# Spectrum of Modular Hamiltonian in the Vacuum and Excited States

## TL;DR

This paper investigates the eigenmodes of the modular Hamiltonian in AdS3/CFT2, providing a perturbative method to construct zero eigenmodes for excited states based on vacuum eigenmodes.

## Contribution

It introduces a perturbative approach to derive zero eigenmodes of the modular Hamiltonian for excited states from vacuum eigenmodes in AdS3/CFT2.

## Key findings

- Perturbative construction of zero eigenmodes for excited states.
- Relation between vacuum and excited state eigenmodes.
- Enhanced understanding of modular Hamiltonian spectrum.

## Abstract

We study the non-zero eigenmodes for the modular Hamiltonian in the context of AdS$_3/$CFT$_2$. We show how to perturbatively construct zero eigenmodes for the modular Hamiltonian of the class of excited states constructed in Lashkari et al.(arxiv:1811.05052), using information about the vacuum non-zero eigen modular modes.