Chiral Representation Research Articles

Topologizations of Chiral Representations

We analyze and compare two families of topologies that have been proposed for representation spaces of chiral algebras by Huang and Gaberdiel & Goddard respectively. We show, in particular, that for suitable pairs the topology of Gaberdiel & Goddard is coarser. We also give a new proof that the chiral two-point blocks are continuous in the topology of Huang.

Particle-like solutions to higher-order curvature Einstein–Yang–Mills systems in d dimensions

We consider the superposition of the first two members of the gravitational hierarchy (Einstein plus first Gauss–Bonnet (GB)) interacting with the superposition of the first two members of the Yang–Mills (YM) hierarchy, in d dimensions. The YM fields are taken to be in the chiral representations of the gauge groups, (i) SO(±)(d), and (ii) SO(±)(d − 1), respectively, for (i) even d and (ii) odd d. Such systems can occur in the low energy effective action of string theory. Particle-like solutions in dimensions d = 6, 8, and d = 7, are constructed, respectively. Our results reveal qualitatively new properties featuring double-branch solutions with critical behaviour. In this preliminary study, we have restricted numerical study to one-node solutions.

Chiral symmetry of baryons

Chiral symmetry aspects for baryon properties are studied. After a brief discussion on general framework, we introduce two distinctive chiral group representations for baryons: the naive and mirror assignments. Using linear sigma models, nucleon properties are studied in both representations. Finally, we propose an experiment to distinguish the two assignments in pion and eta productions.

A conjecture about hadrons

We conjecture that in the chiral limit of QCD the spectrum of hadrons is comprised of decoupled, reducible chiral multiplets. A simple rule is developed which identifies the chiral representations filled out by the ground-state hadrons. Our arguments are based on the algebraic structure of superconvergence relations derived by Weinberg from the high-energy behavior of pion–hadron scattering amplitudes.

Chiral Symmetry Aspects of Positive and Negative Parity Baryons

Chiral symmetry aspects for baryon properties are studied. After a brief discussion on general framework, we introduce two distinctive chiral group representations for baryons: the naive and mirror assignments. Using linear sigma models, nucleon properties are studied in both representations. Finally, we propose an experiment to distinguish the two assignments in the reactions of pion and eta productions.

Intersecting branes flip SU(5)

Within a toroidal orbifold framework, we exhibit intersecting brane-world constructions of flipped SU(5)× U(1) GUT models with various numbers of generations, other chiral matter representations and Higgs representations. We exhibit orientifold constructions with integer winding numbers that yield 8 or more conventional SU(5) generations, and orbifold constructions with fractional winding numbers that yield flipped SU(5)× U(1) models with just 3 conventional generations. Some of these models have candidates for the 5 and 5 Higgs representations needed for electroweak symmetry breaking, but not for the 10 and 10 representations needed for GUT symmetry breaking. We have also derived models with complete GUT and electroweak Higgs sectors, but these have undesirable extra chiral matter.

Logarithmic conformal field theories via logarithmic deformations

We construct logarithmic conformal field theories starting from an ordinary conformal field theory—with a chiral algebra C and the corresponding space of states V—via a two-step construction: (i) deforming the chiral algebra representation on V⊗End K[[ z, z −1]], where K is an auxiliary finite-dimensional vector space, and (ii) extending C by operators corresponding to the endomorphisms End K. For K= C 2 , with End K being the two-dimensional Clifford algebra, our construction results in extending C by an operator that can be thought of as ∂ −1 E, where ∮ E is a fermionic screening. This covers the (2, p) Virasoro minimal models as well as the sl (2) WZW theory.

Quaternionic Lorentz Group and Dirac Equation

We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time transformations, we combine these one-dimensional spinors into bi-dimensional column vectors. From the transformation properties of the two-component spinors, we derive a quaternionic chiral representation for the space-time algebra. Finally, we obtain a quaternionic bi-dimensional version of the Dirac equation.

The ππS-wave scattering lengths

We match the known chiral perturbation theory representation of the ππ scattering amplitude to two loops with a phenomenological description that relies on the Roy equations. On this basis, the corrections to Weinberg's low energy theorems for the S-wave scattering lengths are worked out to second order in the expansion in powers of the quark masses. The resulting predictions, a 0 0=0.220±0.005, a 0 2=−0.0444±0.0010, contain remarkably small uncertainties and thus allow a very sensitive experimental test of the hypothesis that the quark condensate is the leading order parameter of the spontaneously broken chiral symmetry.

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 σ-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.

Low-energy constants from high-energy theorems

New constraints on resonance saturation in chiral perturbation theory are investigated. These constraints arise because each consistent saturation scheme must map to a representation of the full QCD chiral symmetry group. The low-energy constants of chiral perturbation theory are then related by a set of mixing angles. It is shown that vector meson dominance is a consequence of the fact that nature has chosen the lowest-dimensional nontrivial chiral representation. It is further shown that chiral symmetry places an upper bound on the mass of the lightest scalar in the hadron spectrum.

D=5 simple supergravity on AdS3× S2 and N=4 superconformal field theory

We study the Kaluza–Klein spectrum of D=5 simple supergravity on S 2 with special interest in the relation to a two-dimensional N=4 superconformal field theory. The spectrum is obtained around the maximally supersymmetric Freund–Rubin-like background AdS 3× S 2 by closely following the well-known techniques developed in D=11 supergravity. All the vector excitations turn out to be “(anti-)self-dual”, having only one dynamical degree of freedom. The representation theory for the Lie superalgebra SU(1,1|2) is developed by means of the oscillator method. We calculate the conformal weight of the boundary operator by estimating the asymptotic behavior of the wave function for each Kaluza–Klein mode. All the towers of particles are shown to fall into four infinite series of chiral primary representations of SU(1,1|2)× SL(2, R) (direct product), or OSp(2,2|2;−1)≅ SU(1,1|2)× SL(2, R) (semi-direct product).

