The Spectrum of the Neumann Matrix with Zero Modes

Details The Spectrum of the Neumann Matrix with Zero Modes The Spectrum of the Neumann Matrix with Zero Modes

2002-02-26

arxiv.org/abs/hep-th/0202176v2

JHEP 0204 (2002) 038

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/1126-6708/2002/04/038

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.

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