Genus two correlation functions in CFTs with $T\bar T$ deformation

deformation in the curved Riemann surface is obstructive in the literature, we propose a way to do the deformation in the genus two Riemann surfaces by sewing prescription. We construct the correlation functions of conformal field theories (CFTs) on genus two Riemann surfaces with the

T\bar T

deformation in terms of the perturbative CFT approach. Thanks to sewing construction to form higher genus Riemann surfaces from lower genus ones and conformal symmetry, we systematically obtain the first-order

T\bar T

correction to the genus two correlation functions in the

T\bar T

deformed CFTs, e.g., partition function and one/higher-point correlation functions.

Note:

58 pages, 4 figures. Match the published version

conformal field theory
gauge/gravity duality
TT¯\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document} $T\bar T$ \end{document} deformation
higher genus correlation function
11.10.Kk
11.25.Hf
11.25.Tq
11.25.Db
field theory: conformal
field theory: deformation

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Genus two correlation functions in CFTs with $T\bar T$ deformation