Massive inter-particle symmetry and Ward identity in fermionic string theory

We show that there exist enlarged stringy (α′→∞) symmetries for (evenG-parity) massive modes in the 10D fermionic string theory. These symmetries are derived from on-shell Ward identities corresponding to the decoupling of massive gauge states in the spectrum. In the generalized massive supersymmetric σ-model formalism, some symmetry transformations relate particles with different spins in the first order weak field approximation.     

Exact analysis of Coulomb gauge vacuum degeneracies in (2 + 1) dimensions

The solutions of the two-dimensional euclidean σ-model provide an infinite number of pure gauge field configurations satisfying the Coulomb gauge condition, in (2 + 1) dimensions. For vacuum gauge fields associated with finite action instanton solutions of the σ-model, we find that the winding number n configuration leads to n negative eigenvalues for the ghost operator, up to a finite calculable degeneracy.     

Chan–Paton soliton gauge states of the compactified open string

We study the mechanism of the enhanced gauge symmetry of the bosonic open string compactified on a torus by analyzing the zero-norm soliton (non-zero winding of the Wilson line) gauge states in the spectrum. Unlike the closed string case, we find that the soliton gauge state exists only at massive levels. These soliton gauge states correspond to the existence of enhanced massive gauge symmetries with transformation parameters containing both Einstein and Yang–Mills indices. In the T-dual picture, these symmetries exist only at some discrete values of compactified radii when N D-branes are coincident. Received: 14 May 1999 / Published online: 17 March 2000     

Conformal invariance of σ-models and classical string physics

We show that the identification of the conformal anomaly of the general bosonic two-dimensional non-linear σ-model as the generating functional for on-shell string scattering amplitudes is correct up toO(α′) terms. The absence, in the loop corrections to the spacetime effective action, of contributions from the explicit coupling to the dilaton field is suggested as a general feature for σ-models describing tree-level string physics.     

Supersymmetry breaking for the observable sector in superstring models

We discuss the supersymmetry breaking in four-dimensional supergravity models from superstrings including perturbative or non-perturbative string σ-model corrections. It is found that various soft supersymmetry breaking terms can appear with values of the order ofm _3/2 even at the tree level of effective field theory and of string theory.     

Spectra in Standard-like Z3 Orbifold Models

General features of the spectra of matter states in all 175 models found in a previous work by the author are discussed. Only 20 patterns of representations are found to occur. Accomodation of the minimal supersymmetric standard model (MSSM) spectrum is addressed. States beyond those contained in the MSSM and nonstandard hypercharge normalization are shown to be generic, though some models do allow for the usual hypercharge normalization found in SU(5) embeddings of the standard model gauge group. The minimum value of the hypercharge normalization consistent with accommodation of the MSSM is determined for each model. In some cases, the normalization can be smaller than that corresponding to an SU(5) embedding of the standard model gauge group, similar to what has been found in free fermionic models. Bizarre hypercharges typically occur for exotic states, allowing for matter which does not occur in the decomposition of SU(5) representations—a result which has been noted many times before in four-dimensional string models. Only one of the 20 patterns of representations, comprising seven of the 175 models, is found to be without an anomalous U(1). The sizes of nonvanishing vacuum expectation values induced by the anomalous U(1) are studied. It is found that large radius moduli stabilization may lead to the breakdown of σ-model perturbativity. Various quantities of interest in effective supergravity model building are tabulated for the set of 175 models. In particular, it is found that string moduli masses appear to be generically quite near the gravitino mass. String scale gauge coupling unification is shown to be possible, albeit contrived, in an example model. The intermediate scales of exotic particles are estimated and the degree of fine-tuning is studied.     

Gauge invariant and gauge fixed actions for various higher-spin fields from string field theory

We propose a systematic procedure for extracting gauge invariant and gauge fixed actions for various higher-spin gauge field theories from covariant bosonic open string field theory. By identifying minimal gauge invariant part for the original free string field theory action, we explicitly construct a class of covariantly gauge fixed actions with BRST and anti-BRST invariance. By expanding the actions with respect to the level N   of string states, the actions for various massive fields including higher-spin fields are systematically obtained. As illustrating examples, we explicitly investigate the level N?3$N?3$ part and obtain the consistent actions for massive graviton field, massive 3rd rank symmetric tensor field, or anti-symmetric field. We also investigate the tensionless limit of the actions and explicitly derive the gauge invariant and gauge fixed actions for general rank n symmetric and anti-symmetric tensor fields.     

The cosmological constant,broken gauge theories and 3 K black-body radiation

It is suggested that the cosmological constant today be identified with the one provided by gauge theories at T = 3 K and not T = 0 K or T = 10¹⁵ K as done so far. We then calculate Λ(3 K) in the σ-model, Weinberg-Salam model and Mohapatra and Sidhu model. While an acceptable value is obtained with the rather ideal σ-model, a very small Λ is obtained with the WS model. For the MS model, Λ can be fitted only if at least one of the Higgs mesons has a very light mass (≈3 K).     

