Built on

N. Seiberg, “Notes on quantum Liouville theory and quantum gravity,” Prog. Theor. Phys. Suppl. 102
1990
Earlier work this paper cites.
H. Dorn and H. J. Otto, “Two and three point functions in Liouville theory,” Nucl. Phys. B 429
1994
Earlier work this paper cites.
A. B. Zamolodchikov and A. B. Zamolodchikov, “Structure constants and conformal bootstrap in Liouville field theory,” Nucl. Phys. B 477
1996
Earlier work this paper cites.
K. Krasnov, “3-D gravity, point particles and Liouville theory,” Class. Quant. Grav. 18
2001
Earlier work this paper cites.
J. Teschner, “Liouville theory revisited,” Class. Quant. Grav. 18
2001
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal four point functions and the operator product expansion,” Nucl. Phys. B 599
2001
Earlier work this paper cites.
P. Menotti and G. Vajente, “Semiclassical and quantum Liouville theory on the sphere,” Nucl. Phys. B 709
2004
Earlier work this paper cites.
P. Menotti and E. Tonni, “Quantum Liouville theory on the pseudosphere with heavy charges,” Phys. Lett. B 633
2005
Earlier work this paper cites.
P. Menotti and E. Tonni, “Liouville field theory with heavy charges. I. The Pseudosphere,” JHEP 0606
2006
Earlier work this paper cites.
P. Menotti and E. Tonni, “Liouville field theory with heavy charges. II. The Conformal boundary case,” JHEP 0606
2006
Earlier work this paper cites.
L. Hadasz and Z. Jaskolski, “Liouville theory and uniformization of four-punctured sphere,” J. Math. Phys. 47
2006
Earlier work this paper cites.

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2017

Heavy-Heavy-Light-Light correlators in Liouville theory

Balasubramanian, Vijay, Bernamonti, Alice, Craps, Ben et al.

Understand

We compute four-point functions of two heavy and two "perturbatively heavy" operators in the semiclassical limit of Liouville theory on the sphere.

We obtain these "Heavy-Heavy-Light-Light" (HHLL) correlators to leading order in the conformal weights of the light insertions in two ways: (a) via a path integral approach, combining different methods to evaluate correlation functions from complex solutions for the Liouville field, and (b) via the conformal block expansion.
This latter approach identifies an integral over the continuum of normalizable states and a sum over an infinite tower of lighter discrete states, whose contribution we extract by analytically continuing standard results to our HHLL setting.
The sum over this tower reproduces the sum over those complex saddlepoints of the path integral that contribute to the correlator.

Built on

N. Seiberg, “Notes on quantum Liouville theory and quantum gravity,” Prog. Theor. Phys. Suppl. 102
1990
Earlier work this paper cites.
H. Dorn and H. J. Otto, “Two and three point functions in Liouville theory,” Nucl. Phys. B 429
1994
Earlier work this paper cites.
A. B. Zamolodchikov and A. B. Zamolodchikov, “Structure constants and conformal bootstrap in Liouville field theory,” Nucl. Phys. B 477
1996
Earlier work this paper cites.
K. Krasnov, “3-D gravity, point particles and Liouville theory,” Class. Quant. Grav. 18
2001
Earlier work this paper cites.
J. Teschner, “Liouville theory revisited,” Class. Quant. Grav. 18
2001
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal four point functions and the operator product expansion,” Nucl. Phys. B 599
2001
Earlier work this paper cites.
P. Menotti and G. Vajente, “Semiclassical and quantum Liouville theory on the sphere,” Nucl. Phys. B 709
2004
Earlier work this paper cites.
P. Menotti and E. Tonni, “Quantum Liouville theory on the pseudosphere with heavy charges,” Phys. Lett. B 633
2005
Earlier work this paper cites.
P. Menotti and E. Tonni, “Liouville field theory with heavy charges. I. The Pseudosphere,” JHEP 0606
2006
Earlier work this paper cites.
P. Menotti and E. Tonni, “Liouville field theory with heavy charges. II. The Conformal boundary case,” JHEP 0606
2006
Earlier work this paper cites.
L. Hadasz and Z. Jaskolski, “Liouville theory and uniformization of four-punctured sphere,” J. Math. Phys. 47
2006
Earlier work this paper cites.