Chiral Field Theory Research Articles

Spectral discontinuities in constrained dynamical models

As examples of models having interesting constraint structures, we derive a quantum mechanical model from the spatial freezing of a well-known relativistic field theory—the chiral Schwinger model. We apply the Hamiltonian constraint analysis of Dirac (1964 Lectures on Quantum Mechanics (New York: Belfer Graduate School of Science)) and find that the nature of constraints depends critically on a c-number parameter present in the model. Thus, a change in the parameter alters the number of dynamical modes in an abrupt and non-perturbative way. We have obtained new real energy levels for the quantum mechanical model as we explore complex domains in the parameter space. These were forbidden in the parent chiral Schwinger field theory where the analogue Jackiw–Rajaraman parameter is restricted to be real. We explicitly show the existence of modes that satisfy the higher derivative Pais–Uhlenbeck form of dynamics (Pais and Uhlenbeck 1950 Phys. Rev. 79 145). We also show that the Cranking model (Valatin 1956 Proc. R. Soc. A 238 122), well known in nuclear physics, can be interpreted as a spatially frozen version of another well-studied relativistic field theory in (2 + 1)-dimensions—the Maxwell–Chern–Simons–Proca model (Deser et al 1982 Phys. Rev. Lett. 48 975, Deser et al 1982 Ann. Phys. 140 372).

Localization over complex-analytic groupoids and conformal renormalization

We present a higher index theorem for actions of a discrete group on the complex plane by local conformal mappings. The novelty is the use of the local anomaly formula established in a previous paper, which represents the bivariant Chern character of a quasihomomorphism as the chiral anomaly associated to a renormalized noncommutative chiral field theory. In the present situation the geometry is non-metric and the corresponding field theory can be renormalized in a purely conformal way, exploiting the complex-analytic structure of the groupoid only. The index formula is automatically localized at the automorphism subset of the groupoid and involves a cap-product with the sum of two different cyclic cocycles over the groupoid algebra. The first cocycle is a trace involving a generalization of the Lefschetz numbers to higher-order fixed points. The second cocycle is a noncommutative Todd class, constructed from the modular automorphism group of the algebra.

Holographic renormalization group flow dual to attractor flow in extremal black holes

We extend the discussion of the 'Kerr/CFT correspondence' and its recent developments to the more general gauge/gravity correspondence in the full extremal black hole space-time of the bulk by using a technique of the holographic renormalization group (RG) flow. It is conjectured that the extremal black hole space-time is holographically dual to the chiral two-dimensional field theory. Our example is a typical four-dimensional Reissner-Nordstrom black hole, a system in which the M5-brane is wrapped on four cycles of Calabi-Yau threefold. In the five-dimensional supergravity viewpoint, this near horizon geometry is AdS{sub 3}xS{sup 2}, and three-dimensional gravity coupled to moduli fields is effectively obtained after a dimensional reduction on S{sup 2}. Constructing the Hamilton-Jacobi equation, we define the holographic RG flow from the three-dimensional gravity. The central charge of the Virasoro algebra is calculable from the conformal anomaly at the point where the beta function defined from the gravity side becomes zero. In general, we can also identify the c function of the dual two-dimensional field theory. We show that these flow equations are completely equivalent to not only BPS but also non-BPS attractor flow equations of the moduli fields. The attractor mechanism by which the values of the moduli fieldsmore » are fixed at the event horizon of the extremal black hole can be understood equivalently to the fact that the RG flows are fixed at the critical points in the dual field theory.« less

Modern theory of nuclear forces: status and perspectives

I present and discuss recent results on nuclear forces and few-nucleon systems obtained in the framework of chiral effective nuclear field theory.

Algebraic Supersymmetry: A Case Study

The treatment of supersymmetry is known to cause difficulties in the C*–algebraic framework of relativistic quantum field theory; several no–go theorems indicate that super–derivations and super–KMS functionals must be quite singular objects in a C*–algebraic setting. In order to clarify the situation, a simple supersymmetric chiral field theory of a free Fermi and Bose field defined on $${\mathbb{R}}$$ is analyzed. It is shown that a meaningful C*–version of this model can be based on the tensor product of a CAR–algebra and a novel version of a CCR–algebra, the “resolvent algebra”. The elements of this resolvent algebra serve as mollifiers for the super–derivation. Within this model, unbounded (yet locally bounded) graded KMS–functionals are constructed and proven to be supersymmetric. From these KMS–functionals, Chern characters are obtained by generalizing formulae of Kastler and of Jaffe, Lesniewski and Osterwalder. The characters are used to define cyclic cocycles in the sense of Connes’ noncommutative geometry which are “locally entire”.

