Closed String Theory Research Articles

The explicit gauge invariance of the free closed bosonic strings and open fermionic string

We derive the gauge invariant equations of motion for the open Ramond superstring and closed string theories. We show that the actions which give the equations of motion for all the closed string theories are quite similar in form and require the introduction of an auxiliary field.

Covariant one-loop fermion emission amplitudes in closed string theories

We calculate the 2 fermion-2 boson and the 4 fermion scattering amplitudes at one loop in the NSR formulation of the heterotic and type II superstring theories using the covariant fermion emission vertex. The results are shown to agree with well known amplitudes calculated in the light-cone gauge in the Green-Schwarz formulation. The agreement of the 4-fermion amplitude entails the use of a new ϑ-function identity which we also prove.

Functional determinants on punctured Riemann surfaces and their application to string theory

We compute functional determinants on punctured Riemann surfaces by integrating the corresponding energy-momentum tensors. The results are applied to the bosonic closed string theory in two ways. We first give a rigorous proof of the relation between the scalar and ghost determinants for the singular metrics which are squares of meromorphic one-forms. This relation played an important role in the recent proof of the equivalence between the light-cone and Polyakov approaches given by D'Hoker and Giddings. Secondly we give explicit formulae for the scattering amplitudes as integrals over the moduli space of punctured Riemann surfaces.

Four-dimensional superstrings

We solve completely the constraints of factorization and multiloop modular invariance for closed string theories in which all internal quantum numbers of the string are carried by free periodic and antiperiodic world-sheet fermions. We derive a simple set of necessary and sufficient rules, and illustrate how they can be used to find the spectrum, one-loop amplitudes and low-energy lagrangian of many realistic four-dimensional chiral models. We prove that modular invariance and factorization ensure the presence of a massless graviton and the correct connection between spin and statistics. We also prove that the existence of a massless spin- 3 2 state ensures the absence of tachyons and the vanishing of the one-loop cosmological constant.

Anomalies, characters and strings

One-loop modular invariant heterotic and type II closed string theories are proved to be anomaly free, apart from terms proportional to Tr F 2 − Tr R 2. It is shown why this conclusion holds with remarkable generality for any conceivable fermionic string theory, regardless even of conformal invariance. A detailed discussion is given of the modular properties of character valued partition functions, upon which the proof is based. The fact that Tr F 2 − Tr R 2 terms remain in the fermionic contribution to the anomaly is shown to be a consequence of Quille's holomorphic anomaly.

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.

Superstrings from 26 dimensions

Consistent closed superstrings are contained in the 26-dimensional bosonic closed string theory. We explain in detail how the states, operators and interaction vertices of superstrings emerge in this way. We also discuss possibilities for obtaining new string theories.

Consistent superstrings as solutions of the D = 26 bosonic string theory

Consistent closed ten-dimensional superstrings, i.e., the two N = 1 heterotic strings and the two N = 2 superstrings, are contained in the 26-dimensional bosonic closed string theory. The latter thus appears as the fundamental string theory.

Supersymmetrical string theories

A supersymmetrical light-cone-gauge string action is presented. It provides a basis for understanding the previously- studied supersymmetrical dual string theory as well as two new closed-string theories that have extended supersymmetry in ten dimensions, corresponding to N=8 supersymmetry in four dimensions.

Topological gravity as large N topological gauge theory

We consider topological closed string theories on Calabi-Yau manifolds which compute superpotential terms in the corresponding compactified type II effective action. In particular, near certain singularities we compare the partition function of this topological theory (the Kodaira-Spencer theory) to $SU(\infty)$ Chern-Simons theory on the vanishing 3-cycle. We find agreement between these theories, which we check explicitly for the case of shrinking $S^3$ and Lens spaces, at the perturbative level. Moreover, the gauge theory has non-perturbative contributions which have a natural interpretation in the Type IIB picture. We provide a heuristic explanation for this agreement as well as suggest further equivalences in other topological gravity/gauge systems.