[Paper Review] On 2D gauge theories in Jackiw-Teitelboim gravity

Luca V. Iliesiu|arXiv (Cornell University)|Sep 11, 2019

Black Holes and Theoretical Physics92 references17 citations

TL;DR

This paper presents a soluble 2D gauge-gravity model in Jackiw-Teitelboim (JT) gravity coupled to Yang-Mills theory, showing that the partition function on surfaces of arbitrary genus is described by a double-scaled matrix integral. For disk topology, the theory reduces to a Schwarzian theory coupled to a particle on the gauge group manifold, with exact boundary descriptions of diffeomorphism-invariant observables at arbitrary gauge coupling.

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.

Motivation & Objective

• To develop a soluble 2D effective field theory for near-extremal black holes using JT gravity coupled to Yang-Mills theory.
• To compute the partition function on Riemann surfaces of arbitrary genus and number of boundaries.
• To derive exact boundary descriptions of diffeomorphism-invariant observables, including quark worldline operators.
• To extend the solvability of pure JT gravity to include gauge degrees of freedom beyond the S-wave sector.
• To provide a framework for studying low-energy physics of near-extremal black holes beyond the weak-coupling limit.

Proposed method

• The model is formulated using an effective action in Euclidean signature, combining Jackiw-Teitelboim gravity with Yang-Mills theory via a linearized dilaton coupling.
• The partition function on disk topology is derived using Dirichlet boundary conditions and counter-terms for boundary condition changes.
• For higher genus surfaces, the partition function is constructed via a genus expansion using topological building blocks and a double-scaled matrix integral with group-valued matrix elements.
• The theory is quantized using path integral methods with careful treatment of integration contours and gauge-fixing in the presence of boundaries.
• Diffeomorphism and gauge invariance are preserved by constructing observables as functionals of the metric, dilaton, and gauge field, with explicit boundary duals.
• Quark worldline operators are analyzed in the weak-coupling limit and extended to arbitrary coupling using diffeomorphism invariance and boundary condition-changing defects.

Experimental results

Research questions

• RQ1 How can the partition function of JT gravity coupled to Yang-Mills theory be computed exactly on surfaces of arbitrary genus and boundary structure?
• RQ2 What is the boundary dual description of diffeomorphism-invariant observables, such as quark worldlines, in this gravitational gauge theory?
• RQ3 How does the inclusion of gauge fields modify the solvability of JT gravity beyond the pure gravity case?
• RQ4 Can the genus expansion of the partition function be expressed as a double-scaled matrix integral with group-valued matrix elements?
• RQ5 What is the role of topologically non-trivial worldlines and self-intersections in the path integral for quark operators in higher-genus geometries?

Key findings

• The partition function on surfaces of arbitrary genus is exactly described by a double-scaled matrix integral where matrix elements map the gauge group to complex or real numbers.
• For disk topology, the theory reduces to a Schwarzian theory coupled to a particle moving on the gauge group manifold, with exact boundary dynamics.
• The expectation values of diffeomorphism-invariant observables, including quark worldlines, are computed exactly and expressed in terms of boundary data.
• The contribution of gauge fields to the partition function is not suppressed in the extremal limit, even at weak coupling, when mixed boundary conditions are imposed.
• The theory remains soluble at arbitrary gauge coupling, with the path integral for topologically non-trivial worldlines requiring tracking of self-intersection contributions via 6j-symbols.
• The results provide a framework for studying non-S-wave modes in near-extremal black holes, including Kaluza-Klein modes from dimensional reduction on internal spheres.