EDGE STATE IN ATOMIC HALL EFFECT

We study the edge state of atomic Hall fluids. It is described by a chiral 1D bosonic field theory and the atomic excitations are a type of bosonic Luttinger liquid. We investigate the dynamical property of edge state and propose an experiment to measure the topological number, which could be verified experimentally in future.

Puzzles for matrix models of chiral field theories

AbstractWe summarize the field‐theory/matrix model correspondence for a chiral 𝒩= 1 model with matter in the adjoint, antisymmetric and conjugate symmetric representations as well as eight fundamentals to cancel the chiral anomaly. The associated holomorphic matrix model is consistent only for two fundamental fields, which requires a modification of the original Dijkgraaf‐Vafa conjecture. The modified correspondence holds in spite of this mismatch.

Chiral field theories, Konishi anomalies and matrix models

We study a chiral N=1, U(N) field theory in the context of the Dijkgraaf-Vafa correspondence. Our model contains one adjoint, one conjugate symmetric and one antisymmetric chiral multiplet, as well as eight fundamentals. We compute the generalized Konishi anomalies and compare the chiral ring relations they induce with the loop equations of the (intrinsically holomorphic) matrix model defined by the tree-level superpotential of the field theory. Surprisingly, we find that the matrix model is well-defined only if the number of flavors equals two! Despite this mismatch, we show that the 1/N expansion of the loop equations agrees with the generalized Konishi constraints. This indicates that the matrix model - gauge theory correspondence should generally be modified when applied to theories with net chirality. We also show that this chiral theory produces the same gaugino superpotential as a nonchiral SO(N) model with a single symmetric multiplet and a polynomial superpotential.

Dynamically spontaneous symmetry breaking and masses of lightest nonet scalar mesons as composite Higgs bosons

Based on the (approximate) chiral symmetry of QCD Lagrangian and the bound state assumption of effective meson fields, a nonlinearly realized effective chiral Lagrangian for meson fields is obtained from integrating out the quark fields by using the new finite regularization method. As the new method preserves the symmetry principles of the original theory and meanwhile keeps the finite quadratic term given by a physically meaningful characteristic energy scale $M_c$, it then leads to a dynamically spontaneous symmetry breaking in the effective chiral field theory. The gap equations are obtained as the conditions of minimal effective potential in the effective theory. The instanton effects are included via the induced interactions discovered by 't Hooft and found to play an important role in obtaining the physical solutions for the gap equations. The lightest nonet scalar mesons($\sigma$, $f_0$, $a_0$ and $\kappa$) appearing as the chiral partners of the nonet pseudoscalar mesons are found to be composite Higgs bosons with masses below the chiral symmetry breaking scale $\Lambda_{\chi} \sim 1.2$ GeV. In particular, the mass of the singlet scalar (or the $\sigma$) is found to be $m_{\sigma} \simeq 677$ MeV.

Chiral field theories from conifolds

We discuss the geometric engineering and large n transition for an N=1 U(n) chiral gauge theory with one adjoint, one conjugate symmetric, one antisymmetric and eight fundamental chiral multiplets. Our IIB realization involves an orientifold of a non-compact Calabi-Yau A_2 fibration, together with D5-branes wrapping the exceptional curves of its resolution as well as the orientifold fixed locus. We give a detailed discussion of this background and of its relation to the Hanany-Witten realization of the same theory. In particular, we argue that the T-duality relating the two constructions maps the Z_2 orientifold of the Hanany-Witten realization into a Z_4 orientifold in type IIB. We also discuss the related engineering of theories with SO/Sp gauge groups and symmetric or antisymmetric matter.

Gauging by Stückelberg field-shifting symmetry

We embed second class constrained systems by a formalism that combines concepts of the BFFT method and the unfixing gauge formalism. As a result, we obtain a gauge-invariant system where the introduction of the Wess–Zumino (WZ) field is essential. The initial phase-space variables are gauging with the introduction of the WZ field, a procedure that resembles the Stückelberg field-shifting formalism. In some cases, it is possible to eliminate the WZ field and, therefore, obtain an invariant system written only as a function of the original phase-space variables. We apply this formalism to important physical models: the reduced-SU(2) Skyrme model and the two-dimensional chiral bosons field theory. In these systems, the gauge-invariant Hamiltonians are derived in a very simple way when compared with other usual formalisms.

GAUGING BY SYMMETRIES

We propose a new procedure to embed second class systems by introducing Wess–Zumino (WZ) fields in order to unveil hidden symmetries existent in the models. This formalism is based on the direct imposition that the new Hamiltonian must be invariant by gauge-symmetry transformations. An interesting feature in this approach is the possibility to find a representation for the WZ fields in a convenient way, which leads to preserve the gauge symmetry in the original phase space. Consequently, the gauge-invariant Hamiltonian can be written only in terms of the original phase-space variables. In this situation, the WZ variables are only auxiliary tools that permit to reveal the hidden symmetries present in the original second class model. We apply this formalism to important physical models: the reduced-SU(2) Skyrme model, the Chern–Simons–Proca quantum mechanics and the chiral bosons field theory. In all these systems, the gauge-invariant Hamiltonians are derived in a very simple way.

