Heriot-Watt Mathematics Report Series
HWM07-17, 22 Jun 2007
DLCQ Strings, Twist Fields and One-Loop Correlators on a Permutation Orbifold
H C D Cove, Z Kadar and R J Szabo
Abstract
We investigate some aspects of the relationship between matrix
string theory and light-cone 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.
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