Tensor constructions of open string theories II: Vector bundles, D-branes and orientifold groups

A generalized Chan-Paton construction is presented which is analogous to the tensor product of vector bundles. To this end open string theories are considered where the space of states decomposes into sectors whose product is described by a semigroup. The cyclicity properties of the open string theory are used to prove that the relevant semigroups are direct unions of Brandt semigroups. The known classification of Brandt semigroups then implies that all such theories have the structure of a theory with Dirichlet-branes. We also describe the structure of an arbitrary orientifold group, and show that the truncation to the invariant subspace defines a consistent open string theory. Finally, we analyze the possible orientifold projections of a theory with several kinds of branes.     

The finite gauge transformations in closed string field theory

The finite gauge transformations for the classical nonpolynomial closed string field theory are constructed by iteration of infinitesimal transformations. A simple rule for the determination of the coefficients of the arising series is found.Supported by funds provided by the Max Kade Foundation.     

Local Higgs-Kibble type theories in the unitary gauge

A general formal foundation of local theories using the Higgs-Kibble mechanism is given in the unitary gauge. The general term that is added to the Lagrangian owing to the presence of a gauge group is found both when the gauge group has and has not a non-trivial unbroken subgroup. The conjecture made by Weinberg about the form of this term when there is a non-trivial unbroken subgroup is found to be false in general. However when the unbroken subgroup is Abelian the conjecture is shown to be correct.     

D-branes as coherent states in the open string channel

We show that bosonic D-branestates may be represented as coherent states in an open string representation. By using the thermo field dynamics (TFD) formalism, we may construct a condensed state of open string modes that encodes the information on the D-braneconfiguration. We also introduce a construction alternative to TFD, which does not require one to assume thermal equilibrium. It is shown that the dynamics of the system combined with the geometric properties of the duplication rules of TFD is sufficient to obtain the thermal states and their analytic continuations in a geometric fashion. We use this approach to show that a bosonic D-branestate in the open string sector may also be built as boundary states in a special sense. Some implications of this study for the interpretation of the open/closed duality and on the kinematic/algebraic structure of an open string field theory are also commented on.     

General theory of renormalization of gauge theories in nonlinear gauges

We discuss the general theory of renormalization of unbroken gauge theories in the nonlinear gauges in which the gauge-fixing term is of the form We show that higher loop renormalization modifiesfα [A] to contain ghost terms of the form and show how the corresponding ghost terms are deduced fromfα [A, c, c] uniquely. We show that the theory can be renormalized while preserving a modified form of BRS invariance by multiplicative and independent renormalizations onA, c, g, η, ζ, τ. We briefly discuss the independence of the renormalized S-matrix from η,ζ, τ.     

Charged surfaces and the analyticity properties of the string tension in lattice gauge theories

A method to prove the fact that the string tension in strongly coupled lattice gauge theories is of the form =–log +, where is an analytic function of the inverse coupling =1/g², is presented. Its relation to random surface methods, in particular to the work of Debrushin and Holický, Kotecký, and Zahradník, is discussed.This paper is based on a talk presented at the conference on Statistical Mechanics of Phase Transitions—Mathematical and Physical Aspects, Trebon, September 1–6, 1986.     

Phase transitions from preheating in gauge theories

We show by studying the Abelian Higgs model with numerical lattice simulations that nonthermal phase transitions arising out of preheating after inflation are possible in gauge-Higgs models under rather general circumstances. This may lead to the formation of gauged topological defects and, if the scale at which inflation ends is low enough, to electroweak baryogenesis after preheating.     

Gauge invariant and gauge fixed actions for various higher-spin fields from string field theory

We propose a systematic procedure for extracting gauge invariant and gauge fixed actions for various higher-spin gauge field theories from covariant bosonic open string field theory. By identifying minimal gauge invariant part for the original free string field theory action, we explicitly construct a class of covariantly gauge fixed actions with BRST and anti-BRST invariance. By expanding the actions with respect to the level N   of string states, the actions for various massive fields including higher-spin fields are systematically obtained. As illustrating examples, we explicitly investigate the level N?3$N?3$ part and obtain the consistent actions for massive graviton field, massive 3rd rank symmetric tensor field, or anti-symmetric field. We also investigate the tensionless limit of the actions and explicitly derive the gauge invariant and gauge fixed actions for general rank n symmetric and anti-symmetric tensor fields.     

Supersymmetrical string theories

A supersymmetrical light-cone-gauge string action is presented. It provides a basis for understanding the previously- studied supersymmetrical dual string theory as well as two new closed-string theories that have extended supersymmetry in ten dimensions, corresponding to N=8 supersymmetry in four dimensions.