Do Drinfeld twists of $AdS_5 \times S^5$ survive light-cone quantization?

TL;DR

This paper investigates whether Abelian Yang-Baxter deformations of the AdS5 x S5 string, related to Drinfeld twists, remain consistent at the quantum level by analyzing scattering matrices and Bethe equations.

Contribution

It provides the first quantum-level analysis of these deformations, confirming their classical Drinfeld twist interpretation for certain string backgrounds.

Findings

Successfully expressed the S matrix via Drinfeld twist or momentum shift for gamma deformations of BMN string.

Identified calculational obstacles in analyzing GKP string deformations around the null-cusp.

Supported the conjecture that these deformations are dual to certain noncommutative and dipole deformations of SYM.

Abstract

We study how a wide class of Abelian Yang-Baxter deformations of the AdS$_\mathsf{5} \times $S$^\mathsf{5}$ string behave at the quantum level. These deformations are equivalent to TsT transformations and conjectured to be dual to beta, dipole, and noncommutative deformations of SYM. Classically they correspond to Drinfeld twists of the original theory. To verify this expectation at the quantum level we compute and match (1) the bosonic two-body tree-level worldsheet scattering matrix of these deformations in the uniform light-cone gauge, and (2) the Bethe equations of the equivalent model with twisted boundary conditions. We find that for a generalization of gamma deformations of the BMN string the we are able to express the S matrix either through a Drinfeld twist or a shift of momenta. For deformations of the GKP string around the null-cusp solution we encounter calculational obstacles that prevent us from calculating the scattering matrix.