Highest states in light-cone $AdS_5\times S^5$ superstring

TL;DR

This paper analyzes the highest states in the light-cone superstring on AdS5×S5 using Bethe Ansatz equations, providing strong coupling expansions and comparing results across different limits and sectors.

Contribution

It introduces strong coupling expansions for highest states in the light-cone Bethe Ansatz framework, including new results in the su(1|1) and su(2) sectors.

Findings

Reproduces known results in the lambda, L -> infinity limit

Provides new strong coupling expansions in the su(1|1) sector

Confirms agreement with previous Bethe Ansatz analysis in the su(2) sector

Abstract

We study the highest states in the compact rank-1 sectors of the AdS5 X S5 superstring in the framework of the recently proposed light cone Bethe Ansatz equations. In the su(1|1) sector we present strong coupling expansions in the two limits L,lambda -> OO (expanding in power of lambda^{-1/4} with fixed large L) and lambda, L -> OO (expanding in power of 1/L with fixed large lambda) where lambda is the 't Hooft coupling and L is the number of Bethe momenta. The two limits do not commute apart from the leading term which reproduces the result obtained with the Arutyunov-Frolov-Staudacher phase in the lambda, L -> OO limit. In the su(2) sector we perform the strong coupling expansions in the L->OO limit up to O(lambda^{-1/4}), and our result is in agreement with previuos String Bethe Ansatz analysis.