paper

The Spectrum of the Neumann Matrix with Zero Modes

arXiv:hep-th/0202176 · doi:10.1088/1126-6708/2002/04/038

Abstract

We calculate the spectrum of the matrix M' of Neumann coefficients of the Witten vertex, expressed in the oscillator basis including the zero-mode a_0. We find that in addition to the known continuous spectrum inside [-1/3,0) of the matrix M without the zero-modes, there is also an additional eigenvalue inside (0,1). For every eigenvalue, there is a pair of eigenvectors, a twist-even and a twist-odd. We give analytically these eigenvectors as well as the generating function for their components. Also, we have found an interesting critical parameter b_0 = 8 ln 2 on which the forms of the eigenvectors depend.

25+1 pages, 3 Figures; typos corrected and some comments added

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