Gauge invariant field theory of free strings

We present the gauge invariant and covariant equations of motion for free strings and superstrings, using a simple method of successive gauge transformations. Gauge invariance is enforced by introducing both subsidiary and Stueckelberg fields. We use methods of cohomology associated with the various Virasoro algebras, and derive the cohomology algebras associated with the boson and fermion sector of the open and closed superstrings.     

Interacting field theory of open superstrings

A proposal for a gauge invariant nonlinear classical field theory of open superstrings is explored. The gauge fixing that gives rise to the standard structure in the Ramond sector is described, answering questions that have been raised in recent literature. The model is shown to possess space-time supersymmetry as well as gauge invariance. The proof of space-time supersymmetry uses the covariant form of the fermion emission vertex and the associated picture changing operation, in accord with suggestions by several authors. Also discussed are the canonical formulation of the theory, and some issues connected with the extension of the work to closed strings.     

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.     

The gauge-covariant formulation of interacting strings and superstrings

The local gauge-covariant free actions of open and closed bosonic strings and superstrings are constructed. The unique local covariant actions for interacting bosonic strings (open and closed) are determined and the corresponding one for superstrings is proposed.     

Open strings on orbifolds

We consider propagation of type I SO(32) superstrings on orbifolds. It is shown that anomaly cancellation requires the existence of “twisted” open strings and we determine the Chan-Paton factors for these strings in a simple example.     

Finite-energy static solutions to chiral models in three space dimensions

Finite-energy static kink solutions in three space dimensions, carrying a topologically conserved charge, are exhibited for a new type of chiral pion model. The usual scaling instability problems are circumvented by an unconventional choice of action. This action has no free field sector, but small excitations about classical static solutions of exhibit causal propagation and are candidates for quantization. Another type of scaling stable chiral model is also discussed. It does have a free field sector but involves fourth-order derivatives in the action.Some global aspects of solutions to non-linear chiral theories are discussed in the appendix.     

Anomalies of the products of vertex functions in the superstring theories

We obtain the two-dimensional anomalous transforms of the products of several vertex functions (of Neveu-Schwarz sector) in the path integral formulation of closed superstrings: type II super and heterotic strings. The products of vertex functions are free from local anomalies except for Weyl anomalies. In the presence of background fields this kind of Weyl anomalies leads to interaction terms in the background field equations of motion, which are derived by the requirement of the cancellation of Weyl anomalies.     

Non-commutative geometry and string field theory

An attempt is made to interpret the interactions of bosonic open strings as defining a non-cummulative, associative algebra, and to formulate the classical non-linear field theory of such strings in the language of non-commulative geometry. The point of departure is the BRST approach to string field theory. A setting is given in which there is a unique gauge invariant action, whose linearized approximation reproduces the conventional Veneziano spectrum. A derivation of conventional Veneziano model amplitudes from this gauge invariant action is sketched. Some brief comments are made about attempts to extend these results to open superstrings and to closed strings.     

Beta-functions and superstring compactifications

It is shown that quartic curvature modifications to the gravitational effective action derived from superstrings agree on Ricci-flat Kähler backgrounds with a recently-proposed four-loop counterterm in N = 2 Ricci-flat σ-models. These results seem to suggest that Calabi-Yau manifolds may not provide consistent compactifications of the superstring.     

Convergence of U(1)3 lattice gauge theory to its continuum limit

It is shown that in three space-time dimensions the pure U(1) lattice gauge theory with Villain action and fixed coupling constant converges to the free electromagnetic field as the lattice spacing approaches zero. The same holds for the Wilson action on the electric sector.     

Supersymmetry among free fermions and superstrings

A complete classification is given of all supersymmetric theories of free massless two-dimensional fermions. This, in particular, implies a classification of all free-fermion representations of super Kac-Moody algebras. It is shown that these cannot be used to construct new string theories with unbroken supersymmetry in Minkowski space-time, other than the torus-compactifications of the known ten-dimensional superstrings. Assuming anti-de-Sitter space-time could restore conformal invariance, it is shown how one could construct a string theory whose low-lying excitations form a multiplet of gauged N = 8 supergravity.     

