Localization of matters on the bent brane in bulk

We investigate the possibility of localizing various matter fields on a bent AdS₄ (dS₄) thick brane in AdS₅. For spin 0 scalar field, we find a massless zero mode and an excited state which can be localized on the bent brane. For spin 1 vector field, there is only a massless zero mode on the bent brane. For spin 1/2 fermion field, it is shown that, in the case of no Yukawa coupling of scalar-fermion, there is no existence of localized massless zero mode for both left and right chiral fermions. In order to localize massless fermions, some kind of Yukawa coupling must be included. We study two types of Yukawa couplings as examples. Localization property of chiral fermions is related to the parameters of the brane model, the Yukawa coupling constant and the cosmological constant of the 4-dimensional space–time.     

Super-WZNW with reductions to supersymmetric and fermionic integrable models

A systematic construction for an action describing a class of supersymmetric integrable models as well as for pure fermionic theories is discussed in terms of the gauged WZNW model associated to half integer graded affine Kac–Moody algebras. Explicit examples of the N=1,2 super-sinh(sine)-Gordon models are discussed in detail. Pure fermionic theories arises for cosets sl(p,1)/sl(p)u(1) when a maximal kernel condition is fulfilled. The integrability condition for such models is discussed and it is shown that the simplest example when p=2 leads to the constrained Bukhvostov–Lipatov, Thirring, scalar massive and pseudo-scalar massless Gross–Neveu models.     

Multiscale Formalism for Correlation Functions of Fermions. Infrared Analysis of the Tridimensional Gross–Neveu Model

We present a multiscale formalism for fermionic systems (with a smooth UV cutoff ) establishing a trivial link between the correlation functions and the effective potential flow, and study the k-point truncated functions of the tridimensional Gross–Neveu model. A new efficient method is used to bound these correlation functions and show polynomial tree decay for long distances. We are guided by a block lattice mechanism with a property of orthogonality between terms in different scales, which leads to simple formulas for the correlations.     

Wilson fermions in a two-dimensional model

Wilson's action for fermions on a lattice is compared to the continuum action in a model obtained from the chiral Gross-Neveu model by performing a chiral transformation. The local definition of the axial current leads to two anomalies unrelated by the constraint of Lorentz invariance. In the large-N limit, the mass counterterm of the action is determined; this term is unnecessary in the Osterwalder-Seiler regularization. An expansion in the fermion propagator and in the axial current coupling may be formulated and summed to all orders for large N.     

Critical boundary sine-Gordon revisited

We revisit the exact solution of the two space-time dimensional quantum field theory of a free massless boson with a periodic boundary interaction and self-dual period. We analyze the model by using a mapping to free fermions with a boundary mass term originally suggested in Ref. [J. Polchinski, L. Thorlacius, Phys. Rev. D 50 (1994) 622]. We find that the entire SL (2, C) family of boundary states of a single boson are boundary sine-Gordon states and we derive a simple explicit expression for the boundary state in fermion variables and as a function of sine-Gordon coupling constants. We use this expression to compute the partition function. We observe that the solution of the model has a strong–weak coupling generalization of T-duality. We then examine a class of recently discovered conformal boundary states for compact bosons with radii which are rational numbers times the self-dual radius. These have simple expression in fermion variables. We postulate sine-Gordon-like field theories with discrete gauge symmetries for which they are the appropriate boundary states.     

Instability at the origin in (2+1)-dimensional QED

Stability at the origin in (2+1)-dimensional QED withN four-component Dirac fermions is studied by keeping the leading order terms in 1/N in the effective potential. It is shown that the effective potential in the direction of fermion wave-function renormalization is always unstable for any flavor numberN, which reconfirms that chiral symmetry is broken for anyN.     

