English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We calculate the spectrum of the matrix M' of Neumann coefficients of theWitten 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) ofthe matrix M without the zero-modes, there is also an additional eigenvalueinside (0,1). For every eigenvalue, there is a pair of eigenvectors, atwist-even and a twist-odd. We give analytically these eigenvectors as well asthe generating function for their components. Also, we have found aninteresting critical parameter b_0 = 8 ln 2 on which the forms of theeigenvectors depend.Comment: 25+1 pages, 3 Figures; typos corrected and some comments adde

The Spectrum of the Neumann Matrix with Zero Modes