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The antibracket formalism for gauge theories, at both the classical and quantum level, is reviewed. Gauge transformations and the associated gauge structure are analyzed in detail. The basic concepts involved in the antibracket formalism are elucidated. Gauge-fixing, quantum effects, and anomalies within the field-antifield formalism are developed. The concepts, issues and constructions are illustrated using eight gauge-theory models., Comment: 191 pages in three files which must be put together, in Latex, to appear in Physics Reports

If certain long-ranged interactions between instantons are present, the θ parameter relaxes to zero. The question is raised as to whether this can happen in Yang-Mills theory thereby leading to a natural solution of the strong CP problem. A lattice gauge theory simulation is proposed to decide the issue.

We investigate the implications for experiment of the existence of compactified dimensions with a scale much larger than the Planck length. Such manifolds might occur in certain string models, for instance, if the compactification process is related to the mechanism generating electroweak or supersymmetry breaking. Model-independent upper bounds on the size of any extra dimensions are obtained by examining a wide range of experimental data.

The integrand and integration region for the N-point amplitude in the open oriented bosonic string are obtained to all orders in perturbation theory. The result is derived from the Witten covariant string field theory by using on-shell and off-shell conformal methods and Riemann surface mathematics. Although only the off-shell g-loop tachyon amplitudes are computed explicitly, the methods generalize to other external states. We derive the g-loop ghost-Jacobi identity in which the ghost correlation function cancels the jacobian factor in changing from second-quantized to first-quantized variables. Moduli space is discussed from several viewpoints and it is shown that string field theory provides an algorithm for its determination.

In the context of covariant string field theory, we investigate the existence and properties of nonperturbative vacua for the open bosonic string. The study is performed using successive orders in a level-truncation method. We find a candidate nonperturbative vacuum and obtain numerical values for nonzero expectation values of all fields to level two. Perturbation theory about this vacuum is shown to be well defined. The occurence and location of poles in the propagators of all fields to level two are established. We observe that string theories necessarily have running couplings at tree level and that the open bosonic string is asymptotically free. The nontrivial momentum dependence means that certain poles seen in the canonical vacuum are absent in the nonperturbative vacuum. This result follows from the nature of the string as an extended object and is likely to hold for general string theories.

Energy eigenstates for N=2 supersymmetric gauged quantum mechanics are found for the gauges groups SU(n) and U(n). The analysis is aided by the existence of an infinite number of conserved operators. The spectum is continuous. Perturbative eigenstates for $N>2$ are also presented, a case which is relevant for the conjectured description of M theory in the infinite momentum frame., 10 pages, LATEX, no figures

A second-quantized analysis is performed to examine many-body phenomena in closed bosonic strings. The covariant nonpolynomial closed-string field theory is developed in terms of particle fields and shown to contain interactions triggering a nonperturbative condensation of the tachyon field. We study the possibility that the higher-dimensional Lorentz symmetry spontaneously breaks. We show that the theory has asymptotic freedom due to a tree-level running coupling. The spectrum of states in the nonperturbative ground state is radically changed relative to the free case; in particular, there is no massless graviton. Similar effects are anticipated in any nonperturbative vacuum.

A violation of gauge invariance in Witten's open superstring field theory has recently been discovered. We propose a modification which resolves this problem by avoiding the collision of picture-changing operators. Feynman rules for the modified, gauge-invariant theory are presented, including a useful representation for the Ramond propagator. All four-point amplitudes are off-shell finite, agree on-shell with the Polyakov approach and exhibit decoupling of spurious physical states.

Formulas for the evaluation of all U(N) integrals are derived. Tables display the results for integrands involving up to six U’s and six U°’s. The complete pole structure of De Wit–’t Hooft anomalies is unveiled. The effects of 1/N2 corrections and De Wit–’t Hooft anomalies on two‐dimensional U(N) lattice gauge theories in the strong coupling 1/N expansion is discussed.

We employ BRST invariance to explicitly determine the ghost part of the four-point vertex in Witten's open, bosonic, string field theory. This allows the computation of any covariant off-shell four-point amplitude involving physical as well as first-quantized auxiliary or second-quantized Faddeev-Popov ghost fields. We display some examples and complete the proof of associativity of the star product.

The bosonic vertex associated with the covariant bosonic string field theory recently proposed by Witten is constructed in terms of creation operators. This provides the off-shell couplings between physical string states. The ghost vertex is also computed in terms of the oscillators of the anticommuting c(σ) and c (σ) . Together, the two vertices provide all couplings between physical and auxiliary fields.

A thorough investigation of the non-linear realization of supersymmetry is carried out both in flat space and in curved space (supergravity). A manageable superfield formulation is developed which allows one to evaluate the physical effects of the non-linear field when it is coupled to other multiplets. We present several interesting applications (mostly in the context of supergravity) useful in model building.