Strings at nonzero temperature

String theory at nonzero temperature is reviewed. A bosonic string at nonzero temperature is studied and the calculation of its free energy in both the one-loop approximation and the case of arbitrary genus (multiloop analysis) is discussed. A string at nonzero temperature is compared with a string compacted on a one-dimensional torus. The properties of modular invariance and dual symmetry are discussed at both the one-loop and multiloop levels. The thermodynamics of superstrings, including also superstrings compactified on a torus, is also studied. Possible cosmological applications are briefly considered. It is shown that many features of string thermodynamics (in particular, the existence of the Hagedorn temperature and dual symmetry) also occur in the theory of noncritical strings.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 12, pp. 3–49, December, 1991.     

Truncations of the D9-brane action and type-I strings

The low-energy effective action of type-I superstring theory in ten dimensions is obtained performing a truncation of type-IIB supergravity in a background where D9-branes are present. The open sector corresponds to the first order in the low-energy expansion of the D9-brane action in a type-I background. In hep-th/9901055 it was shown that there are two ways of performing a type-I truncation of the D9-brane action, and the resulting truncated action was obtained in a flat background. We extend this result to a generic type-I background, and argue that the two different truncations are in correspondence with the open sector of the low-energy effective action of the two different consistent ten-dimensional type-I string theories, namely the SO(32) superstring and the USp(32) non-supersymmetric string.     

Alternative formulations of first quantized covariant string action

In the covariant formulation of the first quantized action for a string propagating in Minkowski space it is natural to introduce a field (called dualbein) which is a worldsheet vector as well as a spacetime vector. The dualbein is a logical generalization of the zweibein. In terms of the dualbein field we construct new covariant actions for the bosonic strings and the superstrings. The casev of massless superparticles is also discussed.     

Off-shell d=10, N=1 Poincaré supergravity and the embeddibility of higher-derivative field theories in superspace

The constraints on the supertorsion are presented which lead to off-shell d=10, N=2 Poincaré supergravity and the superfluids which are known to enter the superspace action are identified. It is pointed out that Poincaré off-shell constraints have to be used in a superspace formulation of the low-energy effective actions of N=1 superstrings. However, current formulations of N=1 superstrings propagating in arbitrary supergravity backgrounds are incompatible with these off-shell constraints.     

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.     

Supertubes versus superconducting tubes

In this paper we show the relationship between cylindrical D2-branes and cylindrical superconducting membranes described by a generic effective action at the bosonic level. In the first case the extended objects considered, arose as blown up type IIA superstrings to D2-branes, named supertubes. In the second one, the cosmological objects arose from some sort of field theories. The Dirac–Born–Infeld action describing supertubes is shown to be equivalent to the generic effective action describing superconducting membranes via a special transformation. (Dedicated to Prof. Alberto García on the occasion of his 60th birthday)     

Scherk-Schwarz mechanism and superstrings

It is shown that a particular choice of massless classical backgrounds provides an exact solution to the equations of motion of closed superstrings while spontaneously breaking supersymmetry at an arbitrary scale.     

Properties of the covariant formulation of superstring theories

The covariant two-dimensional action principle that describes the dynamics of free superstrings in a Minkowski background is reviewed. Covariant gauge conditions are formulated, which simplify the equations of motion of the superspace coordinates to free equations. In this gauge there are bosonic and fermionic constraints whose generators give a supersymmetric generalization of the Virasoro algebra. As in certain supersymmetric field theories, closure of the algebra requires using the equations of motion. Covariant constrained bracket relations are obtained for the classical theory, but it is very difficult to extend them to quantum mechanical commutation relations. Interaction vertices satisfying supersymmetry and the necessary gauge conditions are constructed. They reduce in a special frame to ones found in earlier work in the light-cone gauge, and then can be interpreted quantum mechanically.     

Constraints and actions in two and three dimensionalN=1 conformal supergravity

We investigate closure of the gauge algebra and constraints inN=1 conformal supergravity in 2 and 3 dimensions. In the 2 dimensional case, contrary to 3 or higher dimensions, some parts of the gauge fields are algebraically unsolvable in the constraint equations on group curvatures. It will be shown that these unsolvable parts are decoupled from the transformation law as well as from the kinetic multiplets. Hence they are absent in the invariant action for matter multiplets coupled to conformal supergravity which is relevant to the old superstrings. Explicit construction of the invariant actions are illustrated for the case of spinning strings and locally supersymmetric σ-models with the Wess-Zumino term.