DLCQ strings, twist fields and one-loop correlators on a permutation orbifold

Abstract

We investigate some aspects of the relationship between matrix string theory and lightcone string field theory by analysing the correspondence between the two-loop thermal partition function of DLCQ strings in flat space and the integrated two-point correlator of twist fields in a symmetric product orbifold conformal field theory at one-loop order. This is carried out by deriving combinatorial expressions for generic twist field correlation functions in permutation orbifolds using the covering surface method, by deriving the one-loop modification of the twist field interaction vertex, and by relating the two-loop finite temperature DLCQ string theory to the theory of Prym varieties for genus two covers of an elliptic curve. The case of bosonic Z 2 orbifolds is worked out explicitly and precise agreement between both amplitudes is found. We use these techniques to derive explicit expressions for Z 2 orbifold spin twist field correlation functions in the Type II and heterotic string theories.

Diagrams for symmetric product orbifolds

“…They arise in the "secondquantization" of a configuration space -the procedure of forming products of identical copies of the space, and imposing equivalence under permutation of the copies. Symmetric product orbifolds of two-dimensional conformal field theories (CFTs) [1] appear in many related contexts: as instanton moduli spaces [2], in the counting problem of black hole microstates [3], in matrix string theory [4,5,6,7,8], in the AdS 3 /CFT 2 correspondence [9,10,11,12,13,14,15,16,17,18,19,20,21]. See also [22,23,24,25] for more examples.…”