Wiggling boundary and corner edge modes in JT gravity with defects

TL;DR

This paper investigates boundary and corner edge modes in JT gravity with defects, revealing how boundary wiggles influence topological constraints, degrees of freedom, and algebraic structures in the presence of conical and wormhole defects.

Contribution

It introduces a generalized boundary action for wiggling boundaries in JT gravity, classifies corner systems with constraints, and links edge modes to algebraic structures like 1(2,2) and Maurer-Cartan forms.

Findings

Boundary action depends on local temperature and horizon dynamics.

Corner variables form a discrete 1(2,2) algebra under unitary representation.

Edge modes can be expressed via Maurer-Cartan forms, revealing 1(2,2) symmetry.

Abstract

We study the gravitational edge modes (GrEMs) and gauge edge modes (GaEMs) in Jackiw-Teitelboim (JT) gravity on a wiggling boundary. The wiggling effect manifests as a series of spacetime topological and bulk constraints for both conical and wormhole defect solutions. For the conical defect solution, we employ the generalized Fefferman-Graham (F-G) gauge to extend the boundary action, allowing for non-constant temperature and horizon position. We find that the infrared behavior of this boundary action is determined by the local dynamics of the temperature and horizon. For the wormhole defect solution, the boundary action can, in special cases, be described by a field with variable mass subject to a constant external force. We classify this corner system as a first-class constrained system influenced by field decomposition, confirming that the physical degrees of freedom are determined by constraints from the wiggling boundary information. We find that GrEMs and GaEMs can be linked at the corners by imposing additional constraints. Additionally, we show that the ``parallelogram'' composed of corner variables exhibits discreteness under a unitary representation. Finally, we explore that information from extrinsic vectors can be packaged into the GaEMs via a Maurer-Cartan form, revealing the boundary degrees of freedom as two copies of the $\mathfrak{sl}(2,\mathbb{R})$ algebra. By separating pure gauge transformations, we identify the gluing condition for gauge invariance and the corresponding integrable charges.