Batalin-Tyutin quantization of dynamical boundary of AdS$_2$

TL;DR

This paper applies Batalin-Tyutin quantization to a dynamical boundary in AdS$_2$, transforming a second-class constrained system into a first-class one to explore the boundary-bulk correspondence in AdS/CFT.

Contribution

It introduces a Lagrangian formulation for the boundary Hamiltonian and employs Batalin-Tyutin method to handle second-class constraints, extending the boundary theory.

Findings

Successfully constructed a first-class constraint system from the original second-class system.

Demonstrated the extended system reduces to the original under unitary gauge.

Raised questions about the existence of a consistent extended bulk theory in AdS/CFT context.

Abstract

In a two-dimensional AdS space, a dynamical boundary of AdS space was described by a one-dimensional quantum-mechanical Hamiltonian with a coupling between the bulk and boundary system. In this paper, we present a Lagrangian corresponding to the Hamiltonian through the Legendre transformation with a constraint. In Dirac's constraint analysis, we find two primary constraints without secondary constraints; however, they are fully second-class. In order to make the second-class constraint system into a first-class constraint system, we employ the Batalin-Tyutin Hamiltonian method, where the extended system reduces to the original one for the unitary gauge condition. In the spirit of the AdS/CFT correspondence, it raises a question whether a well-defined extended bulk theory corresponding to the extended boundary theory can exist or not.