Meeting the constraint of neutrino—Higgsino mixing in gravity unified theories

In gravity unified theories all operators that are consistent with the local gauge and discrete symmetries are expected to arise in the effective low-energy theory. Given the absence of multiplets like 126 of SO(10) in string models, and assuming that B - L is violated spontaneously to generate light neutrino masses via a seesaw mechanism, it is observed that string theory solutions generically face the problem of producing an excessive mixing mass at the GUT scale, which is some nineteen orders of magnitude larger than the experimental bound of 1 MeV. The suppression of mixing, like proton longevity, thus provides one of the most severe constraints on the validity of any string theory solution. We examine this problem in a class of superstring derived models. We find a family of solutions within this class for which the symmetries of the models and an allowed pattern of VEVs, surprisingly, succeed in adequately suppressing the neutrino-Higgsino mixing terms. At the same time they produce the terms required to generate small neutrino masses via a seesaw mechanism.     

Supersymmetric string theories,superconformal algebras and exceptional groups

We study the relation between extended space-time supersymmetry and extended worldsheet symmetries within the context of four-dimensional heterotic string theories. It is shown how these symmetries follow from an underlying E₇ and E₈ symmetry which also explains the appearance of extra U(1) gauge bosons. Supersymmetry transformation aalways act within a given multiplet of E₇ and E₈.     

The T-dual symmetries of a bosonic string

We investigate whether the symmetry transformations of a bosonic string are connected by T-duality. We start with a standard closed string theory. We continue with a modified open string theory, modified to preserve the symmetry transformations possessed by the closed string theory. Because the string theory is conformally invariant world-sheet field theory, in order to find the transformations which preserve the physics, one has to demand the isomorphism between the conformal field theories corresponding to the initial and the transformed field configurations. We find the symmetry transformations corresponding to the similarity transformation of the energy-momentum tensor, and find that their generators are T-dual. Particularly, we find that the general coordinate and local gauge transformations are T-dual, so we conclude that T-duality in addition to the well-known exchanges, transforms symmetries of the initial and its T-dual theory into each other.     

Event-Symmetry for Superstrings

I apply the principle of event-symmetry tosimple string models and discuss how these lead to theconviction that multiple quantization is linked todimension. It may be that string theory has to beformulated in the absence of space-time, which will thenemerge as a derived property of the dynamics. Anotherinterpretation of the event-symmetric approach whichembodies this is that instantons are fundamental. Just as solitons may be dual to fundamentalparticles, instantons may be dual to space-time events.Event-symmetry is then dual to instanton statistics. Inthat case a unification between particle statistics and gauge symmetry follows on naturally fromthe principle of event-symmetry. I build algebras whichrepresent symmetries of superstring theories extendingevent-symmetry, but which are also isomorphic to an algebra of creation and annihilationoperators for strings of fermionic partons.     

Top quark mass in exophobic Pati-Salam heterotic string model

We analyse the phenomenology of an exemplary exophobic Pati-Salam heterotic string vacuum, in which no exotic fractionally charged states exist in the massless string spectrum. Our model also contains the Higgs representations that are needed to break the gauge symmetry to that of the Standard Model and to generate fermion masses at the electroweak scale. We show that the requirement of a leading mass term for the heavy generation, which is not degenerate with the mass terms of the lighter generations, places an additional strong constraint on the viability of the models. In many models a top quark Yukawa may not exist at all, whereas in others two or more generations may obtain a mass term at leading order. In our exemplary model a mass term at leading order exist only for one family. Additionally, we demonstrate the existence of supersymmetric F- and D-flat directions that give heavy mass to all the colour triplets beyond those of the Standard Model and leave one pair of electroweak Higgs doublets light. Hence, below the Pati-Salam breaking scale, the matter states in our model that are charged under the observable gauge symmetries, consist solely of those of the Minimal Supersymmetric Standard Model.     

BRST symmetry for finite-dimensional invariances: Applications to global zero modes in string theory

We show that the BRST formalism which is commonly used for infinite-dimensional gauge symmetries is also of interest in the case of continuous finite-dimensional symmetries stemming from global properties. We give as examples the simple case of a massless field on a finite-volume space and the less trivial one of the ghost lagrangian in string theory. In the latter case, we obtain an alternative way to derive the integration measure on moduli space. We also exhibit the BRST type invariance which is hidden in the collective coordinate method.     

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.     

