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.     

Anomalies in Witten's field theory of the NSR string

We show that Witten's action for the NSR superstring on the space of non-smooth vectors generated by SUSY transformations depends on regularization that demonstrates the presence of anomalies in the theory. The necessity of choosing the regularization is connected with the appearance of the product of picture-changing operators at coincident points. Using one of the possible types of regularization, we get the minimal formulation involving truncated fields, and adopting another one, we get the scheme implied in Witten's paper.     

Conformal field theory and the symmetries of string field theory

The two-dimensional conformal field theory representation of Witten's bosonic string field theory is discussed. The basic overlap equations, K_n symmetry and BRST invariance are proved directly, without the usual expansion in oscillators. The conformal field theory approach naturally provides local overlap identities which (when integrated over half the string) can be used to verify properties of the cubic action. In particular, a recently proposed diffeomorphism invariance is shown to be free of anomalies. Finally, a new class of symmetries, including generalizations of the K_n symmetries which are local in spacetime, are presented.     

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.     

Pregeometry of open superstring field theory

We show that the conventional action for interacting open superstring field theory is contained in a purely cubic action which does not depend on the background induced by the super BRST charge.     

BRST-symmetries in free string field theory

A unitary field transformation useful for examination of the BRST-symmetries in free bosonic open-string field theory is introduced. It is similar to Siegel and Zwiebach's transformation, but leads to a hermitian BRST-charge in contrast to theirs. The transformed BRST-transformation factorizes into two parts, making the gauge-unfixing procedure rather trivial. Both the minimal-type gauge-invariant action and Witten's action are dealt with.     

General covariance and open string interactions

It has been suggested that Witten's open string cubic interaction is independent of the background geometry. We investigate this suggestion in detail with a view to understanding the rôle of closed strings in Witten's open string field theory. The standard oscillator formulation of the vertex requires the use of a metric, if it is to be generally covariant, indicating that closed string interactions are required. However by changing to variables better suited to treating the midpoint, we show explicitly that it is possible to transform away all reference to the background metric. This supports the assertion that the cubic action (of Horowitz, Lykken, Rohm and Strominger) can also describe closed strings.     

Off-shell conformal methods for the superstring

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 g².     

Supersymmetric instantons and topological quantum field theory

We present an action which generates the supersymmetric self-dual equations corresponding to euclidean super Yang-Mills theory in four dimensions. By adding additional constraint fields with new local symmetries, the classical equations of this system are the usual super self-dual equations when a gauge is chosen for the constraint fields. This construction is a supersymmetric generalization of the Labastida-Pernici action which corresponds to a gauge unfixed version of Witten's topological quantum field theory. We discuss some topological prospects for this model, and the role of supersymmetric instantons in Donaldson theory.     

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.     

Hamiltonian formulation of string field theory

Witten's string field theory is quantized in the hamiltonian formalism. The constraints are solved and the hamiltonian is expressed in terms of only physical degrees of freedom. Thus, no Faddeev-Popov ghosts are introduced. Instead, the action contains terms of arbitrarily high order in the string functionals. Agreement with the standard results is demonstrated by an explicit calculation of the residues of the first few poles of the four-tachyon tree amplitude.     

Closed string-open string transitions and Witten's string field theory

Using conformal mapping techniques, we obtain a new BRST invariant operator ϒ encoding in closed form transition amplitudes between open strings and closed strings. The residues of the closed string poles in the non-planar one-loop two-point diagram of Witten's string field theory are finite sums of products of these amplitudes.     

A covariant open bosonic string field theory including the endpoint and middlepoint interaction

Extending the usual endpoint and midpoint interactions, we introduce numerous kinds of interactions, labelled by a parameter λ and obtain a non-commutative and associative string field algebra by adding up all interactions. With this algebra we develop a covariant open bosonic string field theory, which reduces to Witten's open bosonic string field theory under a special string length choice.     

Gauge invariant actions of free closed superstring field theories

A gauge invariant action of free N=1 closed superstring field theory is presented using BRS charges. This action is shown to take a similar form to that of open superstring. The N=2 closed superstring is also discussed.     

String field theory and infinite grassmannian

An interesting connection between Witten's string field theory and the infinite grassmannian, and the possible characterization of the group orbit on the grassmannian by the bilinear identity are examined.     

Superfield approach to the construction of effective action in quantum field theory with extended supersymmetry

We review the current state of research on the construction of effective actions in supersymmetric quantum field theory. Special attention is paid to gauge models with extended supersymmetry in the superfield approach. The advantages of formulation of such models in harmonic superspace for the calculation of effective action are emphasized. Manifestly supersymmetric and manifestly gauge-invariant methods for constructing the low-energy effective actions and deriving the corrections to them are considered and the possibilities to obtain the exact solutions are discussed. The calculations of one-loop effective actions in N = 2 supersymmetric Yang–Mills theory with hypermultiplets and in N = 4 supersymmetric Yang–Mills theory are analyzed in detail. The relationship between the effective action in supersymmetric quantum field theory and the low-energy limit in superstring theory is discussed.     

Gauge fixing and renormalization in topological quantum field theory

We show how Witten's topological Yang-Mills and gravitational quantum field theories may be obtained by a straightforward BRST gauge fixing procedure. We investigate some aspects of the renormalization of the topological Yang-Mills theory. It is found that the beta function for the Yang-Mills coupling constant is not zero.     

Scattering amplitude for Witten's open superstring field theory

From Witten's open-superstring theory, four-point scattering amplitudes are derived. The results coincide with those of Green and Schwarz in the light-cone approach.     

Operator expression of Witten's superstring vertex

The explicit operator expressions of both the 3-Neveu-Schwarz (NS) and Neveu-Schwarz-Ramond-Ramond vertices in Witten's superstring field theory are given by using the method recently developed by Kunitomo and the author. The BRST invariance of these vertices is proved at the critical dimension d=10. Further, we clarify the relation between the prefactor of the 3-NS vertex required by the BRST invariance and the picture changing operator.     

Vector field effective action in the open superstring theory

Using a path integral technique we find a closed expression (to all orders in α′) for the abelian, constant field strenght limit of the (tree) effective action for the massless vector field in the open superstring theory. The result is a modification of the Born-Infeld action found in the Bose string theory case. One-loop correction to the effective action is computed and shown to be finite if the gauge group is SO(32). It is demonstrated how the on-shell superstring scattering amplitudes can be calculated in the path-integral approach. We determine the leading (O(α') and O(α′²)) terms in the full non-abelian effective action starting from the known results for the 3-point and 4-point amplitudes. We find that because of the equivalence theorem the coefficients of some of the invariant structures in the effective lagrangian cannot be fixed from the S-matrix. In the path integral approach this ambiguity manifests itself as a 2d renormalization scheme (and Weyl gauge choice) ambiguity. We also discuss the leading terms in the gravitational effective actions in the closed (super) string theories and point out that whether or not the R² terms form the “Gauss-Bonnet” combination depends on choice of a renormalization (massless exchange subtraction) scheme.