Extremal correlators and Hurwitz numbers in symmetric product orbifolds

Abstract

We study correlation functions of single-cycle chiral operators in Sym N T 4 , 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.

Kerr/CFT, dipole theories and nonrelativistic CFTs

“…Applying symmetric orbifold techniques to a free field realisation, the chiral primary operators can be easily constructed [60,93] and their correlation functions explicitly computed [94][95][96][97][98]. Even though the free orbifold point may be a singular point in the moduli space of the D1-D5 CFT [99], it has been shown that the three-point correlation functions of chiral primaries computed at this point perfectly match those computed in the worldsheet WZW model CFT [100,101], as well as those computed in supergravity [56].…”

Deforming the D1D5 CFT away from the orbifold point

“…These changes move us to different points in the moduli space of the CFT. It has been conjectured that we can move to a point called the 'orbifold point' where the CFT is particularly simple [51][52][53][54][55][56][57][58][59][60]. At this orbifold point the CFT is a 1+1 dimensional sigma model.…”

Excitations in the deformed D1D5 CFT

“…These changes move us to different points in the moduli space of the CFT. It has been conjectured that we can move to a point called the 'orbifold point' where the CFT is particularly simple [59][60][61][62][63][64][65][66][67][68]. At this orbifold point the CFT is a 1+1 dimensional sigma model.…”