N-Superstring vertex and the vertex operator for the emission of the superstring

The BRST invariant, supersymmetric N-string vertex which applies to both, the Neveu-Schwarz and Ramond sector of the superstring is formulated using the vertex operator for the emission of a superstring. It is shown that the N-superstring vertex thus obtained is cyclic symmetric when GSO projected on-shell states and operators for the external strings are applied. The constraint equations of this vertex and their singularity structure are examined and we show that this vertex also has the required property of a transition operator. We also give a proof of its BRST invariance and supersymmetry.     

Interacting physical states of the bosonic string. I

A preliminary discussion on the importance of the contact terms in relation with the existence of many string vacua is presented. The problem of the BRST invariance of the string states transition amplitudes is considered in the sigma model approach to the string. It is shown that the BRST invariance is controlled by a gravitational (Diff) anomaly, and its connections with the standard Virasoro constraints are illustrated. The tachyon amplitudes are analysed and the BRST invariant dilaton vertex operator for non flat world-sheet is constructed.     

Canonical BRST quantisation of worldsheet gravities

We reformulate the BRST quantisation of chiral Virasoro and W₃ worldsheet gravities. Our approach follows directly the classic BRST formulation of Yang-Mills theory in employing a derivative gauge condition instead of the conventional conformal gauge condition, supplemented by an introduction of momenta in order to put the ghost action back into first-order form. The consequence of these simple changes is a considerable simplification of the BRST formulation, the evaluation of anomalies and the expression of Wess-Zumino consistency conditions. In particular, the transformation rules of all fields now constitute a canonical transformation generated by the BRST operator Q, and we obtain in this reformulation a new result that the anomaly in the BRST Ward identity is obtained by application of the anomalous operator Q², calculated using operator products, to the gauge fermion.     

Absolutely anticommuting (anti-)BRST symmetry transformations for topologically massive Abelian gauge theory

We demonstrate the existence of the nilpotent and absolutely anticommuting Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations for the four (3+1)-dimensional (4D) topologically massive Abelian U(1) gauge theory that is described by the coupled Lagrangian densities (which incorporate the celebrated (B∧F) term). The absolute anticommutativity of the (anti-) BRST symmetry transformations is ensured by the existence of a Curci–Ferrari type restriction that emerges from the superfield formalism as well as from the equations of motion which are derived from the above coupled Lagrangian densities. We show the invariance of the action from the point of view of the symmetry considerations as well as superfield formulation. We discuss, furthermore, the topological term within the framework of superfield formalism and provide the geometrical meaning of its invariance under the (anti-)BRST symmetry transformations.     

A reparametrization-invariant approach to string field theory

Using reparametrization invariance as the only requirement, we show, by a series of algebraic steps, how the only reparametrization-invariant generalization of d'Alembert's operator for both open and closed bosonic strings, is in fact nilpotent and thus the BRST charge. The construction follows a proposal made many years ago by one of the authors.     

From conformal quantum mechanics on bordered Riemann surfaces to covariant string field theory

The Faddeev-Popov determinant of the reparametrization ghosts of the closed bosonic string on bordered Riemann surfaces is investigated. It is found that the standard ghost action has to be supplemented by additional boundary terms. These additional terms lead to a nontrivial ghost transition amplitude. It is shown that boundary variations of ghost transition amplitudes are generated by the ghost Virasoro operators. The relevance of the boundary variation operator for string field theory is illustrated. A new interpretation of the BRST operator in terms of boundary variations is obtained and the BRST invariance of the transition amplitudes is demonstrated. A generalization of the Siegel gauge of second quantized closed bosonic string field theory is presented.     

BRST operator on a Riemann surface

We discuss construction of the BRST operator for the bosonic closed string theory on an arbitrary Riemann surface of genus g>1. Using the BRST operator we prove the decoupling of the bosonic spurious physical states in general.     

On the reanimation of a local BRST invariance in the (Refined) Gribov–Zwanziger formalism

We localize a previously established nonlocal BRST invariance of the Gribov–Zwanziger (GZ) action by the introduction of additional fields. We obtain a modified GZ action with a corresponding local, albeit not nilpotent, BRST invariance. We show that correlation functions of the original elementary GZ fields do not change upon evaluation with the modified partition function. We discuss that for vanishing Gribov mass, we are brought back to the original Yang–Mills theory with standard BRST invariance.     

