Chiral bosons

The local lagrangian formulation for chiral bosons recently suggested by Floreanini and Jackiw is analyzed. We quantize the system and explain how the unconventional Poincaré generators of left and right chiral bosons combine to form the standard generators. The left-U(1) Kac-Moody algebra and the left-Virasoro algebra are shown to be the same as for left Weyl fermions. We compare the partition functions, on the torus, of a chiral boson and a chiral fermion. The left-moving boson is coupled to gauge fields producing the same anomalies as in the fermionic formulation. It is pointed out that the unconventional Lorentz transformations are inapplicable for the coupled system and a set of different transformations is presented. A coupling to gravity is proposed. We present the theory of chiral bosons on a group manifold, the chiral WZW model. The (1,0) supersymmetric abelian and non-abelian chiral bosons are described.     

Self-dual tensors and gravitational anomalies in 4n + 2 dimensions

Starting from a manifestly Lorentz- and diffeomorphism-invariant classical action we perform a perturbative derivation of the gravitational anomalies for chiral bosons in 4n + 2 dimensions. The manifest classical invariance is achieved using a newly developed method based on a scalar auxiliary field and two new bosonic local symmetries. The resulting anomalies coincide with the ones predicted by the index theorem. In the two-dimensional case, moreover, we perform an exact covariant computation of the effective action for a chiral boson (a scalar) which is seen to coincide with the effective action for a two-dimensional complex Weyl fermion. All these results support the quantum reliability of the new, at the classical level manifestly invariant, method.     

Chiral magnetic effect without chirality source in asymmetric Weyl semimetals

We describe a new type of the chiral magnetic effect (CME) that should occur in Weyl semimetals (WSMs) with an asymmetry in the dispersion relations of the left- and right-handed (LH and RH) chiral Weyl fermions. In such materials, time-dependent pumping of electrons from a non-chiral external source can generate a non-vanishing chiral chemical potential. This is due to the different capacities of the LH and RH chiral Weyl cones arising from the difference in the density of states in the LH and RH cones. The chiral chemical potential then generates, via the chiral anomaly, a current along the direction of an applied magnetic field even in the absence of an external electric field. The source of chirality imbalance in this new setup is thus due to the band structure of the system and the presence of (non-chiral) electron source, and not due to the parallel electric and magnetic fields. We illustrate the effect by an argument based on the effective field theory, and by the chiral kinetic theory calculation for a rotationally invariant WSM with different Fermi velocities in the left and right chiral Weyl cones; we also consider the case of a WSM with Weyl nodes at different energies. We argue that this effect is generically present in WSMs with different dispersion relations for LH and RH chiral Weyl cones, such as SrSi₂ recently predicted as a WSM with broken inversion and mirror symmetries, as long as the chiral relaxation time is much longer than the transport scattering time.     

外尔半金属及其输运特性

外尔半金属是继石墨烯以及拓扑绝缘体之后的又一个研究热点。相比于后两者,外尔半金 属独特的三维无能隙线性色散能带结构使得它有很多奇特的性质,如：手性反常、手性磁效应、 反弱局域化、手性朗道能级和负磁阻效应等。实际样品中无序总是不可避免的,所以考虑无序对 体系的影响是很有必要的。我们回顾了无序下第一类以及第二类外尔半金属的相变特性,并获得 了完整的相图,这些无序诱导的相变丰富了拓扑安德森绝缘体和安德森金属绝缘体相变的物理内 涵。我们同样回顾了长程短程无序影响下的第一类外尔半金属体系的输运,发现了一种不能采用 玻尔兹曼输运方程来描述的输运过程。我们介绍Imbert-Fedorov 位移这一光学中的效应在外尔 半金属中的实现,这为更好地应用外尔半金属提供了更多的可能性,随后采用波包散射,我们解 释了外尔半金属中的超高载流子迁移率问题的原因,最后我们给出一个简要的总结。     