A Gauge Invariant Description for the General Conic Constrained Particle from the FJBW Iteration Algorithm

We consider a second-degree algebraic curve describing a general conic constraint imposed on the motion of a massive spinless particle. The problem is trivial at classical level but becomes involved and interesting concerning its quantum counterpart with subtleties in its symplectic structure and symmetries. We start with a second-class version of the general conic constrained particle, which encompasses previous versions of circular and elliptical paths discussed in the literature. By applying the symplectic FJBW iteration program, we proceed on to show how a gauge invariant version for the model can be achieved from the originally second-class system. We pursue the complete constraint analysis in phase space and perform the Faddeev-Jackiw symplectic quantization following the Barcelos-Wotzasek iteration program to unravel the essential aspects of the constraint structure. While in the standard Dirac-Bergmann approach there are four second-class constraints, in the FJBW they reduce to two. By using the symplectic potential obtained in the last step of the FJBW iteration process, we construct a gauge invariant model exhibiting explicitly its BRST symmetry. We obtain the quantum BRST charge and write the Green functions generator for the gauge invariant version. Our results reproduce and neatly generalize the known BRST symmetry of the rigid rotor, clearly showing that this last one constitutes a particular case of a broader class of theories.     

Weighted power counting and Lorentz violating gauge theories. I: General properties

We construct local, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. They contain higher space derivatives, which improve the behavior of propagators at large momenta, but no higher time derivatives. We show that the regularity of the gauge-field propagator privileges a particular spacetime breaking, the one into space and time. We then concentrate on the simplest class of models, study four dimensional examples and discuss a number of issues that arise in our approach, such as the low-energy recovery of Lorentz invariance.     

Gauge coupling unification in realistic free-fermionic string models

We discuss the unification of gauge couplings within the framework of a wide class of realistic free-fermionic string models which have appeared in the literature, including the flipped SU(5), SO(6) × SO(4), and various SU(3) × SU(2) × U(1) models. If the matter spectrum below the string scale is that of the Minimal Supersymmetric Standard Model (MSSM), then string unification is in disagreement with experiment. We therefore examine several effects that may modify the minimal string predictions. First, we develop a systematic procedure for evaluating the one-loop heavy string threshold corrections in free-fermionic string models, and we explicitly evaluate these corrections for each of the realistic models. We find that these string threshold corrections are small, and we provide general arguments explaining why such threshold corrections are suppressed in string theory. Thus heavy thresholds cannot resolve the disagreement with experiment. We also study the effect of non-standard hypercharge normalizations, light SUSY thresholds, and intermediate-scale gauge structure, and similarly conclude that these effects cannot resolve the disagreement with low-energy data. Finally, we examine the effects of additional color triplets and electroweak doublets beyond the MSSM. Although not required in ordinary grand unification scenarios, such states generically appear within the context of certain realistic free-fermionic string models. We show that if these states exist at the appropriate thresholds, then the gauge couplings will indeed unify at the string scale. Thus, within these string models, string unification can be in agreement with low-energy data.     

Stabilizing the axion by discrete gauge symmetries

The axion solution to the strong CP problem makes use of a global Peccei–Quinn U(1) symmetry which is susceptible to violations from quantum gravitational effects. We show how discrete gauge symmetries can protect the axion from such violations. PQ symmetry emerges as an approximate global symmetry from discrete gauge symmetries. Simple models based on Z_N symmetries with N=11,12, etc., are presented realizing the DFSZ axion and the KSVZ axion. The discrete gauge anomalies are canceled by a discrete version of the Green–Schwarz mechanism. In the supersymmetric extension our models provide a natural link between the SUSY breaking scale, the axion scale, and the SUSY-preserving μ term.     

Are (0, 2) models string miracles?

String theory exhibits a number of string miracles. These are “accidental” relations between couplings in the low-energy effective action which cannot be understood in terms of the symmetries of that action. It is shown that the existence of (0, 2) models need not be a string miracle, but can often be understood in terms of a discrete R symmetry. This understanding points to many new (0, 2) models, including some with gauge group SU(3) × SU(2) × U(1). Discrete R symmetries also protect some massless particles from acquiring a mass at special points in the moduli space of the conformal field theory. From a two dimensional point of view, this can be understood in terms of index theorems not only in the R but also in the NS sector. An important tool in the study of string compactification and conformal field theory is the perturbative expansion around a conformal field theory. We prove that the expansion of the space time superpotential around a space-time supersymmetric vacuum does not miss non-perturbative effects (as long as we do not expand around a boundary of moduli space). This shows that certain results which have been obtained to all orders in this expansion are exact. Also, it shows that the construction of the (0, 2) models in perturbation theory around (2, 2) models is exact as well.     

Gauge invariance based on the extrinsic geometry in the rigid string

The string model with the extrinsic curvature is studied which is a gauge invariant field theory with higher order derivatives. We present an equivalent action without any higher order derivatives which keeps the gauge invariance. We point out the difficulty caused by the second class constraints in Dirac's canonical method. Following a new method for dynamical systems with second class constraints, we construct an equivalent model which has no second class constrants but as a new gauge invariance. This gauge invariance guarantees the equivalence between the original model and the new one. We show that the model can be quantized in this formalism. We find the unitarity violation of the model.     