Solving general gauge theories on inner product spaces

By means of a generalized quartet mechanism we show in a model independent way that a BRST quantization on an inner product space leads to physical states of the form ph〉 = exp [Q, ψ]ph〉₀ where Q is the nilpotent BRST operator, ψ a hermitian fermionic gauge-fixing operator, and ph〉_o BRST invariant states determined by a hermitian set of BRST doublets in involution. ph〉₀ does not belong to an inner product space although ph〉 does. Since the BRST quartets are split into two sets of hermitian BRST doublets there are two choices for ph〉₀ and the corresponding ψ. When applied to general, both irreducible and reducible, gauge theories of arbitrary rank within the BFV formulation we find that ph〉₀ are trivial BRST invariant states which only depend on the matter variables for one set of solutions, and for the other set ph〉₀ are solutions of a Dirac quantization. This generalizes previous Lie group solutions obtained by means of a bigrading.     

Ghost vertices for the bosonic string using the group-theoretic approach to string theory

The N-string tree-level scattering vertices for the bosonic string are extended to include anticommuting (ghost) oscillators. These vertices behave correctly under the action of the BRST charge Q and reproduce the known results for the scattering of physical states. This work is an application of the group-theoretic approach to string theory.     

BRST invariant tadpole operator in the bosonic string

Using a BRST invariant three-reggeon vertex we construct an explicit expression for the BRST invariant planar tadpole operator for the bosonic string. Joined to an (N+1)-reggeon vertex it yields the correct expression for the one-loop N-tachyon amplitude.     

Nilpotency ofQBRST and the vanishing ß-function in string theories

We study the conformal Ward identities following from the BRST invariance in string theories and show that the nilpotency of Q_BRST implies a vanishing ß-function and vice versa.     

Cumulative author index B751–B754

The paper is devoted to the study of BRST charge in perturbed two-dimensional conformal field theory. The main goal is to write the operator equation expressing the conservation law of BRST charge in perturbed theory in terms of purely algebraic operations on the corresponding operator algebra, which are defined via the OPE. The corresponding equations are constructed and their symmetries are studied up to the second order in formal coupling constant. It appears that the obtained equations can be interpreted as generalized Maurer–Cartan ones. We study two concrete examples in detail: the bosonic nonlinear sigma model and perturbed first order theory. In particular, we show that the Einstein equations, which are the conformal invariance conditions for both these perturbed theories, expanded up to the second order, can be rewritten in such generalized Maurer–Cartan form.     

Nilpotent symmetry invariance in the non-Abelian 1-form gauge theory: Superfield formalism

We demonstrate that the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four (3 + 1)-dimensional (4D) non-Abelian 1-form gauge theory with Dirac fields can be captured within the framework of the superfield approach to BRST formalism. The above 4D theory, where there is an explicit coupling between the non-Abelian 1-form gauge field and the Dirac fields, is considered on a (4,2)-dimensional supermanifold, parametrized by the bosonic 4D spacetime variables and a pair of Grassmannian variables. We show that the Grassmannian independence of the super-Lagrangian density, expressed in terms of the (4,2)-dimensional superfields, is a clear signature of the presence of the (anti-)BRST invariance in the original 4D theory.      

From points to gauge fields

We show that several classes of free field theories with local gauge invariance (e.g. the Yang-Mills, Einstein and p-forms linearized actions) can be constructed from classical actions for a finite number of points by applying the BRST quantization initiated by Siegel. We briefly outline the generalization of this construction for strings.     

Temperature and the critical dimension of strings

Thermofield dynamics is used to generalize the BRST invariance of strings to nonzero temperature. The requirement that the BRST generator is nilpotent implies thatd=26 even at nonzero temperature.     

Generalized Slavnov-Taylor,BRST and covariance identities from the geometry of the gauge surface

We establish the equivalence between the extended BRST invariances, and the conventional Slavnov-Taylor transformations together with a new “dual” analogue. However, the latter (a non-local gauge transformation, generating anA-dependent translation of the gauge-fixing surface) isnot an invariance of the Faddeev-Popov determinant, contrary to the published claim.     

BRST quantization of the superparticle

We show that the quantization of the superparticle action is possible. This is done by shifts in the BRST operator and the resulting action has an infinite number of ghosts. The total BRST operator is given by an infinite sum and is shown to be nilpotent. We also obtain a BRST invariant kinetic operator that contains the dynamical, auxiliary and gauge pieces in it.     

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.