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

van Tongeren, Stijn J.; Zimmermann, Yannik

doi:10.21468/SciPostPhysCore.5.2.028

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

Dec 19, 2021

34 pages

Published in:

SciPost Phys.Core 5 (2022) 028

Published: May 19, 2022

e-Print:

2112.10279 [hep-th]

DOI:

10.21468/SciPostPhysCore.5.2.028

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Abstract: (SciPost Fundation)

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.

Note:

expanded on several points raised by peer review

deformation: noncommutative
quantization: light cone
boundary condition: twist
S-matrix
string
abelian
T-duality
Yang-Baxter
AdS(5) x S(5)

References(54)

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