The one-loop off-shell N -point tachyon amplitude is obtained for Witten's covariant string field theory, using off-shell conformal methods. An identity is derived which relates the ghost correlation function to the javobian in changing to standard variables. This identity is used to show that the correct integration measure is obtained. The covering of moduli space by the field theory Feynman diagrams is shown. Complete on-shell agreement is found with first-quantized results. Finally, the off-shell singularity structure is discussed.

A superfield formulation of gauge invariant σ-models, previously written in component form, is given. Both the N = 1 global supersymmetry case and the N = 1 supergravity case are treated. A superfield formulation of σ-models involving abelian and non-abelian N = 2 vector multiplets coupled to N = 2 supergravity is also presented. In the non-abelian case, this is a new class of models.

We analyze disorder operators in the chiral models in order to better understand the behavior of 't Hooft loops in four-dimensional gauge theories. We use both theoretical and numerical approaches.

Superconformal field theory is used to compute off-shell amplitudes for the superstring. Off-shell three- and four-point functions in Witten's superstring field theory are obtained. The problem of gauge invariance due to the associativity anomaly in the bosonic sector is resolved to order g 2 .

The flat-space limit of a supergravity theory involving the Akulov-Volkov field as well as other matter multiplets is found to be an ordinary renormalizable globally supersymmetric theory with explicit soft-breaking mass terms. This allows one to easily construct realistic models of nature which are analyzable at the tree and one-loop level. This is carried out for QED-like and Weinberg-Salam-like models.

The subject of off-shell conformal field theory is developed and is used to produce the off-shell amplitudes of string field theory. The method is also applied to the reparametrization ghosts.

In an effort to understand whether the open bosonic string theory has a stable vacuum, the four-point contribution to the static tachyon potential is computed. This off-shell calculation is carried out using covariant string field theory.

When ghost coordinates are used in combination with the ∂ X μ and ψ μ degrees of freedom, an infinite set of operators of conformal dimension one can be constructed for the open superstring. These conservation laws aid in computing the string scattering amplitudes for bosons and fermions. Using them and an additional trick, N -point correlation functions can be reduced to ( N − 1)-point ones, so that any superstring tree-amplitude can be calculated in a manifestly Lorentz covariant form if the two-point correlation functions are known. The method is applicable to both closed and open strings and can be adapted to heterotic strings. Sample calculations are presented.

Rules are provided for the calculation of string amplitudes on all exotic topologies to one loop. These topologies include the real projective plane, the disk, the annulus, the Mobius strip, the torus and the Klein bottle. The rules are valid for bosonic strings, superstrings, and heterotic strings either in their critical dimensions or toroidally compactified, and they are applicable to amplitudes with arbitrary external bosonic and fermionic states, including mixed open- and closed-string transitions. The modular invariance of the torus amplitudes is discussed.

Covariant off-shell dual-resonance model amplitudes for four reggeons are computed in the open bosonic string using Witten's string field theory. The four-tachyon, the two-tachyon two-vector and the four-vector cases are explicitly worked out, although the formalism applies to higher mass states as well. Properties of the amplitudes are analyzed. Finally, a demonstration of associativity of the ∗ product is given for a certain set of Fock-space states.

The physical and ghost vertex operators in covariant superstring field theory are obtained. The integral and star operations are given in oscillator form and the free and interaction lagrangians are explicitly displayed for the massless fields.

The conformal equivalence of the Caneschi-Schwimmer-Veneziano vertex and the Witten vertex is established. This proves that, for all levels, the Witten vertex yields the same couplings as the Caneschi-Schwimmer-Veneziano vertex for on-shell physical string states.

Using covariant spin fields, the tree amplitude for six massless fermions in the open ten-dimensional superstring is calculated by superconformal field-theoretic methods. The amplitude is presented in a manifestly Lorentz-covariant form.

Calculational tools are provided allowing the determination of tree-level amplitudes for processes involving fermions and bosons in heterotic and superstring theories. A simple representation is given of the cocycle operators that are needed for bosonization of conformal operators, including spin fields and ghosts. This permits explicit computation of all correlation functions. The general m -boson, 2 n -fermion tree-level scattering amplitude in the open superstring is derived and a typical calculation of a four-point amplitude in the o(16) × o(16) heterotic string is presented in manifestly Lorentz-covariant form. An analysis of the branch-cut singularities in the o(16) × o(16) model is performed. In addition, the covariant form of the “new formalism” is developed. Particular attention is given to a lattice viewpoint of these results.

The manner by which topological symmetry breakdown leads to confinement in a non-Abelian gauge theory is discussed.

The possibility of spontaneous breakdown of Lorentz symmetry in string theory is explored via covariant string field theory. A potential mechanism is suggested for the Lorentz breaking that may be generic in many string theories.