Fermionic solutions of chiral Gross–Neveu and Bogoliubov–de Gennes systems in nonlinear Schrödinger hierarchy

The chiral Gross–Neveu model or equivalently the linearized Bogoliubov–de Gennes equation has been mapped to the nonlinear Schrödinger (NLS) hierarchy in the Ablowitz–Kaup–Newell–Segur formalism by Correa, Dunne and Plyushchay. We derive the general expression for exact fermionic solutions for all gap functions in the arbitrary order of the NLS hierarchy. We also find that the energy spectrum of the n  -th NLS hierarchy generally has n+1$n+1$ gaps. As an illustration, we present the self-consistent two-complex-kink solution with four real parameters and two fermion bound states. The two kinks can be placed at any position and have phase shifts. When the two kinks are well separated, the fermion bound states are localized around each kink in most parameter region. When two kinks with phase shifts close to each other are placed at distance as short as possible, the both fermion bound states have two peaks at the two kinks, i.e., the delocalization of the bound states occurs.     

The Phase Structure of a Generalized Gross–Neveu Model in (2+1)-Dimensional Space–Time

The phase structure of a (2+1)-dimensional Gross–Neveu model with four different channels of fermion–antifermion interaction, and, correspondingly, four different coupling constants, is studied. It is shown that the model describes five different phases of the interaction of planar fermions in which either spatial parity or chiral symmetry can be broken. The existence of a phase that is characterized by simultaneous spontaneous breaking of both these symmetries that was not observed earlier in such models is demonstrated.     

A Wilson-Yukawa Model with undoubled chiral fermions in 2D

We consider the fermion mass spectrum in the strong coupling vortex phase (VXS) of a lattice fermion-scalar model with a global U(1)_L × U(1)_R, in two dimensions, in the context of a recently proposed two-cutoff lattice formulation. The fermion doublers are made massive by a strong Wilson-Yukawa coupling, but in contrast with the standard formulation of these type of models, in which the light fermion spectrum was found to be vector-like, we find massless fermions with chiral quantum numbers at finite lattice spacing. When the global symmetry is gauged, this model is expected to give rise to a lattice chiral gauge theory.     

(Z N×) n−1 generalization of the chiral Potts model

We show that theR-matrix which intertwines twon-by-N ^n–1 state cyclicL-operators related with a generalization ofU _q(sl(n)) algebra can be considered as a Boltzmann weight of four-spin box for a lattice model with two-spin interaction just as theR-matrix of the checkerboard chiral Potts model. The rapidity variables lie on the algebraic curve of the genusg=N ^{2(n–1)((n–1)N-n)+1} defined by 2n–3 independent moduli. This curve is a natural generalization of the curve which appeared in the chiral Potts model. Factorization properties of theL-operator and its connection to the SOS models are also discussed.     

Strong coupling Hubbard model and superconductivity

We have shown that systems open to fermion number fluctuations and described by the Hubbard model can be superconducting. This superconductivity must be accompanied by a special type of magnetic order. A unitary transformation is explicitly constructed by which the large interaction term of the Hubbard model is exactly diagonalized. Order parameters of the system related to Green functions of fermions are explicitly evaluated in the strong coupling limit. This model applied to copper-oxygen chains provides a theoretical explanation of highT _c superconductivity in compounds of the type YBa₂Cu₃O_7–x .Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.     

Numerical study of dense adjoint matter in two color QCD

We identify the global symmetries of SU(2) lattice gauge theory with N flavors of staggered fermion in the presence of a quark chemical potential , for fermions in both fundamental and adjoint representations, and anticipate likely patterns of symmetry breaking at both low and high densities. Results from numerical simulations of the model with N = 1 adjoint flavor on a lattice are presented, using both hybrid Monte Carlo and Two-Step Multi-Boson algorithms. It is shown that the sign of the fermion determinant starts to fluctuate once the model enters a phase with non-zero baryon charge density. HMC simulations are not ergodic in this regime, but TSMB simulations retain ergodicity even in the dense phase, and in addition appear to show superior decorrelation. The HMC results for the equation of state and the pion mass show good quantitative agreement with the predictions of chiral perturbation theory, which should hold only for . The TSMB results incorporating the sign of the determinant support a delayed onset transition, consistent with the pattern of symmetry breaking expected for N = 1. Received: 20 June 2000 / Published online: 31 August 2000     

Exotic phases of finite temperature gauge theories

We calculate the phase diagrams at high temperature of SU(N) gauge theories with massive fermions by minimizing the one-loop effective potential. Considering fermions in the adjoint (Adj) representation at various N we observe a variety of phases when N_f2 Majorana flavours and periodic boundary conditions are applied to fermions. Also the confined phase is perturbatively accessible. For N=3, we add Fundamental (F) representation fermions with antiperiodic boundary conditions to adjoint QCD to show how the Z(3)-symmetry breaks in the confined phase.     

