ONE-DIMENSIONAL STRING THEORY WITH VORTICES AS THE UPSIDE-DOWN MATRIX OSCILLATOR

Abstract

Matrix quantum mechanics at a finite temperature is considered, which is equivalent to the one-dimensional compactified string field theory with vortex excitations. It is explicitly demonstrated that states transforming under nontrivial U(N) representations describe different vortex-antivortex configurations. For example, for the adjoint representation, corresponding Feynman graphs always contain two big loops wrapping around the compactified t space, which corresponds to the vortex–antivortex pair. The technique is developed to calculate the partition functions in given representations for the standard matrix oscillator, and then the procedure of their analytical continuation to the upside-down case is worked out. This procedure enables us to obtain the partition function in the presence of the vortex–antivortex pair in the double scaling limit. Using this result, we calculate the critical temperature for the Berezinski-Kosterlitz–Thouless phase transition. A possible generalization of our technique for the D+1 dimensional matrix model is sketched out.