Abstract
The relationship between $T\bar{T}$ deformations and the uniform light-cone gauge, first noted in arXiv:1804.01998, provides a powerful generating technique for deformed models. We recall this construction, distinguishing between changes of the gauge frame, which do not affect the theory, and genuine deformations. We investigate the geometric interpretation of the latter and argue that they affect the global features of the geometry before gauge fixing. Exploiting a formal relation between uniform light-cone gauge and static gauge in a T-dual frame, we interpret such a change as a TsT transformation involving the two light-cone coordinates. In the static-gauge picture, the $T\bar{T}$ CDD factor then has a natural interpretation as a Drinfel'd-Reshetikhin twist of the worldsheet S matrix. To illustrate these ideas, we find the geometries yielding a $T\bar{T}$ deformation of the worldsheet S matrix of pp-wave and Lin-Lunin-Maldacena backgrounds.
Highlights
The study of two-dimensional quantum field theories (QFTs) plays an important role in our understanding of condensed matter systems, string theory—where the string worldsheet is two dimensional—and QFT in general, providing useful toy models that may capture interesting physical features of higher-dimensional theories
We investigate the geometric interpretation of the latter and argue that they affect the global features of the geometry before gauge fixing
We find the geometries yielding a TTdeformation of the worldsheet S matrix of pp-wave and Lin-Lunin-Maldacena backgrounds
Summary
The study of two-dimensional quantum field theories (QFTs) plays an important role in our understanding of condensed matter systems, string theory—where the string worldsheet is two dimensional—and QFT in general, providing useful toy models that may capture interesting physical features of higher-dimensional theories. For genuine deformations the change of the Hamiltonian density is not compensated by a redefinition of the worldsheet length, and the spectrum changes as for a TTdeformation We consider this case and study the effect of the deformation on the uplifted geometry. From the point of view of the deformed geometry, a TsT transformation in general leads to a Drinfeld-Reshetikhin twist [51,52] of the worldsheet S matrix [53,54] Taking this view, we can interpret the Castillejo-Dalitz-Dyson (CDD) factor [55] arising from TTdeformation [2,3] as such a Drinfeld-Reshetikhin twist based on the Cartan charges corresponding to the two longitudinal directions. Our results can be straightforwardly generalized to the case of current-current deformations involving a uð1Þ current J, such as JTor TJdeformations; we briefly discuss this in the Appendix
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