Correlation Functions for MN/SN Orbifolds

By O. Lunin, Samir D. Mathur. 2000

245 citations recorded by the source corpus.

Abstract: We develop a method for computing correlation functions of twist operators in the bosonic 2-d CFT arising from orbifolds MN/SN, 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.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2c2e7e1507f7c879a79ad6b7ff2b331ec0d0f770

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In Geometry and Topology

1. Sergei Gukov
2. Andrew Strominger
3. E. Martinec
4. G. Moore
5. J. Dubail
6. Ashoke Sen
7. E. Witten
8. Tudor Dimofte

In Mathematical Physics

1. Sergei Gukov
2. E. Martinec
3. G. Moore
4. Andrew Strominger
5. J. Dubail
6. E. Witten
7. Tudor Dimofte
8. Ashoke Sen

In Nuclear and High Energy Physics

1. G. Moore
2. E. Martinec
3. E. Witten
4. Ashoke Sen
5. Sergei Gukov
6. Andrew Strominger
7. J. Dubail
8. N. Seiberg

Citations in the corpus

• Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1  +  1d (2016, background): “In general, calculating correlation functions of more than three twist operators is a difficult task; early attempts include [96].”
• The Search for a Holographic Dual to AdS(3)xS(3)xS(3)xS(1) (2004, methodology): “the twist operators for cycles as the creation/annihilation operators for single particles. This structure will be important below in understanding the Hilbert space. 23 The discussion here parallels [57]. 47 5.2. Twist operators and moduli of the symmetric product As explained in section 4.4, the m”