-manifold boundary theory.

Abstract

The low-energy behavior of near-extremal black holes can be understood from the near-horizon AdS_2 region. In turn, this region is effectively described by using Jackiw-Teitelboim gravity coupled to Yang-Mills theory through the two-dimensional metric and the dilaton field. We show that such a two-dimensional model of gravity coupled to gauge fields is soluble for an arbitrary choice of gauge group and gauge couplings. Specifically, we determine the partition function of the theory on two-dimensional surfaces of arbitrary genus and with an arbitrary number of boundaries. When solely focusing on the contribution from surfaces with disk topology, we show that the gravitational gauge theory is described by the Schwarzian theory coupled to a particle moving on the gauge group manifold. When considering the contribution from all genera, we show that the theory is described by a particular double-scaled matrix integral, where the elements of the matrix are functions that map the gauge group manifold to complex or real numbers. Finally, we compute the expectation value of various diffeomorphism invariant observables in the gravitational gauge theory and find their exact boundary description.

Figures (4)

• Figure 1: Schematic representation of the equivalence between the gravitational gauge theory at weak gauge coupling and the Schwarzian decoupled from a particle moving on the group manifold $G$.
• Figure 2: Schematic representation of the equivalence between the gravitational gauge theory and the Schwarzian coupled to a particle moving on the group manifold $G$.
• Figure 3: Schematic representation of the equivalence between the gravitational gauge theory in the genus expansion, a collection of Hermitian random matrix ensembles $\prod_R^\otimes H_{N_R\times N_R}$ and a single Hermitian random matrix ensemble with elements in $\mathbb C[G]$.
• Figure 4: Schematic representation of the equivalence between the gravitational gauge theory in the genus expansion on orientable and unorientable surfaces, a collection of random matrix ensembles $\prod_R^\otimes H_{N_R\times N_R}$ whose class is specified by $f_R$ and a single GOE-like random matrix ensemble with elements in $\mathbb R[G]$.