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

Abstract

We study how a wide class of Abelian Yang-Baxter deformations of the AdS_5 \times S^5AdS5×S5 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.

Gauge theory on twist-noncommutative spaces

“…Applied to maximally supersymmetric Yang-Mills theory, the noncommutative deformations we consider are conjectured to be dual to homogeneous Yang-Baxter deformations of the AdS 5 ×S 5 superstring [21], giving rise to a variety of integrable deformations of AdS/CFT. In this setting we would like to understand the twisting of the integrable structures arising in the computation of two and higher point correlation functions in planar SYM, and match them with the expected twists of the underlying integrable model [89][90][91][92][93]. The Lorentz deformation is the natural deformation to study here, as it involves the Cartan generators of the conformal symmetry of SYM, whose associated eigenvalues play a central role in quantum integrability in AdS/CFT.…”

“…See also [87] and the recent [88] for algebraic interpretations of the Seiberg-Witten map. 47 While the other deformations are classically integrable on the string theory side, their quantum integrable description is currently unclear since the typical exact S matrix approach appears difficult [93]. The recently constructed classical spectral curve of these deformed strings [20] may provide a systematic path forward here.…”