Uniform Light-Cone Gauge for Strings in AdS_5 x S^5: Solving su(1|1) Sector

TL;DR

This paper introduces a uniform light-cone gauge for strings in AdS_5 x S^5, enabling exact solutions in the su(1|1) sector, and connects the spectrum to Bethe ansatz methods, reproducing known asymptotics.

Contribution

It develops a new gauge fixing method for string theory in AdS space and solves the su(1|1) sector exactly, linking it to Bethe ansatz equations.

Findings

Exact quadratic fermionic action in the su(1|1) sector.

Reproduction of 1/J corrections in the near BMN spectrum.

Derivation of /4 asymptotics at strong coupling.

Abstract

We introduce a uniform light-cone gauge for strings propagating in AdS space-time. We use the gauge to analyze strings from the su(1|1) sector, and show that the reduced model is described by a quadratic action for two complex fermions. Thus, the uniform light-cone gauge allows us to solve the model exactly. We analyze the near BMN spectrum of states from the su(1|1) sector and show that it correctly reproduces the 1/J corrections. We also compute the spectrum in the strong coupling limit, and derive the famous \lambda^{1/4} asymptotics. We then show that the same string spectrum can be also derived by solving Bethe ansatz type equations, and discuss their relation to the quantum string Bethe ansatz for the su(1|1) sector.