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Correlation Functions for MN/SN Orbifolds

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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 N – this is a manifestation of the stringy exclusion principle.

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Received: 20 July 2000 / Accepted: 17 December 2000

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Lunin, O., Mathur, S. Correlation Functions for MN/SN Orbifolds. Commun. Math. Phys. 219, 399–442 (2001). https://doi.org/10.1007/s002200100431

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  • DOI: https://doi.org/10.1007/s002200100431

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