# The holographic interpretation of JT¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J\overline{T}$$\end{document}-deformed CFTs

Authors
• 1 Institut de Physique Théorique, CEA Saclay, Orme des Merisiers, Gif-sur-Yvette, 91191, France , Gif-sur-Yvette (France)
• 2 Uppsala University, Department of Physics and Astronomy, Lägerhyddsvägen 1, Uppsala, 75108, Sweden , Uppsala (Sweden)
• 3 Nordita, Stockholm University and KTH Royal Institute of Technology, Roslagstullsbacken 23, Stockholm, 10691, Sweden , Stockholm (Sweden)
Type
Published Article
Journal
Journal of High Energy Physics
Publisher
Springer-Verlag
Publication Date
Jan 25, 2019
Volume
2019
Issue
1
Identifiers
DOI: 10.1007/JHEP01(2019)198
Source
Springer Nature
Keywords
Recently, a non-local yet possibly UV-complete quantum field theory has been constructed by deforming a two-dimensional CFT by the composite operator JT¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J\overline{T}$$\end{document}, where J is a chiral U(1) current and T¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{T}$$\end{document} is a component of the stress tensor. Assuming the original CFT was a holographic CFT, we work out the holographic dual of its JT¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J\overline{T}$$\end{document} deformation. We find that the dual spacetime is still AdS3, but with modified boundary conditions that mix the metric and the Chern-Simons gauge field dual to the U(1) current. We show that when the coefficient of the chiral anomaly for J vanishes, the energy and thermodynamics of black holes obeying these modified boundary conditions precisely reproduce the previously derived field theory spectrum and thermodynamics. Our proposed holographic dictionary can also reproduce the field-theoretical spectrum in presence of the chiral anomaly, upon a certain assumption that we justify. The asymptotic symmetry group associated to these boundary conditions consists of two copies of the Virasoro and one copy of the U(1) Kač-Moody algebra, just as before the deformation; the only effect of the latter is to modify the spacetime dependence of the right-moving Virasoro generators, whose action becomes state-dependent and effectively non-local.