Extremal Correlators and Hurwitz Numbers in Symmetric Product Orbifolds

Abstract

We study correlation functions of single-cycle chiral operators in the symmetric product orbifold of N supersymmetric four-tori. Correlators of twist operators are evaluated on covering surfaces, generally of different genera, where fields are single-valued. We compute some simple four-point functions and study how the sum over inequivalent branched covering maps splits under OPEs. We then discuss extremal n-point correlators, i.e. correlators of n-1 chiral and one anti-chiral operators. They obey simple recursion relations involving numbers obtained from counting branched covering maps with particular properties. In most cases we are able to solve explicitly the recursion relations. Remarkably, extremal correlators turn out to be equal to Hurwitz numbers.

arXiv comment36 pages, 3 figures, v2: minor improvements

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Cited by in corpus (48)

• The Worldsheet Dual of the Symmetric Product CFT
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• Kerr/CFT, dipole theories and nonrelativistic CFTs
• A Spin Chain for the Symmetric Product CFT_2
• Deforming the D1D5 CFT away from the orbifold point
• S-matrix for magnons in the D1-D5 system
• Excitations in the deformed D1D5 CFT
• Correlators of the symmetric product orbifold
• Emission from the D1D5 CFT
• From Matrix Models and quantum fields to Hurwitz space and the absolute Galois group
• Emission from the D1D5 CFT: Higher Twists
• Operator mixing for string states in the D1-D5 CFT near the orbifold point
• Lifting of D1-D5-P states
• Modave Lectures on Fuzzballs and Emission from the D1-D5 System
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• Analyzing the squeezed state generated by a twist deformation
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• Full action of two deformation operators in the D1D5 CFT
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• Microstate Renormalization in Deformed D1-D5 SCFT
• Universal lifting in the D1-D5 CFT
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• Worldsheet four-point functions in AdS(3)/CFT(2)
• Correlation functions of composite Ramond fields in deformed D1-D5 orbifold SCFT${}_2$
• On the Dynamics of Protected Ramond Ground States in the D1-D5 CFT
• Lifting 1/4-BPS States on K3 and Mathieu Moonshine
• The Stranger Things of Symmetric Product Orbifold CFTs
• Lifting of states in 2-dimensional $N=4$ supersymmetric CFTs
• Intertwining Relations for the Deformed D1D5 CFT
• Permutation Orbifolds in the large N Limit
• Dynamics of R-neutral Ramond fields in the D1-D5 SCFT
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• Fractional Conformal Descendants and Correlators in General 2D $S_N$ Orbifold CFTs at Large $N$
• The Topological Symmetric Orbifold
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• The Dual of a Tidal Force in the D1D5 CFT
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• Symmetric Group Gauge Theories and Simple Gauge/String Dualities
• ${\text{AdS}}_3/{\text{CFT}}_2$ at higher genus
• A New Supersymmetry Index for the D1-D5 CFT
• Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality