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.     

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.     

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.     

Integration over moduli space in superstring theory

A calculation of multiloop superstring amplitudes is considered, the equivalence of popular approaches to determining these amplitudes being discussed. A calculation of poorly defined integrals over singular configurations is clarified. Amplitudes obtained by a correct method do not involve divergences in any order of perturbation theory.     

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.     

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.     

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.     

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.     

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.     

T-dualization of type II superstring theory in double space

In this article we offer a new interpretation of the T-dualization procedure of type II superstring theory in the double space framework. We use the ghost free action of type II superstring in pure spinor formulation in approximation of constant background fields up to the quadratic terms. T-dualization along any subset of the initial coordinates, \(x^a\), is equivalent to the permutation of this subset with subset of the corresponding T-dual coordinates, \(y_a\), in double space coordinate \(Z^M=(x^\mu ,y_\mu )\). Requiring that the T-dual transformation law after the exchange \(x^a\leftrightarrow y_a\) has the same form as the initial one, we obtain the T-dual NS–NS and NS–R background fields. The T-dual R–R field strength is determined up to one arbitrary constant under some assumptions. The compatibility between supersymmetry and T-duality produces a change of bar spinors and R–R field strength. If we dualize an odd number of dimensions \(x^a\), such a change flips type IIA/B to type II B/A. If we T-dualize the time-like direction, one imaginary unit i maps type II superstring theories to type \(\hbox {II}^\star \) ones.     

On the field theory expansion of superstring five point amplitudes

A simple recursive expansion algorithm for the integrals of tree level superstring five point amplitudes in a flat background is given which reduces the expansion to simple symbol(ic) manipulations. This approach can be used for instance to prove the expansion is maximally transcendental to all orders and to verify several conjectures made in recent literature to high order. Closed string amplitudes follow from these open string results by the KLT relations. To obtain insight into these results in particular the maximal R-symmetry violating amplitudes (MRV) in type IIB superstring theory are studied. The obtained expansion of the open string amplitudes reduces the analysis for MRV amplitudes to the classification of completely symmetric polynomials of the external legs, up to momentum conservation. Using Molien?s theorem as a counting tool this problem is solved by constructing an explicit nine element basis for this class. This theorem may be of wider interest: as is illustrated at higher points it can be used to calculate dimensions of polynomials of external momenta invariant under any finite group for in principle any number of legs, up to momentum conservation.     

A Hilbert space for the classical electromagnetic field

The synthetic Maxwell equation, uniting all Maxwell equations within the framework of a Clifford algebra, can be treated as a first-order wave equation. A Hilbert space of its solutions describing classical free electromagnetic fields is introduced. This Hilbert space can be called classical, which means that the Planck constant is absent. The scalar square of an element of this space is the total energy of the field. The time independence of the scalar product is demonstrated. The time and space translation generators are found; they are shown to not coincide with the energy and momentum operators.