Holographic integration of $$ T\overline{T} $$ & $$ J\overline{T} $$ via O(d, d)

Abstract

Prompted by the recent developments in integrable single trace TT and JT deformations of 2d CFTs, we analyse such deformations in the context of AdS 3 /CFT 2 from the dual string worldsheet CFT viewpoint. We observe that the finite form of these deformations can be recast as O(d, d) transformations, which are an integrated form of the corresponding Exactly Marginal Deformations (EMD) in the worldsheet Wess-Zumino-Witten (WZW) model, thereby generalising the Yang-Baxter class that includes TsT. Furthermore, the equivalence between O(d, d) transformations and marginal deformations of WZW models, proposed by Hassan & Sen for Abelian chiral currents, can be extended to non-Abelian chiral currents to recover a well-known constraint on EMD in the worldsheet CFT. We also argue that such EMD are also solvable from the worldsheet theory viewpoint.

TT¯ deformations as TsT transformations

“…In a similar way, the classical Hamiltonian and Lagrangian obey an ODE in the space of fields, which can be often solved in closed form [3,4]. Over the last three years, T T deformations of a number of integrable [3,5,6], as well as of more general [7][8][9][10] theories have been considered. 1 A particularly striking link emerged between string theory and T T deformations, fueled by the initial observation that the T T deformation of a theory of free bosons is related to strings in flat space [3], see also refs.…”

TT¯ deformations with N=(0,2Jiang1, Sfondrini2, Tartaglino‐Mazzucchelli3 2019Phys. Rev. D576770View full textAdd to dashboardCite

“…Indeed TT deformations are naturally related [15,16] to the "uniform" light-cone gauge which is quite natural for the study of integrable strings theories [17][18][19], and the TT CDD factor also describes the scattering on more general backgrounds such as AdS 3 Wess-Zumino-Witten backgrounds [15,20,21]. 2 A separate, but equally interesting link between TT deformations and AdS 3 strings appears in the context of holography [27][28][29][30][31][32][33][34], where the deformed two-dimensional theory is the holographic dual of some (AdS 3 ) gravity or string theory, rather than being a worldsheet theory.…”

Nonlocal charges from marginal deformations of 2D CFTs: Holographic TT¯ & TJ¯<

“…(1) Unimodular deformations: As we have just said, these deformations give consistent string theory solutions; therefore, they are obtained from exactly marginal operators and on top of that, the unimodularity condition is satisfied. That also means that such deformations satisfy the so-called (weak) Chaudhuri-Schwartz (CS) conditions defined in [43]; see also [44,45,112]. (2) Nonunimodular deformations: In this case we do not find consistent string theory solutions, but two interesting things may happen.…”

“…Unfortunately, we have not been able to define the expressions for the nonlocal terms for exactly marginal deformations. The recent discussions of these issues (at the classical level) in terms of Oðd; dÞ transformations may be the correct direction to address this problem, and it is an interesting direction to explore [42,112]. At any rate, one needs to ensure that the net effect of the nonlocality is summarized in the algebraic discussion of Sec.…”