One-loop gauge anomaly in type-1 superstring theory

The vanishing of the hexagon gauge anomaly of type-I superstring was shown previously by Green and Schwarz in the case that the gauge group is SO(32). The result, as well as the finiteness f the one-loop amplitude, makes the superstring theory a candidate for the unified theory including gravity. The vanishing of the gauge anomaly can be established for all N-point functions. The one-loop gauge anomaly is shown to be absent if the gauge group is SO(32).     

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.     

Conformal field theory representation and background-independent action for superstring field theory

The two-dimensional conformal field theory representation of Witten's open superstring field theory is discussed. We argue that the previously suggested cubic action for the superstring is actually dependent on the spacetime background, and suggest a modification which formally removes this dependence. The transformation from the new version of the superstring cubic action to Witten's action for open string states is discussed. A class of linearized solutions to the equations of motion of the open superstring cubic action are exhibited. These solutions are in one-to-one correspondence with the physical excitations (both massless and massive) of the open and closed type I superstrings.     

Interaction of moving branes with background massless and tachyon fields in superstring theory

Using the boundary state formalism, we study a moving Dp-brane in a partially compact space-time in the presence of background fields: the Kalb-Ramond field B _μν, a U(1) gauge field A _α, and the tachyon field. The boundary state enables us to obtain the interaction amplitude of two branes with the above back-ground fields. The branes are parallel or perpendicular to each other. Because of the presence of background fields, compactification of some space-time directions, motion of the branes, and the arbitrariness of the dimensions of the branes, the system is rather general. Due to the tachyon fields and velocities of the branes, the behavior of the interaction amplitude reveals obvious differences from the conventional behavior.     

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.     

One-loop string corrections to the effective field theory

We calculate the parity-conserving one-loop string corrections to the bosonic part of the 10-dimensional effective field theory for the heterotic string. There is no renormalization of the Chamseddine-Chapline-Manton supergravity action, but terms of fourth order in the curvature tensors are generated. Most of these are of the same forms as those found at the tree level of the string topological expansion, such as (TrR²)², (TrR²)(TrF²) and (TrF²)². However, we also find a non-zero Tr(F⁴) coupling which was not present at the tree level. We comment on the phenomenological implications of these results, which include absences of renormalization of the Kähler metric and of the gauge kinetic function of the effective field theory in four dimensions after compactification, and a modification of the classical equations to be obeyed by the manifold of compactification.     

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.     

The antisymmetric tensor field in superstring theory

We discuss various aspects of the role of the antisymmetric tensor field in superstring theory, including the quantization law obeyed by its field strength and its role in topological defects and in vacuum configurations.     

Space-time supersymmetry in covariant superstring field theory

It is shown that the existence of a transition operator, which interchanges the BRS charges of the Neveu-Schwarz and the Ramond sectors, implies space-time supersymmetry in the covariant free open superstring field theory proposed previously by the present authors.     

Background formalism for superstring field theory

In the framework of the background formalism we analyse possible versions of the Witten-type NSR superstring field theory. We find the picture for string fields to be uniquely fixed by the requirement that the perturbative classical solutions are well-defined. This uniquely defined picture and the corresponding action are different from the ones in Witten's theory and coincide with the ones proposed from different reasons in our previous paper. Following the same background method we calculate the tree-level scattering amplitudes for the new action and argue that in contrast to the ones in Witten's original theory, the amplitudes are singularity-free and hence there is no need to add any tree-level counterterms. We also prove the amplitudes to reproduce correctly the first quantized results.     

Mathematical formulation of Witten's superstring field theory

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.