Neumann Coefficients Research Articles

Exact Results on Twist Anomaly

In vacuum string field theory, the sliver state solution has been proposed as a candidate of a D-brane configuration. Physical observables associated with this solution, such as its energy density and the tachyon mass, are written in terms of the Neumann coefficients. These observables, though vanish naively due to twist symmetry, acquire non-vanishing values arising from their singular behavior. Therefore, this phenomenon is called twist anomaly. In this paper we present an analytical derivation of these physical observables with the help of the star algebra spectroscopy. We also identify in our derivation the origin of the twist anomaly in the finite-size matrix regularization.

Open string states around a classical solution in vacuum string field theory

We construct a classical solution of vacuum string field theory (VSFT) and study whether it represents the perturbative open string vacuum. Our solution is given as a squeezed state in the Siegel gauge, and it fixes the arbitrary coefficients in the BRST operator in VSFT. We identify the tachyon and massless vector states as fluctuation modes around the classical solution. The tachyon mass squared \alpha m_t^2 is given in a closed form using the Neumann coefficients defining the three-string vertex, and it reproduces numerically the expected value of -1 to high precision. The ratio of the potential height of the solution to the D25-brane tension is also given in terms of the Neumann coefficients. However, the behavior of the potential height in level truncation does not match our expectation, though there are subtle points in the analysis.

Comma vertex and string field algebra

We study the matter part of the algebra of open string fields using the 3-string vertex over the sliver state, which we call ``comma vertex''. By generalizing this comma vertex to the $N$-string overlap, we obtain a closed form of the Neumann coefficients in the $N$-string vertex and discuss its relation to the oscillator representation of wedge states.

Vertices in the abelized picture

Covariant vertices of open bosonic string theory are transformed to the abelized picture. The way the pure transverse (light-cone gauge) vertex is contained therein is exhibited explicitly. The formalism shows in a quite transparent way that all further content of a convariant vertex is of gauge type. By applying the transverse projection operator in the abelized picture, an algebraic condition whether a set of Neumann coefficients define a vertex for string theory is obtained. A speculation concerning field redefinitions in string field theory is added.

Magnetic string fields

We construct the string field in Witten's open bosonic string field theory which corresponds to a constant magnetic field. We express the answer both in the standard basis of open string modes, and in more natural basis which requires changes in the zero-zero Neumann coefficients of the three-string vertex. We discuss the feasibility of using string field theory to search for new solutions of the classical string equations.

String couplings from meromorphic differentials

The “Neumann-function method” which allows one to determine oscillator representation of multiple string vertices is put on firm basis. The Neumann coefficients are related to the Laurent coefficients of certain meromorphic differentials. A systematic procedure of constructing the differentials is developed. The method is exemplified by the “covariantized” light-cone vertex. Our results on the ghost part of this vertex are in disagreement with various proposals in the literature,

Operator approach to purely cubic string field theory

A formulation of Witten's field theory of interacting open bosonic strings has been given based on a purely cubic action principle; however, the construction involves formal arguments which could in principle be invalidated by anomalies. We establish that the potential quantum anomalies cancel identically, making use of the recently developed operator formalism of Witten's theory. We first give an operator construction of the BRST current j( σ), determining its proper normal-ordering prescription through the requirement that j( σ) itself be BRST invariant. (As a by-product, we also obtain its anomalous current-current anticommutator.) The anomaly calculation then involves numerous nontrivial identities for the Neumann coefficients occurring in the oscillator form of the vertex, and gives a stringent consistency check upon the form of j( σ). Finally, we comment upon further issues to be resolved in pursuing this approach to string field theory.