The string spectrum on the horizon of a non-extremal black hole

We investigate the conformal string σ-model corresponding to a general five-dimensional non-extremal black hole solution. In the horizon region the theory reduces to an exactly solvable conformal field theory. We determine the modular invariant spectrum of physical string states, which expresses the Rindler momentum operator in terms of three charges and string oscillators. For black holes with winding and Kaluza-Klein charges, we find that states made with only right-moving excitations have ADM mass equal to the black hole ADM mass, and thus they can be used as sources of the gravitational field. A discussion on statistical entropy is included.     

Generalized non-linear σ-models with gauge invariance

Generalizations of the non-linear σ-model and of the CP^N model are considered. They are invariant under a global group G and under a local gauge subgroup H. Whenever G/H defines a symmetric space, we can show that these models are asymptotically free. Furthermore, in two dimensions the local gauge invariance leads to confinement.     

Four-dimensional σ-model on quaternionic projective space

A four-dimensional σ-model based on the quaternionic projective space is constructed. The model possesses SU(2) gauge invariance and has one-instanton solutions analogous to those in the CPⁿ model in D=2.     

Anomalous gauge theories as constrained Hamiltonian systems

Anomalous gauge theories considered as constrained systems are investigated. The effects of chiral anomaly on the canonical structure are examined first for nonlinear σ-model and later for fermionic theory. The breakdown of the Gauss law constraints and the anomalous commutators among them are studied in a systematic way. An intrinsic mass term for gauge fields makes it possible to solve the Gauss law relations as second class constraints. Dirac brackets between the time components of gauge fields are shown to involve anomalous terms. Based upon the Ward-Takahashi identities for gauge symmetry, we investigate anomalous fermionic theory within the framework of path integral approach.     

Superconformal deformation,zero-norm states and space-time symmetries of the superstring theories

We present a formalism to study type II and Heterotic superstrings with massless and massive background fields in the bosonic sector. This formalism is appropriate to study high energy symmetries of the superstring. As an example, we explicitly relate all massless symmetries to the massless zero-norm states in the spectrum. This includes theE ₈ ?E ₈ andSO (32) gauge symmetries in the ten-dimensional Heterotic string. The first (evenG-parity) massive level is briefly described. We then argue the existence of new symmetries for the massive Yang-Mills-like gauge bosons and tensor fields at each fixed mass level. These enlarged stringy symmetries correspond to the decoupling of massive zero-norm states in the spectrum.     

Dynamical symmetry breaking due to vacuum misalignment

We show that under a certain assumption systems with second-class constraints can be regarded as gauge-fixed systems with first-class constraints. The massive Yang-Mills theory, a point particle on a sphere and theO(N) symmetric non-linear σ-model are considered as concrete examples.     

The topological sigma model

We obtain the invariants of Witten's topologicalσ-model by gauge fixing a topological action and using BRST symmetry. The fields and the BRST formalism are interpreted geometrically.     

Supercompositeness from superstrings

String Unified Models based on the k = 1 level of the Kac-Moody Algebra, predict the existence of “exotic” new states which carry fractional electric charges. We analyse the possibility of considering these “exotics” as preonic matter which can be used to form the families and the gauge group breaking higgs scalars. It is proposed that such a formation may occur provided that these states transform non-trivially under a non-Abelian gauge group with a relatively large rank in order to confine them at a sufficiently large scale. Such a situation is natural in string derived unified models, since the role of the confining group can be played by (part of) the Hidden symmetry. As an example, we present a string derived toy model based on the SU(4) × SU(2) _L × SU(2) _R Pati-Salam gauge group.     

Antisymmetric tensor gauge theories and non-linear σ-models

Antisymmetric tensor fields B_μν subject to the gauge transformation δB_μν = ?_μξ_ν ? ?_νξ_μ can describe spinless particles. We investigate the properties of field theories with a “non-abelian generalization” of this invariance. One class of such theories is equivalent to non-linear principal chiral σ-models, another to massive Yang-Mills theories. A supersymmetric analogue in 2 + 2 superspace is constructed and leads to the supersymmetric σ-model defined on a general riemannian manifold.     

XIV. Topology and higher symmetries of the two-dimensional non-linear σ-model

We formulate the O(3) non-linear σ-model and its supersymmetric extension as Abelian gauge theories. As in the Higgs model the instanton number is related to winding properties of the gauge field at infinity. In the new language, a higher symmetry becomes obvious and Pohlmeyer's conserved currents can be derived easily.     

THE LOCALLY PRODUCT STRUCTURE OF INTERNAL SPACE AND SOME OF THE PROPERTIES IN HETEROTIC STRING ACTION

This paper is devoted to a study of the heterotic string action described by a (p,q)-type supersymmetric σ-model involving a two-rank antisymmetric tensor field (Wess-Zumino-Witten term). We discussed a certain quantization procedure of W-Z-W term and its impact on heterotic string by using the locally product structure of internal compact space.     

Fuzzy topology, quantization and gauge invariance

Quantum space-time with Dodson-Zeeman topological structure is studied. In its framework the states of massive particle m correspond to elements of fuzzy set called fuzzy points. Due to their weak (partial) ordering, m space coordinate x acquires principal uncertainty σ _x . Quantization formalism is derived from consideration of m evolution in fuzzy phase space with minimal number of additional assumptions. Particle’s interactions on fuzzy manifold are studied and shown to be gauge invariant.