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arXiv · hep-th/0202176

The Spectrum of the Neumann Matrix with Zero Modes

Bo Feng·Yang-Hui He·Nicolas Moeller
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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.

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Bo Feng, Yang-Hui He, Nicolas Moeller. 2002-03-20. The Spectrum of the Neumann Matrix with Zero Modes. https://doi.org/10.1088/1126-6708%2F2002%2F04%2F038

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