Star Algebra Spectroscopy
Preprint
Abstract
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.Keywords
All Related Versions
- Version 1, 2001-11-30, ArXiv
- Published version: Journal of High Energy Physics, 2002 (3), 029.
This publication has 18 references indexed in Scilit:
- Open string states around a classical solution in vacuum string field theoryJournal of High Energy Physics, 2001
- Comma vertex and string field algebraJournal of High Energy Physics, 2001
- Tachyon potentials, star products and universalityJournal of High Energy Physics, 2001
- Split string field theory IIJournal of High Energy Physics, 2001
- Operator formulation of interacting string field theory (II)Nuclear Physics B, 1987
- Operator formulation of interacting string field theory (I)Nuclear Physics B, 1987
- The physical and ghost vertices in witten's string field theoryPhysics Letters B, 1986
- The vertex function in Witten's formulation of string field theoryPhysics Letters B, 1986
- Interacting field theory of open superstringsNuclear Physics B, 1986
- Non-commutative geometry and string field theoryNuclear Physics B, 1986