Integrable crosscaps in classical sigma models

TL;DR

This paper investigates the classical integrability conditions of boundaries and crosscaps in sigma models, classifying integrable crosscaps relevant to AdS/CFT correspondence and establishing classical analogs of quantum integrability relations.

Contribution

It introduces a classical integrability condition for boundaries and crosscaps in sigma models and classifies integrable crosscaps, connecting to quantum spin chain relations.

Findings

Established a classical analog of the quantum KT-relation.

Classified integrable crosscaps for various sigma models.

Identified models relevant to AdS/CFT at strong coupling.

Abstract

We study the integrable boundaries and crosscaps of classical sigma models. We show that there exists a classical analog of the integrability condition and KT-relation of the boundary and crosscap states of quantum spin chains. We also classify the integrable crosscaps for various sigma models including examples which are relevant in the AdS/CFT correspondence at strong coupling.