String Theory on a Circle, Fredholm determinants and Toda Lattice Hierarchy

Ivan Kostov
CEA Saclay, France
SPhT

The partition function of Euclidean 2D string theory compactified on a
circle of radius R is given by certain Fredholm determinant, which is also
a tau function of the Toda lattice hierarchy. In the particular case R=1/2
such Fredholm determinant has been studied by Fendley, Saleur and
Zamolodchikov. We derive a constraint (string equation), which allows to
evaluate explicitly the tau function in the dispersionless limit.


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