Interface Correlators in Symmetric Product Orbifolds

TL;DR

This paper introduces a new class of generalized covering maps for symmetric product orbifolds, enabling efficient computation of interface correlators that match string theory results, thus advancing understanding of gauge-holography dualities.

Contribution

It develops a novel framework of generalized covering maps and diagrammatic rules for symmetric orbifolds, facilitating the calculation of interface correlators and their comparison to string perturbation theory.

Findings

New generalized covering maps for symmetric orbifolds

Efficient evaluation of interface correlators

Matching string perturbation theory to all orders

Abstract

Symmetric product orbifolds provide a controlled environment to explore generic features of gauge theory and holography. The tractability of these theories lies in the complete characterisation of their gauge structure through holomorphic covering maps. In this paper, we introduce a novel class of generalised covering maps, which define a universal family of interfaces between symmetric product orbifolds. These interfaces coincide with the holographic interfaces that were recently proposed as duals to AdS$_2$ branes in pure NSNS AdS$_3$ backgrounds. The new covering-map description enables efficient evaluation of interface correlators via a generalisation of the Lunin-Mathur method. To organise these computations, we derive a generalised Riemann-Hurwitz formula for interface coverings and introduce novel diagrammatic rules that systematically classify these maps. The new framework allows us to define a concrete grand-canonical ensemble that has the correct properties to compute correlation functions dual to open string scattering amplitudes. Using the generalised Riemann-Hurwitz formula, we explicitly show that the correlators of the ensemble structurally match string perturbation theory to all orders in the string coupling.