BRST invariance of the measure in string field theory

The BRST transformations, given by gauge-fixing Witten's string field theory in the Seigel gauge, are applied to the string measure. It is shown that the simple measure (just the product of differentials of all the fields) is BRST invariant, thus maintaining the invariance of the gauge-fixed action at the quantum level.     

Supersymmetric quantization of linearized supergravity

We give a manifestly supersymmetric quantization scheme for linearized supergravity, motivated by the desire to develop a background field method for the full non-linear theory. Supersymmetric gauge-fixing constraints are constructed and the corresponding ghost action is discussed. It is found that the Faddeev-Popov action itself possesses invariances, requiring “secondary” gauge fixing, which in turn leads to “secondary” ghost fields, the latter having normal statistics. The gauge-fixing constraints are used to construct gauge-fixing terms in the action, with a total of four gauge-fixing parameters. The superpropagators are found and may be greatly simplified by certain choices of these parameters.     

Finite BRST Mapping in Higher-Derivative Models

We continue the study of finite field-dependent BRST (FFBRST) symmetry in the quantum theory of gauge fields. An expression for the Jacobian of path integral measure is presented, depending on a finite field-dependent parameter, and the FFBRST symmetry is then applied to a number of well-established quantum gauge theories in a form which incudes higher-derivative terms. Specifically, we examine the corresponding versions of the Maxwell theory, non-Abelian vector field theory, and gravitation theory. We present a systematic mapping between different forms of gauge-fixing, including those with higher-derivative terms, for which these theories have better renormalization properties. In doing so, we also provide the independence of the S-matrix from a particular gauge-fixing with higher derivatives. Following this method, a higher-derivative quantum action can be constructed for any gauge theory in the FFBRST framework.     

Bosonic strings and complex structures

We write the action of the bosonic string in terms of two-dimensional complex structures rather than of two-dimensional metrics. We describe in some detail the behaviour under reparametrization of the world sheet, and in particular we give an expression for the two-dimensional diffeomorphism anomaly. We describe a possible gauge-fixing procedure for the BRST quantization.     

Remarks on a New Possible Discretization Scheme for Gauge Theories

We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for these discretized action functionals. Heuristic parts are forwarded to the quantization procedure via Feynman integrals and the meaning of the heuristic infinite dimensional Lebesgue integral is questioned.     

Field theory of the interacting string: The closed string

We recast dual models in the language of a quantum field theory of functional fields, restricting ourselves for simplicity to the closed string model. We derive the dynamics for both scalar and spinor functional fields from a unique parametrization invariant action. Passages to the Hamiltonian formalism and second quantization are explicitly worked out for the closed mesonic string in the front form. The results are equivalent to those obtained earlier by GGRT, i.e. no ghost fields at the price of an anomalous number of space-time dimensions and a tachyon. Finally, we use the parametrization invariance requirement on the action to derive couplings of closed strings to local fields by extending a global U(1) invariance built in the free action into a local one in the functional sense. We construct the self-couplings of closed string fields by requiring these to be consistent with the gauge invariance of the external fields. This procedure uniquely leads (for the open string) to the string splitting picture of Nambu and Mandelstam. The closed string is found to cross itself and then split up into two others. Both open and closed strings have quartic interactions corresponding to strand (for the open string) and lobe (for the closed string) exchanges. The case of the interacting fermionic model is not treated here.     

How to fix the gauge in internal and external gauge theories

A recently presented method, that permits one to calculate gauge-fixing conditions from a given gauge-breaking term, is applied to internal as well as external Yang-Mills theories. As to the internal case, the known gauge-fixing conditions can easily be reproduced in a unified way. For the external case, i.e., the Poincaré gauge theory of gravitation, new gauge-fixing conditions are obtained, in particular the full nonlinear generalization of the Coulomb and axial gauge. They prove to be simultaneously valid for theories with or without torsion.     

BRST symmetry for Regge–Teitelboim-based minisuperspace models

The Einstein–Hilbert action in the context of higher derivative theories is considered for finding their BRST symmetries. Being a constraint system, the model is transformed in the minisuperspace language with the FRLW background and the gauge symmetries are explored. Exploiting the first order formalism developed by Banerjee et al. the diffeomorphism symmetry is extracted. From the general form of the gauge transformations of the field, the analogous BRST transformations are calculated. The effective Lagrangian is constructed by considering two gauge-fixing conditions. Further, the BRST (conserved) charge is computed, which plays an important role in defining the physical states from the total Hilbert space of states. The finite field-dependent BRST formulation is also studied in this context where the Jacobian for the functional measure is illustrated specifically.     

