Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-11-29
JHEP 0203:029,2002
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 30 pages, 2 figures
Scientific paper
10.1088/1126-6708/2002/03/029
The spectrum of the infinite dimensional Neumann matrices M^{11}, M^{12} and M^{21} in the oscillator construction of the three-string vertex determines key properties of the star product and of wedge and sliver states. We study the spectrum of eigenvalues and eigenvectors of these matrices using the derivation K_1 = L_1 + L_{-1} of the star algebra, which defines a simple infinite matrix commuting with the Neumann matrices. By an exact calculation of the spectrum of K_1, and by consideration of an operator generating wedge states, we are able to find analytic expressions for the eigenvalues and eigenvectors of the Neumann matrices and for the spectral density. The spectrum of M^{11} is continuous in the range [-1/3, 0) with degenerate twist even and twist odd eigenvectors for every eigenvalue except for -1/3.
Rastelli Leonardo
Sen Ashoke
Zwiebach Barton
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