<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>T</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:math> deformations as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>T</mml:mi><mml:mi>s</mml:mi><mml:mi>T</mml:mi></mml:math> transformations
Alessandro Sfondrini, Stijn J. van Tongeren
Abstract
The relationship between $T\overline{T}$ deformations and the uniform light-cone gauge, first noted by Baggio and Sfondrini [Phys. Rev. D 98, 021902 (2018)], 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 $T$-duality--shift--$T$-duality transformation involving the two light-cone coordinates. In the static-gauge picture, the $T\overline{T}$ Castillejo-Dalitz-Dyson factor then has a natural interpretation as a Drinfeld-Reshetikhin twist of the worldsheet $S$ matrix. To illustrate these ideas, we find the geometries yielding a $T\overline{T}$ deformation of the worldsheet $S$ matrix of $pp$-wave and Lin-Lunin-Maldacena backgrounds.