Optimised Dirac operators on the lattice: construction,properties and applications

We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross‐Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so‐called overlap‐hypercube fermions in the two‐flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p‐regime and in the ϵ‐regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian – the chiral condensate and the pion decay constant – from QCD simulations with extremely light quarks.     

Structural Aspects of the Fermion-Boson Mapping in Two-Dimensional Gauge and Anomalous Gauge Theories with Massive Fermions

Using a synthesis of the functional integral and operator approaches we discuss the fermion-boson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In QED₂ with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In anomalous chiral QED₂ with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of Θ-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content.     

Effective lagrangian and dynamical symmetry breaking in strongly coupled lattice QCD

A method is proposed for computing effective lagrangians in QCD with N colors using lattice regularization. The meson field lagrangian is worked out in detail in the strong coupling limit with various lattice fermion formulations. For generalized Susskind fermions the spontaneous breakdown U(n) ? U(n) → U(n) (diagonal) is found at large N and a generalized version of the non-linear σ model emerges in a natural way. The Nambu-Goldstone spectrum is investigated and a continuous transition is made to Wilson fermions, for which the effective potential and the ππ scattering amplitude are tested on chiral symmetry. Large d (=dimension) approximations are compared with the large N limit and applied to N = 3.     

Large N expansion for strongly-coupled boson–fermion mixtures

We study a many-body mixture of an equal number of bosons and two-component fermions with a strong contact attraction. In this system bosons and fermions can be paired into composite fermions. We construct a large N extension where both bosons and fermions have the extra large N degrees of freedom and the boson–fermion interaction is extended to a four-point contact interaction which is invariant under the O(N) group transformation, so that the composite fermions become singlet in terms of the O(N) group. It is shown that such O(N) singlet fields have controllable quantum fluctuations suppressed by 1/N factors and yield a systematic 1/N-expansion in terms of composite fermions. We derive an effective action described by composite fermions up to the next-to-leading-order terms in the large N expansion, and show that there can be the BCS superfluidity of composite fermions at sufficiently low temperatures.     

Γ(Z → b ): A signature of hard mass terms for a heavy top

We calculate analytically the weak radiative corrections to the weak neutral current gauge boson-bottom fermion vertex, keeping the mass m_t of the internal fermion line for the relevant diagrams. We find, to order α, a hard mass-term dependence m_t²/M_W² of the amplitude, for large m_t values. Its origin comes from the unphysical charged Higgs coupling to fermions in the renormalizable gauge or, equivalently, from the longitudinal charged gauge boson couplings. The diagonal Z⁰ decay width to b-quarks decreases, due to these weak radiative corrections, by 0.6%–2.5% when the top mass m_t varies from 45 to 200 GeV.     

Consistent quantization of a two-dimensional non-abelian chiral theory

A two-dimensional SU(N) gauge model coupled to Weyl fermions is studied following recent suggestions for the quantization of potentially anomalous chiral theories. The Weyl fermion determinant is evaluated and the fermionic current is shown to be conserved due to the gauge invariance of the resulting quantum theory. As in the abelian case, the vector meson acquires a mass and the model is consistent provided a regularization parameter is conveniently chosen.     

Superconductivity in chiral-asymmetric matter within the (2 + 1)-dimensional four-fermion model

The phase structure of chiral-asymmetric matter has been studied within the (2 + 1)-dimensional quantum-field theory with the fermion–antifermion and fermion–fermion (or superconducting) channels of four-fermion interaction. For this purpose, the model takes both the chemical potential of the number of particles μ and the chiral chemical potential μ₅ conjugated to the difference between the numbers of right and left fermions into account. A series of phase diagrams was plotted for different chemical potentials. It is shown that the chemical potential μ promotes the appearance of a superconducting phase, while an increase in the chemical potential μ₅ suppresses the effect of the chemical potential μ on a system. The results of this study may be of interest for high-energy physics, condensed matter physics and, in particular, graphene physics.