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- W2987543855 abstract "Abstract We construct the stress-energy tensor correlation functions in probabilistic Liouville conformal field theory (LCFT) on the two-dimensional sphere $${mathbb {S}}^2$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:math> by studying the variation of the LCFT correlation functions with respect to a smooth Riemannian metric on $${mathbb {S}}^2$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:math> . In particular we derive conformal Ward identities for these correlation functions. This forms the basis for the construction of a representation of the Virasoro algebra on the canonical Hilbert space of the LCFT. In Kupiainen et al. (Commun Math Phys 371:1005–1069, 2019) the conformal Ward identities were derived for one and two stress-energy tensor insertions using a different definition of the stress-energy tensor and Gaussian integration by parts. By defining the stress-energy correlation functions as functional derivatives of the LCFT correlation functions and using the smoothness of the LCFT correlation functions proven in Oikarinen (Ann Henri Poincaré 20(7):2377–2406, 2019) allows us to control an arbitrary number of stress-energy tensor insertions needed for representation theory." @default.
- W2987543855 created "2019-11-22" @default.
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- W2987543855 date "2020-07-04" @default.
- W2987543855 modified "2023-10-16" @default.
- W2987543855 title "Stress-Energy in Liouville Conformal Field Theory" @default.
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- W2987543855 doi "https://doi.org/10.1007/s10955-020-02601-4" @default.
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