Partition Functions of Three-Dimensional Pure Gravity

The three-dimensional pure quantum gravity with a negative cosmological constant has been conjectured to be dual to an extremal conformal field theory (ECFT), of central charge c=24k for some positive integer k. We compute the partition function of the dual ECFT by summing over gravitational instanton contributions. In particular, we conjecture an exact expression for the contribution from handlebodies to the partition function for all genera and all values of k, and provide nontrivial evidences for the conjecture at genus two.

Note:

35 pages, 3 figures

quantum gravity
dimension: 3
partition function
cosmological constant: negative
Riemann surface: higher-order
field theory: conformal

References(18)

Figures(0)

Three-Dimensional Gravity Revisited

Edward Witten
(
- Princeton, Inst. Advanced Study
)

e-Print:
- 0706.3359

- Proc.Indian Natl.Sci.Acad. 81 3256

Genus two partition functions of extremal conformal field theories

- JHEP 08 (2007) 029
•
e-Print:
- 0707.3437
•
DOI:
- 10.1088/1126-6708/2007/08/029

Constraints on extremal self-dual CFTs

Matthias R. Gaberdiel
(
- Zurich, ETH
)

- JHEP 11 (2007) 087
•
e-Print:
- 0707.4073
•
DOI:
- 10.1088/1126-6708/2007/11/087

e-Print:
- math-qa/9910136

AdS(3) black holes and a stringy exclusion principle

Juan Martin Maldacena
(
- Harvard U.
)
,
Andrew Strominger
(
- Harvard U.
)

- JHEP 12 (1998) 005
•
e-Print:
- hep-th/9804085
•
DOI:
- 10.1088/1126-6708/1998/12/005

AdS(3) Partition Functions Reconstructed

Jan Manschot
(
- Amsterdam U.
)

- JHEP 10 (2007) 103
•
e-Print:
- 0707.1159
•
DOI:
- 10.1088/1126-6708/2007/10/103

Holography and Riemann surfaces

Kirill Krasnov
(
- UC, Santa Barbara
)

- Adv.Theor.Math.Phys. 4 (2000) 929-979
•
e-Print:
- hep-th/0005106
•
DOI:
- 10.4310/ATMP.2000.v4.n4.a5

- Math.USSR Sb. 60 297

Holomorphic factorization of determinants of laplacians on Riemann surfaces and a higher genus generalization of kronecker's first limit formula

- Analysis 16 (2006) 1291
•
e-Print:
- math/0410294

The Genus 2 Free Energy of the Closed Bosonic String

Yvan Leblanc
(
- MIT, LNS
)

- Phys.Rev.D 39 (1989) 3731
•
DOI:
- 10.1103/PhysRevD.39.3731

The Asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant

Oliver Coussaert
(
- Brussels U. and
- CECS, Valdivia
)
,
Marc Henneaux
(
- Brussels U. and
- CECS, Valdivia
)
,
Peter van Driel
(
- Brussels U.
)

- Class.Quant.Grav. 12 (1995) 2961-2966
•
e-Print:
- gr-qc/9506019
•
DOI:
- 10.1088/0264-9381/12/12/012

Quantum Liouville theory in the background field formalism. I. Compact Riemann surfaces

- Commun.Math.Phys. 268 (2006) 135-197
•
e-Print:
- hep-th/0508188
•
DOI:
- 10.1007/s00220-006-0091-4

- Am.J.Math. 84 175

- Am.J.Math. 89 817

The Analytic Geometry of Two-Dimensional Conformal Field Theory

Daniel Friedan
(
- Chicago U., EFI and
- Chicago U.
)
,
Stephen H. Shenker
(
- Chicago U., EFI and
- Chicago U.
)

- Nucl.Phys.B 281 (1987) 509-545
•
DOI:
- 10.1016/0550-3213(87)90418-4

A Black hole Farey tail

Robbert Dijkgraaf
(
- Amsterdam U.
)
,
Juan Martin Maldacena
(
- Harvard U.
)
,
Gregory W. Moore
(
- Rutgers U., Piscataway
)
,
Erik P. Verlinde
(
- Princeton U.
)

e-Print:
- hep-th/0005003

Conformal Scalar Field on the Hyperelliptic Curve and Critical Ashkin-teller Multipoint Correlation Functions

A.B. Zamolodchikov
(
- Moscow, Nonlinear Phys. Lab
)

- Nucl.Phys.B 285 (1987) 481-503,
- Also in *Itzykson, C. (ed.) et al.: Conformal invariance and applications to statistical mechanics* 777-799
•
DOI:
- 10.1016/0550-3213(87)90350-6