The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry

TL;DR

This paper develops an algebraic framework using Hopf algebras and generalized rapidities to implement crossing symmetry for the AdS_5xS^5 superstring worldsheet S-matrix, addressing the scalar factor determination.

Contribution

It introduces a novel algebraic approach with generalized rapidities and elliptic curves to fix the scalar factor via crossing relations in the superstring S-matrix.

Findings

Constructed a Hopf-algebraic crossing framework.

Derived functional equations for the scalar factor.

Proposed a universal cover of the parameter space.

Abstract

An S-matrix satisying the Yang-Baxter equation with symmetries relevant to the AdS_5xS^5 superstring has recently been determined up to an unknown scalar factor. Such scalar factors are typically fixed using crossing relations, however due to the lack of conventional relativistic invariance, in this case its determination remained an open problem. In this paper we propose an algebraic way to implement crossing relations for the AdS_5xS^5 superstring worldsheet S-matrix. We base our construction on a Hopf-algebraic formulation of crossing in terms of the antipode and introduce generalized rapidities living on the universal cover of the parameter space which is constructed through an auxillary, coupling constant dependent, elliptic curve. We determine the crossing transformation and write functional equations for the scalar factor of the S-matrix in the generalized rapidity plane.