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arXiv:2001.05129

Logarithmic behaviour of connected correlation function in CFT

Long Jiang

Published Jan 15, 2020• 0 citations
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Abstract

We study $(m)$-type connected correlation functions of OPE blocks with respect to one spatial region in two dimensional conformal field theory. We find logarithmic divergence for these correlation functions. We justify the logarithmic behaviour from three different approaches: massless free scalar theory, Selberg integral and conformal block. Cutoff independent coefficients are obtained from analytic continuation of conformal blocks. A UV/IR relation has been found in connected correlation functions. We could derive a formal ``first law of thermodynamics'' for a subsystem using deformed reduced density matrix. Area law of connected correlation function in higher dimensions is also discussed briefly.

DOI
10.48550/arxiv.2001.05129

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We study (m)(m)(m)-type connected correlation functions of OPE blocks with respect to one spatial region in two dimensional conformal field theory. We find logarithmic divergence for these correlation functions. We justify the logarithmic behaviour from three different approaches: massless free scalar theory, Selberg integral and conformal block. Cutoff independent coefficients are obtained from analytic continuation of conformal blocks. A UV/IR relation has been found in connected correlation functions. We could derive a formal ``first law of thermodynamics'' for a subsystem using deformed reduced density matrix. Area law of connected correlation function in higher dimensions is also discussed briefly.
We study the (m)-type connected correlation functions of OPE blocks with respect to one spatial region in two dimensional conformal field theory. We find a logarithmic divergence for these correlation functions. We justify the logarithmic behaviour from two different approaches: massless free scalar theory and conformal block. Cutoff independent coefficients are obtained from analytic continuation of conformal blocks. A UV/IR relation has been found in the connected correlation functions. We could derive a formal “first law of thermodynamics” for a subsystem using the deformed reduced density matrix. An area law of the connected correlation function in higher dimensions is also discussed briefly.
Abstract The deformation, built from the components of the stress tensor and of a current, is a universal irrelevant deformation of two-dimensional CFTs that preserves the left-moving conformal symmetry, while breaking locality on the right-moving side. Operators in the -deformed CFT are naturally labeled by the left-moving position and right-moving momentum and transform in representations of the one-dimensional extended conformal group. We derive an all-orders formula for the spectrum of conformal dimensions and charges of the deformed CFT, which we cross-check at leading order using conformal perturbation theory. We also compute the linear corrections to the one-dimensional OPE coefficients and comment on the extent to which the correlation functions in -deformed CFTs can be obtained from field-dependent coordinate transformations.