Current-current deformations, conformal integrals and correlation functions

Abstract

Motivated by the recent work on TT -type deformations of 2D CFTs, a especial class of single-trace deformations of AdS 3 /CFT 2 correspondence has been investigated. From the worldsheet perspective, this corresponds to a marginal deformation of the σmodel on AdS 3 that yields a string background that interpolates between AdS 3 and a flat linear dilaton solution. Here, with the intention of studying this worldsheet CFT further, we consider it in the presence of a boundary. In a previous paper, we computed different correlation functions of this theory on the disk, including the bulk 1-point function, the boundary-boundary 2-point function, and the bulk-boundary 2-point function. This led us to compute the anomalous dimension of both bulk and boundary vertex operators, which first required a proper regularization of the ultraviolet divergences of the conformal integrals. Here, we extend the analysis by computing the bulk-bulk 2-point function on the disk and other observables on the sphere. We prove that the renormalization of the vertex operators proposed in our previous works is consistent with the form of the sphere N -point functions.

$$ T\overline{T} $$ deformation of classical Liouville field theory

“…Recent years have seen a lot of attention in the study of specific types of irrelevant deformations of classical and quantum field theories. Particularly, the class of deformations with Zamolodchikov's TT operator [1][2][3] are of interest in the context of AdS/CF T [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and effective String Theory [19][20][21][22][23]. A deformation by a given operator of a known field theory induces a flow which in the case of irrelevant deformations is driven by the deformation at high energies.…”

Random boundary geometry and gravity dual of $$ T\overline{T} $$ deformation

“…We thank Ofer Aharony and Sam van Leuven for discussions on this point. We also note that correlation functions in the SL(2, R) WZW model deformed by a boundary single-trace "TT " operator were computed in [22][23][24]. 3 A very similar idea was proposed in [15] using the results in [26] that is based on the work [27].…”

A pedagogical review on solvable irrelevant deformations of 2D quantum field theory

“…Many physical quantities have been computed, such as correlation functions [24,29], entanglement entropy [25], holographic Wilson loops [26] and complexity [128]. Generalizations to the case with conformal boundaries have been considered in [150,151]. String dynamics for such theories are studied in [152][153][154].…”