Unitarity and modular invariance as constraints on four-dimensional superstrings

It is shown that the requirements of space-time factorization for vertices and one-loop modular invariance guarantee higher-loop modular invariance (as it is presently understood) in the context of string models built out of free fermion fields, either twisted or untwisted. The general solution satisfying these requirements is derived and their relation to the conservation of quantum numbers at general fermionic vertices is discussed. A number of models are discussed using a diagrammatic notation. The natural occurrence in such models of spinor representations which have features in common with the observed quark-lepton multiplets is noted.     

Remarks on Wilson lines,modular invariance and possible string relics in Calabi-Yau compactifications

When one mods out a (2,2) conformal field theory by the action of a discrete group, it is possible to include Wilson lines to break the gauge symmetry. We simplify and generalize an earlier analysis by Witten of the constraints that modular invariance places on the allowed symmetry breaking patterns. The analysis does not depend on the details of the original conformal field theory. We then consider the fractionally charged states in such theories, first discussed by Wen and Witten. We note that these are rather generic, and consider the possibilities for their detection. We also note that, while in general they are expected to be massive (∼M_Planck), in models based on free fields, such as orbifold compactifications, there are likely to be massless (very light) fractionally charged states.     

Nonrenormalizable superpotential in four-dimensional string models

A construction of an effective nonrenormalizable superpotential has been discussed within the approach of a four-dimensional heterotic superstring with free fermions on the world sheet. On the basis of N=2 superconformal theory, useful selection rules that take into account all global symmetries have been obtained within the formalism of covariant vertices and the ghost-picture-changing operation. The results have been applied to the model featuring the effective observable gauge group U(5)×U(3)_H, which includes the non-Abelian horizontal group and which describes (3+1) generation. The full superpotential of the model up to sixth order inclusive has been obtained, and its coupling constants have been calculated. The quark-lepton mass spectrum of the model has been discussed with allowance for contributions from nonrenormalizable terms.     

Ward identities in four-dimensional string theory

A four-dimensional heterotic string theory is envisaged in the background of its massless gauge Ward identities are derived. The spontaneous generating functional is constructed in the hamiltonian phase space and gauge Ward identities are derived. The spontaneous breaking of gauge symmetry is discussed in this approach.     

Logarithmic divergence in four-dimensional string theory

Logarithmic divergences in the one-loop scattering amplitude of the heterotic string compactified on the Z_n-orbifold are investigated. The coefficient of these divergences is shown to be a function of the indices of the representations to which the massless states of the model belong.     

Conformal invariance,current algebra and modular invariance

A large class of conformally invariant models in two dimensions is realised by constraining free fermion theories. The Fock spaces of the constrained theories are described, using the representation theory of affine Kac-Moody algebras. The results are extended to superconformally invariant theories. Projections of the models, producing consistent two-dimensional field theories, are discussed.     

Two-loop modular invariance and spin-statistics

Within the context of a class of fermionic closed string theories I explicitly show some relationships between two-loop modular invariance, factorization, correct spin-statistics and the existence of a massless gravity multiplet.     

Gauge couplings in four-dimensional type I string orbifolds

We compute threshold effects to gauge couplings in four-dimensional _N orientifold models of type I strings with GN = 2 and GN = 1 supersymmetry, and study their dependence on the geometric moduli. We also compute the tree-level (disk) couplings of the open sector gauge fields to the twisted closed string moduli of the orbifold in various models and study their effects and that of the one-loop threshold corrections on gauge coupling unification. We interpret the results from the (supergravity) effective theory point of view and comment on the conjectured heterotic-type I duality.     

Two-loop vacuum amplitude in four-dimensional heterotic string models

The two-loop measure of four-dimensional heterotic strings with N=4, 2 and 1 space-time supersymmetry is explicitly calculated. It is shown that the cosmological constants of these models at two loops are zero.     

Conformal invariance,supersymmetry and string theory

Covariant quantization of string theories is developed in the context of conformal field theory and the BRST quantization procedure. The BRST method is used to covariantly quantize superstrings, and in particular to construct the vertex operators for string emission as well as the supersymmetry charge. The calculation of string loop diagrams is sketched. We discuss how conformal methods can be used to study string compactification and dynamics.     

BRS invariance of the interacting Polyakov string

The modification to the BRS symmetry of Polyakov's string required to ensure the invariance of the generating functional and the decoupling of spurious states in the presence of interactions is calculated.     

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.