The Holography of the 2D inhomogeneously deformed CFT

TL;DR

This paper classifies inhomogeneous Hamiltonians in 2D CFTs using Virasoro coadjoint orbits, explores their holographic duals via generalized Ba ilde{ ext{n}}ados solutions, and extends the analysis to KdV-type boundary conditions, revealing new solvable models.

Contribution

It introduces a classification scheme for inhomogeneous Hamiltonians based on Virasoro coadjoint orbits and connects them to generalized bulk geometries, expanding the understanding of holographic inhomogeneous deformations.

Findings

Classified inhomogeneous Hamiltonians via Virasoro coadjoint orbits.

Linked M"obius Hamiltonian to the 3D C-metric.

Extended analysis to KdV-type boundary conditions with new solvable models.

Abstract

We systematically study inhomogeneous Hamiltonians in two-dimensional conformal field theories within the framework of the AdS/CFT correspondence by relating them to two-dimensional curved backgrounds. We propose a classification of inhomogeneous Hamiltonians based on the Virasoro coadjoint orbit. The corresponding bulk dual geometries are described by the generalized Ba$\tilde{\text{n}}$ados solutions, for which we introduce a generalized Roberts mapping to facilitate their study. Our classification provides previously underexplored classes of deformations, offering fresh insights into their holographic properties. Revisiting the well-known example of the M$\ddot{\text{o}}$bius Hamiltonian, we establish a connection to the 3D C-metric, which describes three-dimensional accelerating solutions. Furthermore, we extend our analysis to KdV-type asymptotic boundary conditions, revealing a broader class of solvable inhomogeneous Hamiltonians that are not linear combinations of Virasoro charges but instead involve KdV charges.