Decoding the geometry of conformal field theories

To certain geometries, string theory associates conformal field theories. We discuss techniques to perform the reverse procedure: To recover geometrical data from abstractly defined conformal field theories. This is done by introducing appropriate notions of limits of conformal field theories and their degenerations, and by applying techniques from noncommutative geometry. This note is a summary of our work hep-th/0308143 , aimed to be less technical than the original paper, along with some new calculations confirming our interpretation of the rescaled limiting zero mode of the Virasoro field.

Note:

12 pages, contribution to the Proceedings of the 7th International Workshop "Lie Theory and Its Applications in Physics", Varna, Bulgaria

talk: Varna 2007/06/18
field theory: conformal
dimension: 2
string model
differential geometry
algebra: Virasoro
n-point function: 4
coset space
operator: differential
zero mode

References(5)

Figures(0)

Noncommutative differential geometry

- Inst.Hautes Etudes Sci.Publ.Math. 62 (1986) 257

Gravity coupled with matter and foundation of noncommutative geometry

Alain Connes
(
- IHES, Bures-sur-Yvette
)

- Commun.Math.Phys. 182 (1996) 155-176
•
e-Print:
- hep-th/9603053
•
DOI:
- 10.1007/BF02506388

Coset Construction from Functional Integrals

K. Gawedzki
(
- IHES, Bures-sur-Yvette
)
,
A. Kupiainen
(
- Helsinki U.
)

- Nucl.Phys.B 320 (1989) 625-668
•
DOI:
- 10.1016/0550-3213(89)90015-1

Limits and degenerations of unitary conformal field theories

Daniel Roggenkamp
(
- Bonn U. and
- King's Coll. London
)
,
Katrin Wendland
(
- Warwick U., Math. Inst.
)

- Commun.Math.Phys. 251 (2004) 589-643
•
e-Print:
- hep-th/0308143
•
DOI:
- 10.1007/s00220-004-1131-6

Effective action of gauged WZW model and exact string solutions

Arkady A. Tseytlin
(
- Imperial Coll., London
)

- Nucl.Phys.B 399 (1993) 601-622
•
e-Print:
- hep-th/9301015
•
DOI:
- 10.1016/0550-3213(93)90511-M