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     

Lattice Wess-Zumino-Witten model and quantum groups

Quantum groups play the role of symmetries of integrable theories in two dimensions. They may be detected on the classical level as Poisson-Lie symmetries of the corresponding phase spaces. We discuss specifically the Wess-Zumino-Witten conformally invariant quantum field model combining two chiral parts which describe the left- and right-moving degrees of freedom. On one hand, the quantum group plays the role of the symmetry of the chiral components of the theory. On the other hand, the model admits a lattice regularization (in Minkowski space) in which the current algebra symmetry of the theory also becomes quantum, providing the simplest example of a quantum group symmetry coupling space-time and internal degrees of freedom. We develop a free field approach to the representation theory of the lattice sl (2)-based current algebra and show how to use it to rigorously construct an exact solution of the quantum SL (2) WZW model on lattice.     

Systematic low-energy effective theory for magnons and charge carriers in an antiferromagnet

By electron or hole doping quantum antiferromagnets may turn into high-temperature superconductors. The low-energy dynamics of antiferromagnets are governed by their Nambu–Goldstone bosons—the magnons—and are described by an effective field theory analogous to chiral perturbation theory for the pions in strong interaction physics. In analogy to baryon chiral perturbation theory—the effective theory for pions and nucleons—we construct a systematic low-energy effective theory for magnons and electrons or holes in an antiferromagnet. The effective theory is universal and makes model-independent predictions for the entire class of antiferromagnetic cuprates. We present a detailed analysis of the symmetries of the Hubbard model and discuss how these symmetries manifest themselves in the effective theory. A complete set of linearly independent leading contributions to the effective action is constructed. The coupling to external electromagnetic fields is also investigated.     

Chiral models in Dilaton—Maxwell Gravity

We study symmetry properties of the Einstein—Maxwell theory nonminimally coupled to the dilaton field. We consider a static case with pure electric (magnetic) Maxwell field and show that the resulting system becomes a nonlinear -model wich possesses a chiral representation. We construct the corresponding chiral matrix and establish a representation which is related to the pair of Ernst-like potentials. These potentials are used for separation of the symmetry group into the gauge and nongauge (charging) sectors. New variables, which linearize the action of charging symmetries, are also established; a solution generation technique based on the use of charging symmetries is formulated. This technique is used for generation of the electrically (magnetically) charged dilatonic fields from the static General Relativity ones.     

Bianchi type I cosmology in generalized Saez–Ballester theory via Noether gauge symmetry

In this paper, we investigate the generalized Saez–Ballester scalar–tensor theory of gravity via Noether gauge symmetry (NGS) in the background of Bianchi type I cosmological spacetime. We start with the Lagrangian of our model and calculate its gauge symmetries and corresponding invariant quantities. We obtain the potential function for the scalar field in the exponential form. For all the symmetries obtained, we determine the gauge functions corresponding to each gauge symmetry which include constant and dynamic gauge. We discuss cosmological implications of our model and show that it is compatible with the observational data.     

Local grand unification in the heterotic landscape

We consider the possibility that the unification of the electroweak interactions and the strong force arises from string theory, at energies significantly lower than the string scale. As a tool, an effective grand unified field theory in six dimensions is derived from an anisotropic orbifold compactification of the heterotic string. It is explicitly shown that all anomalies cancel in the model, though anomalous Abelian gauge symmetries are present locally at the boundary singularities. In the supersymmetric vacuum additional interactions arise from higher‐dimensional operators. We develop methods that relate the couplings of the effective theory to the location of the vacuum, and find that unbroken discrete symmetries play an important role for the phenomenology of orbifold models. An efficient algorithm for the calculation of the superpotential to arbitrary order is developed, based on symmetry arguments. We furthermore present a correspondence between bulk fields of the orbifold model in six dimensions, and the moduli fields that arise from compactifying four internal dimensions on a manifold with non‐trivial gauge background.     

Exotic Tensor Gauge Theory and Duality

 Gauge fields in exotic representations of the Lorentz group in D dimensions – i.e. ones which are tensors of mixed symmetry corresponding to Young tableaux with arbitrary numbers of rows and columns – naturally arise through massive string modes and in dualising gravity and other theories in higher dimensions. We generalise the formalism of differential forms to allow the discussion of arbitrary gauge fields. We present the gauge symmetries, field strengths, field equations and actions for the free theory, and construct the various dual theories. In particular, we discuss linearised gravity in arbitrary dimensions, and its two dual forms. Received: 9 September 2002 / Accepted: 22 October 2002 Published online: 21 February 2003 Communicated by A. Connes