Correlation functions for M-N/S-N orbifolds

Citation
O. Lunin et Sd. Mathur, Correlation functions for M-N/S-N orbifolds, COMM MATH P, 219(2), 2001, pp. 399-442
Citations number
32
Categorie Soggetti
Physics
Journal title
COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN journal
00103616 → ACNP
Volume
219
Issue
2
Year of publication
2001
Pages
399 - 442
Database
ISI
SICI code
0010-3616(200105)219:2<399:CFFMO>2.0.ZU;2-Z
Abstract
We develop a method for computing correlation functions of twist operators in the bosonic 2-d CFT arising from orbifolds M-N/S-N, where M is an arbitr ary manifold. The path integral with twist operators is replaced by a path integral on a covering space with no operator insertions. Thus, even though the CFT is defined on the sphere, the correlators are expressed in terms o f partition functions on Riemann surfaces with a finite range of genus g. F or large N, this genus expansion coincides with a 1/N expansion. The contri bution from the covering space of genus zero is "universal" in the sense th at it depends only on the central charge of the CFT. For 3-point functions we give an explicit form for the contribution from the sphere, and for the 4-point function we do an example which has genus zero and genus one contri butions. The condition for the genus zero contribution to the 3-point funct ions to be non-vanishing is similar to the fusion rules for an SU(2) WZW mo del. We observe that the 3-point coupling becomes small compared to its lar ge N limit when the orders of the twist operators become comparable to the square root of N - this is a manifestation of the stringy exclusion princip le.