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

TL;DR

The paper introduces a uniform light-cone gauge to consistently truncate strings on ${\rm AdS}_5\times{\rm S}^5$ to the ${\frak{su}(1|1)}$ sector, revealing a quadratic, free-fermion Hamiltonian that allows exact spectral determination. It reproduces the leading $1/J$ corrections and the $\lambda^{1/4}$ strong-coupling behavior, and shows compatibility with a Bethe-ansatz framework in the near-BMN regime. However, higher-order corrections and strong-coupling subleading terms differ from quantum string Bethe ansatz predictions, highlighting gauge-dependence and the non-closure of the ${\frak{su}(1|1)}$ sector at the quantum level. The work underscores the utility and limitations of sector truncations for testing integrability-based approaches to AdS/CFT and motivates incorporating the full sigma-model for definitive tests.

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 λ^{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.