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Stress-Energy in Liouville Conformal Field Theory
Antti Kupiainen1, Joona Oikarinen1
1Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014 Helsinki, Finland.
Journal of Statistical Physics
|August 18, 2020
Summary
This study constructs stress-energy tensor correlation functions in probabilistic Liouville conformal field theory (LCFT) on a sphere. This construction enables a representation of the Virasoro algebra, advancing theoretical physics research.
Area of Science:
- Quantum Field Theory
- Conformal Field Theory
- Mathematical Physics
Background:
- Probabilistic Liouville Conformal Field Theory (LCFT) is a key model in 2D quantum gravity.
- Understanding stress-energy tensor correlation functions is crucial for LCFT's mathematical structure.
- Previous work derived conformal Ward identities for limited stress-energy tensor insertions.
Purpose of the Study:
- To construct stress-energy tensor correlation functions in probabilistic LCFT on a sphere.
- To derive conformal Ward identities for these correlation functions.
- To establish a representation of the Virasoro algebra on the LCFT's Hilbert space.
Main Methods:
- Varying LCFT correlation functions with respect to a smooth Riemannian metric.
- Defining stress-energy correlation functions as functional derivatives.
- Utilizing proven smoothness of LCFT correlation functions for arbitrary insertions.
Main Results:
- Successful construction of stress-energy tensor correlation functions in probabilistic LCFT.
- Derivation of conformal Ward identities for these functions.
- Foundation laid for Virasoro algebra representation on the LCFT Hilbert space.
Conclusions:
- The derived conformal Ward identities are essential for representation theory in LCFT.
- This work provides a robust method for handling multiple stress-energy tensor insertions.
- Advances the understanding of the mathematical framework of Liouville conformal field theory.
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