Exact solutions of Dirac equation for neutrinos in presence of external fields

Exact solutions of the Dirac equation in a chiral representation for neutrinos in the presence of external stresses are investigated in terms of special functions, using the algebraic method of the separation of variables in Cartesian, cylindrical, and spherical coordinates.

Lattice QCD without tuning, mixing and current renormalization

The classically perfect action of QCD requires no tuning to get the pion massless in the broken phase: the critical bare mass m q c is zero. Neither the vector nor the flavour non-singlet axial vector currents need renormalization. Further, there is no mixing between 4-fermion operators in different chiral representations. The order parameter of chiral symmetry requires, however, a subtraction which is given here explicitly. These results are based on the fact that the fixed point action satisfies the Ginsparg-Wilson remnant chiral symmetry condition. On chiral symmetry related questions any other local solution of this condition will produce similar results.

Chiral gauge theories from D-branes

We construct brane configurations leading to chiral four dimensional N=1 supersymmetric gauge theories. The brane realizations consist of intersecting Neveu-Schwarz five-branes and Dirichlet four-branes in non-flat spacetime backgrounds. We discuss in some detail the construction in a C^2/Z_M orbifold background. The infrared theory on the four-brane worldvolume is a four dimensional N=1 SU(N)^M gauge theory with chiral matter representations. We discuss various consistency checks and show that the spectral curves describing the Coulomb phase of the theory can be obtained once the orbifold brane construction is embedded in M-theory. We also discuss the addition of extra vectorlike matter and other interesting generalizations.

String scale unification in an SU(6) × SU(2) GUT

We construct and analyze an SU (6) × SU (2) GUT. The model is k = 1 string embedable in the sense that we employ only chiral representations allowed at the k = 1 level of the associated Kač-Moody Algebra. Both cases SU (6) × SU (2) L and SU (6) × SU (2) R are realized. The model is characterized by the SU (6) × SU (2) → SU (4) × SU (2) × SU (2) breaking scale M X , and the SU (4) × SU (2) × SU (2) → SU (3) C × SU (2) L × U (1) Y breaking scale M R . The spectrum bellow M R includes an extra pair of charge- 1 3 colour-triplets of mass M I ≤ M R that does not couple to matter fields and, possibly, an extra pair of isodoublets. Above M X the SU (6) and SU (2) gauge couplings always unify at a scale which can be taken to be the string unification scale M s ∼ 5 × 10 17 GeV. The model has Yukawa coupling unification since quarks and leptons obtain their masses from a single Yukawa coupling. Neutrinos obtain acceptably small masses through a see-saw mechanism. Coloured triplets that couple to matter fields are naturally split from the coexisting isodoublets without the need of any numerical fine tuning.

Chiral multiplets of hadron currents

Using group theoretical methods, we enumerate possible chiral representations in which hadron interpolating currents can be classified. We give simple examples of currents in each representation, some of which are well known. The classification enables one to find relations among current vacuum correlators in a chirally and/or axial U(1) symmetric phase of QCD in a straightforward way. Besides recovering many well-known relations among two-point correlation functions, a number of novel relations are found.

Matrix Ernst potentials for Einstein-Maxwell-dilaton-axion with multiple vector fields

We show that the Einstein-Maxwell-dilaton-axion system with multiple vector fields (bosonic sector of the D = 4, N = 4 supergravity) restricted to spacetimes possessing a non-null Killing vector field admits a concise representation in terms of the Ernst-type matrix valued potentials. A constructive derivation of the SWIP solutions is given and a colliding waves counterpart of the DARN-NUT solution is obtained. SU( m, m) chiral representation of the two-dimensionally reduced system is derived and the corresponding Kramer-Neugebauer-type map is presented.

A covariant approach to gauged 2D self-dual fields

It is shown that the chiral boson model of Floreanini and Jackiw (FJ) and of MClain, Wu and Yu (MWY) are two different representations of the same chiral theory, each displaying different aspects of the bosonic representation for chiral fields: while in the FJ side the spectrum is quite evident from the equations of motion, it lacks manifest covariance making the coupling to external fields particularly difficult. On the MWY side, a symmetry hidden in the FJ version is apparent due to the presence of infinite scalar Wess-Zumino fields that carry the chiral representation in this side of the problem. On the other hand the evidence of physical spectrum is lost. In this work we show how to go from one representation to the other and find that the FJ chiral field is a collective field built by a linear combination of all MWY scalar fields. Using then the manifest covariance of the MWY representation we study the problem of coupling bosonic chiral fields to a background gauge field.

GAUGINO CONDENSATION IN THE CHIRAL AND LINEAR REPRESENTATIONS OF THE DILATON

String effective theories with N=1 supersymmetry in four dimensions are the subject of this discussion. Gaugino condensation in the chiral representation of the dilaton is reviewed in the truncated formalism in the UK(1) superspace. By the use of the supersymmetric duality of the dilaton the same investigation is made in the linear representation of the dilaton. We show that for the simple case of one gaugino condensate the results concerning supersymmetry breaking are independent of the representation of the dilaton.