EVOLUTION OF STRUCTURE FUNCTIONS AND THEIR MOMENTS IN CHIRAL FIELD THEORY

Evolution of structure functions and their moments at low and moderate Q2 is studied in the chiral field theory. Evolution equations based on perturbation expansion in the coupling constant of the effective theory are derived and solved for the moments. The kernels of evolution arising from different processes have been calculated with contributions from direct and cross channels, the interference terms being non-negligible in the kinematic regions under consideration. This is shown to lead to flavor-dependence of the kernels which manifests in observable effects. The invalidity of the probabilistic approach to the evolution process is also pointed out.

Local models for intersecting brane worlds

We describe the construction of configurations of D6-branes wrapped on compact 3-cycles intersecting at points in non-compact Calabi-Yau threefolds. Such constructions provide local models of intersecting brane worlds, and describe sectors of four-dimensional gauge theories with chiral fermions. We present several classes of non-compact manifolds with compact 3-cycles intersecting at points, and discuss the rules required for model building with wrapped D6-branes. The rules to build 3-cycles are simple, and allow easy computation of chiral spectra, RR tadpoles and the amount of preserved supersymmetry. We present several explicit examples of these constructions, some of which have Standard Model like gauge group and three quark-lepton generations. In some cases, mirror symmetry relates the models to other constructions used in phenomenological D-brane model building, like D-branes at singularities. Some simple N=1 supersymmetric configurations may lead to relatively tractable G_2 manifolds upon lift to M-theory, which would be non-compact but nevertheless yield four-dimensional chiral gauge field theories.

On a low energy bound in a class of chiral field theories with solitons

A low energy bound for static classical solutions in a class of chiral solitonic field theories related to the infrared physics of the SU(N) Yang–Mills theory is established.

Chiral bosonic field theories and the quantum Hall effect

The gauge-transformation properties of the actions of certain scalar and Chern–Simons theories are investigated, including contributions from the boundary. By imposing chirality constraints on the fields, these types of theories can be used to describe the quantum Hall effect. It is shown that the corresponding equation of motion for the associated current for the theory generates an anomaly, which can be related directly to the Hall conductivity. PACS Nos.: 73.43, 03.70, 11.10, 11.30R

Formula omitted] symmetry breaking, scalar mesons and the nucleon spin problem in an effective chiral field theory

We establish a relationship between the scalar-meson spectrum and the U A(1) symmetry-breaking 't Hooft interaction on one hand and the constituent-quark flavor singlet axial coupling constant g A,Q (0) on the other, using an effective chiral quark field theory. This analysis leads to the new sum rule g A,Q (0)[m η′ 2+m η 2−2m K 2]≃−m f′ 0 2−m f 0 2+2m K 0 ∗ 2 , where η′,η,K are the observed pseudoscalar mesons, K 0 ∗ is the strange scalar meson at 1430 MeV and f 0,f′ 0 are “the eighth and the ninth” scalar mesons. We discuss the relationship between the constituent-quark flavor singlet axial coupling constant g A,Q (0) and the nucleon one g A,N (0) (“nucleon spin content”) in this effective field theory. We also relate g A,Q (0) as well as the flavour octet constituent-quark axial coupling constant g A,Q (1) to vector and axial-vector meson masses in general as well as in the tight-binding limit.

Second-quantization picture of the edge currents in the fractional quantum Hall effect

We study the quantum theory of two-dimensional electrons in a magnetic field and an electric field generated by a homogeneous background. The dynamics separates into a microscopic and macroscopic mode. The latter is a circular Hall current which is described by a chiral quantum field theory. It is shown how in this second quantized picture a Laughlin-type wave function emerges.

Chiral bosonic field theories and the quantum Hall effect

Chiral bosonic field theories and the quantum Hall effect

Pion–nucleon scattering in an effective chiral field theory with explicit spin- [formula omitted] fields

We analyze elastic–pion nucleon scattering to third order in the so-called small scale expansion. It is based on an effective Lagrangian including pions, nucleons and deltas as active degrees of freedom and counting external momenta, the pion mass and the nucleon–delta mass splitting as small parameters. The fermion fields are considered as very heavy. We present results for phase shifts, threshold parameters and the sigma term. We discuss the convergence of the approach. A detailed comparison with results obtained in heavy-baryon chiral perturbation theory to third and fourth order is also given.