Correlation Functions for M N / S N Orbifolds

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 arbitrary 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 of partition functions on Riemann surfaces with a finite range of genus g. For large N, this genus expansion coincides with a 1/N expansion. The contribution from the covering space of genus zero is 'universal' in the sense that 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 contributions. The condition for the genus zero contribution to the 3-point functions to be non-vanishing is similar to the fusion rules for an SU(2) WZW model. We observe that the 3-point coupling becomes small compared to its large N limit when the orders of the twist operators become comparable to the square root of Nthis is a manifestation of the stringy exclusion principle.

Microscopic formulation of black holes in string theory

“…Higher point correlations functions in the orbifold conformal field theory were determined in [151,152] using general methods of computing correlations functions of twist fields on symmetric product orbifolds developed by [153,154] …”

Worldsheet correlators in AdS3/CFT2

“…As such, they correspond to single-particle states. The theory obviously also has operators for conjugacy classes with more than one cycle; these describe multi-particle states (see also [13,14,5]). In the following we shall however restrict attention to the above n-cycle twist operators.…”

“…The two-and three-point functions of the chiral twist operator Σ (n) m ′ ,m ′ have been calculated, using path integral methods, in [13,14]. The two-point function is given by [13] …”

“…In the boundary conformal field theory their correlation functions were first calculated for a special case in [12] and then, in general, in [13,14] (see also [15] for earlier work). The correlation functions in the world-sheet theory (on the sphere) can be reduced to standard 3-point functions of the SU(2) and SL(2) WZW models that have been determined before in [16,17] and [18,19,20], respectively.…”

“…In section 2, we review the symmetric orbifold theory and the correlators of n-cycle twist operators found by Lunin and Mathur [13,14]. In section 3, we then compute correlation functions of the corresponding primary vertex operator in the worldsheet theory with target space AdS 3 ×S 3 ×T 4 and compare them with those in the boundary conformal field theory.…”