N-string verticles in string field theory

Abstract

A. ~b d u r r a h m a n~ and F. Ant6nWe give the general form of the vertex corresponding to the interaction of an arbitrary number of strings. The technique employed relies on the "comma" representation of string field theory where string fields and interactions are represented as matrices and operations between them such as multiplication and trace. The general formulation presented here shows that the interaction vertex of N strings, for any arbitrary N , is given as a function of particular combinations of matrices corresponding to the change of representation between the full string and the half string degrees of freedom. PACS numberk): 11.25.Sq

String field theory vertices for fermions of integral weight

“…More involved overlap conditions can be proven using techniques developed in [37,38,58]. We postpone their discussion to appendix C.…”

Bose-Fermi equivalence and interacting string field theory

“…The anomaly for the quadratic coordinate piece has been evaluated by many authors [15,11,12,18,16] in the critical dimension D = 26. This result provides a nontrivial consistency check on the validity of the half string theory.…”

Operator approach to the gluing theorem in string field theory

“…The general form of the Neumann coefficients N r,s n,m have been calculated in many works [11], for our purpose it is convenient the representation given in [9] since, for any vertex, they can be written in a compact form in a Ndimensional space spanned by the N strings, as elements of N × N matrix. For instance, one has for the terms which do not involve the zero modes N r,s even even = (…”

“…One can see that, after diagonalization of the S ± matrices, the problem of computing the vertex itself, essentially reduces to calculating the inverse of the matrix (M 1 − cos 2kπ N M 2 ) where k = 1, ..., N. Details of the whole process as well as the general form of this matrix and its inverse have been given in ref. [9]. Now, one can use this result in the proof of the Gluing Theorem [1].…”