# Towards Large-Spin Effective Theory II: $O(2)$ model in $d=4-\epsilon$

## TL;DR

This paper develops a holographic effective theory for the $O(2)$ model in $4- ext{dim}$, accurately reproducing operator dimensions up to second order in $ ext{epsilon}$ and providing insights into the spectrum via bulk interactions.

## Contribution

It constructs a holographic Hamiltonian for the $O(2)$ model in $4- ext{dim}$, incorporating short- and long-distance effects and matching operator dimensions up to $O( ext{epsilon}^2)$.

## Key findings

- Holographic Hamiltonian reproduces operator dimensions at $O( ext{epsilon}^2)$
- Bulk exchange of scalar and ghost fields models spectrum
- Analysis clarifies spectrum interpretation in bulk description

## Abstract

We show how to construct a holographic effective theory for the leading-twist operators in the $O(2)$ model in the $4-d=\epsilon$ expansion up to $O(\epsilon^2)$, based on the separation of short-distance and long-distance effects that arises as a function of spin $J$. We obtain the Hamiltonian of the theory and show that it correctly reproduces all the dimensions at $O(\epsilon^2)$ of the leading twist operators for all values of the charge $Q$ and spin $J$. The holographic Hamiltonian is given by the bulk exchange of a charged scalar $\phi$, neutral scalar $s \sim \phi \phi^*$, and a `ghost' field $c$, as well as a single local bulk interaction $(\phi \phi^*)^2$. We analyze various aspects of the spectrum and discuss their interpretation in light of the bulk description.