Gauge independence of the effective potential revisited

We apply the formalism of extended BRS symmetry to the investigation of the gauge dependence of the effective potential in a spontaneously symmetry broken gauge theory. This formalism, which includes a set of Grassmann parameters defined as the BRS variations of the gauge-fixing parameters, allows us to derive in a quick and unambiguous way the related Nielsen identities, which express the physical gauge independence, in a class of generalized 't Hooft gauges, of the effective potential. We show in particular that the validity of the Nielsen identities does not require any constraint on the gauge-fixing parameters, contrary to some claims found in the literature. We use the method of algebraic renormalization, which leads to results independent of the particular renormalization scheme used.     

BRST quantization of superstring field theory

We write the gauge fixed action which arises in the quantization of Witten's string field theory in a linear gauge, in a form which applies to both the superstring and the bosonic string. The corresponding BRST transformation is nilpotent only on-shell. We construct also an off-shell nilpotent BRST transformation which formally leaves invariant the quantum effective action. This BRST transformation has a geometrical interpretation which could allow to describe the gauge anomalies of the superstring field theory as the nontrivial cohomology of the BRST charge via the Wess-Zumino consistency condition.     

Construction of the BRST-Invariant Action for a Gauged Self-Dual Theory by Making Use of the Batalin-Fradkin Algorithm

The Batalin-Fradkin algorithm combined with the Batalin-Fradkin-Vilkovisky formalism is applied to a two-dimensional model of a self-dual field interacting chirally with a gauge field. A Becchi-Rouet-Stora-Tyutin gauge-fixing action is obtained with auxiliary fields introduced in the algorithm turning into a Wess-Zumino field. The chirality of the Wess-Zumino field appears in a natural way.     

Pre-geometrical field theory of the open string

We propose a gauge invariant, background independent string action, which contains open and closed string fields and no kinetic terms. The kinetic term is generated through the condensation of the string fields, which is the solution of the equations of motion. we solve the equations and show that the action is classically equivalent to the open string action proposed by Hata et al.     

Quenched string field theory

We construct a toy model of Witten's open string field theory by truncating the Virasoro group to its SU(1,1) subgroup. The string field is given in terms of finite-dimensional matrices, which satisfy a non-trivial BRST cohomology. The string gauge group is found to be SO(3). Finally, we perform the gauge fixing of the action, finding an explicit formula for calculating the partition function.     

Non-commutative geometry and the closed bosonic string

We propose an action for an interacting closed bosonic string. Our formalism relies heavily on ideas discussed by Witten for the open bosonic string. We also obtain the gauge fixed quantum action for the fully interacting open bosonic string.     

Heterotic string in background gauge fields

The higher order corrections to the two-dimensional nonlinear σ-model for the heterotic string are considered. The divergent parts of the effective action are calculated explicitly to two-loop order in the presence of arbitrary background gauge fields. It is shown that the full gauge Chern-Simons term appears in the divergent terms. We also discuss its relevance to the equations of motion for the massless modes of the heterotic string with emphasis on the local gauge invariance of the heterotic string theory.     

Fock space formulation of gauge invariant interacting field theories of open and closed strings

We derive the conditions that must be satisfied by three string vertex operators, in order to have a gauge invariant Chern-Simons type action as proposed by Witten for the open bosonic string, in a Fock space formulation. Given a vertex which satisfies these conditions for the open string, we show how to construct an invariant action for the closed string.     

Symmetries of the interacting gauge-covariant bosonic string

We derive in detail the local gauge transformations and interaction lagrangian of the second-quantized bosonic string. We verify at lowest non-trivial order in the coupling constant the gauge invariance of the interacting action, and the closure of the field transformations. This gives the structure constants of the corresponding local gauge group. This group has its generators labelled by all the string states of the theory. We show that the fermionic part of the interaction is just the overlap condition for the ghost coordinates of the three strings, multiplied by an appropriate extra ghost at the point common to the three strings. Our treatment is based on an extensive use of Goto-Naka-type overlap equations. It avoids the use of ill-defined infinite matrices or series, and can be straightforwardly extended to other string theories. We explicitly derive the conformal transformation relating the gauge-covariant three-point function to the old Caneschi-Schwimmer-Veneziano vertex. We also deal with the closed bosonic string.     

Extended string field theory for massless higher-spin fields

We propose a new gauge field theory which is an extension of ordinary string field theory by assembling multiple state spaces of the bosonic string. The theory includes higher-spin fields in its massless spectrum together with the infinite tower of massive fields. From the theory, we can easily extract the minimal gauge-invariant quadratic action for tensor fields with any symmetry. As examples, we explicitly derive the gauge-invariant actions for some simple mixed symmetric tensor fields. We also construct covariantly gauge-fixed action by extending the method developed for string field theory.