Aspects of quantum integrability for pure spinor superstring in AdS(5)xS(5)

TL;DR

This paper investigates the classical integrability of the pure spinor superstring in AdS(5)×S(5) at strong coupling, demonstrating the contour-independence of the monodromy matrix and absence of anomalies at leading order.

Contribution

It provides a first-order perturbative analysis showing the monodromy matrix remains contour-independent and free of divergences, supporting integrability of the pure spinor superstring.

Findings

Monodromy matrix variation is BRST-closed and contour-independent.

Field strength is free from logarithmic divergences at leading order.

No anomalies found, confirming classical integrability at this order.

Abstract

We consider the monodromy matrix for the pure spinor IIB superstring on $AdS_5\times S^5$ at leading order at strong coupling, in particular its variation under an infinitesimal and continuous deformation of the contour. Such variation is equivalent to the insertion of a local operator. Demanding the BRST-closure for such an operator rules out its existence, implying that the monodromy matrix remains contour-independent at the first order in perturbation theory. Furthermore we explicitly compute the field strength corresponding to the flat connections up to leading order and directly check that it is free from logarithmic divergences. The absence of anomaly in the coordinate transformation of the monodromy matrix and the UV-finiteness of the curvature tensor finally imply the integrability of the pure spinor superstring at the first order.