Euclidean D-branes and higher-dimensional gauge theory

We consider euclidean D-branes wrapping around manifolds of exceptional holonomy in dimensions seven and eight. The resulting theory on the D-brane—that is, the dimensional reduction of 10-dimensional supersymmetric Yang-Mills theory—is a cohomological field theory which describes the topology of the moduli space of instantons. The 7-dimensional theory is an N_T = 2 (or balanced) cohomological theory given by an action potential of Chern-Simons type. As a by-product of this method, we construct a related cohomological field theory which describes the monopole moduli space on a 7-manifold of G₂ holonomy.     

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.     

Interactions of strings and D-branes from M theory

We discuss the relation between M theory and type II string theories. We show that, assuming “natural” interactions between membranes and fivebranes in M theory, the known interactions between strings and D-branes in type II string theories arise in appropriate limits. Our discussion of the interactions is purely at the classical level. We remark on issues associated with the M theory approach to enhanced gauge symmetries, which deserve further investigation.     

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.