Derivation of an effective Lagrangian from a generalized scalar curvature

A spinor Lagrangian invariant under global coordinate, local Lorentz and local chiral SU(n) × SU(n) gauge transformations is presented. The invariance requirement necessitates the introduction of boson fields, and a theory for these fields is then developed by relating them to generalizations of the vector connections in general relativity and utilizing an expanded scalar curvature as a boson Lagrangian. In implementing this plan, the local Lorentz group is found to greatly facilitate the correlation of the boson fields occurring in the spinor Lagrangian with the generalized vector connections.The independent boson fields of the theory are assumed to be the inhomogeneously transforming irreducible parts of the connections. It turns out that no homogeneously transforming parts are necessary to reproduce the chiral Lagrangian usually used as a basis for phenomenological field theories. The Lagrangian in question appears when the gravitational interaction is turned off. It includes pseudoscalar, spinor, vector, and axial vector fields, and the vector fields carry mass in spite of the fact that the theory is locally gauge invariant.     

Interplay between chiral magnetic and Kondo effects in Weyl metal phase

We investigate the Kondo effect in a Weyl metal state, which occurs from a spin-orbit coupled Dirac metal phase under magnetic fields. We start from an effective field theory in terms of low-energy fermions on a pair of chiral Fermi surfaces, which takes into account both the Berry curvature and chiral anomaly. Resorting to the U(1) slave-boson mean-field theory, we find that the effective Kondo temperature increases monotonically as a function of the external magnetic field due to enhancement of the density of states. The enhancement is originated from the chiral magnetic effect which is novel feature of Weyl metals. This leads to the prediction of the magnetic-field dependence in the logarithmic temperature dependence of the longitudinal magnetoconductivity.     

On the Gauge and BRST Invariance of the Chiral QED with Faddeevian Anomaly

Chiral Schwinger model with the Faddeevian anomaly is considered. It is found that imposing a chiral constraint this model can be expressed in terms of chiral boson. The model when expressed in terms of chiral boson remains anomalous and the Gauss law of which gives anomalous Poisson brackets between itself. In spite of that a systematic BRST quantization is possible. The Wess-Zumino term corresponding to this theory appears automatically during the process of quantization. A gauge invariant reformulation of this model is also constructed. Unlike the former one gauge invariance is done here without any extension of phase space. This gauge invariant version maps onto the vector Schwinger model. The gauge invariant version of the chiral Schwinger model for a=2 has a massive field with identical mass however gauge invariant version obtained here does not map on to that.     

On the chiral magnetic effect in Weyl superfluid <Superscript>3</Superscript>He-A

In the theory of the chiral anomaly in relativistic quantum field theories (RQFTs), some results depend on a regularization scheme at ultraviolet. In the chiral superfluid ³He-A, which contains two Weyl points and also experiences the effects of chiral anomaly, the “trans-Planckian” physics is known and the results can be obtained without regularization. We discuss this on example of the chiral magnetic effect (CME), which has been observed in ³He-A in the 1990s [1]. There are two forms of the contribution of the CME to the Chern–Simons term in free energy, perturbative and non-perturbative. The perturbative term comes from the fermions living in the vicinity of the Weyl point, where the fermions are “relativistic” and obey the Weyl equation. The non-perturbative term originates from the deep vacuum, being determined by the separation of the two Weyl points in momentum space. Both terms are obtained using the Adler–Bell–Jackiw equation for chiral anomaly, and both agree with the results of the microscopic calculations in the “trans-Planckian” region. Existence of the two nonequivalent forms of the Chern–Simons term demonstrates that the results obtained within the RQFT depend on the specific properties of the underlying quantum vacuum and may reflect different physical phenomena in the same vacuum.     

Weyl geometric gravity and electroweak symmetry “breaking”

A Weyl geometric scale covariant approach to gravity due to Omote, Dirac, and Utiyama (1971ff) is reconsidered. It can be extended to the electroweak sector of elementary particle fields, taking into account their basic scaling freedom. Already Cheng (1988) indicated that electroweak symmetry breaking, usually attributed to the Higgs field with a boson expected at 0.1–0.3 TeV, may be due to a coupling between Weyl geometric gravity and electroweak interactions. Weyl geometry seems to be well suited for treating questions of elementary particle physics, which relate to scale invariance and its “breaking”. This setting suggests the existence of a scalar field boson at the surprisingly low energy of ～ 1 eV. That may appear unlikely; but, as a payoff, the acquirement of mass arises as a result of coupling to gravity in agreement with the understanding of mass as the gravitational charge of fields.     

Hidden symmetry of the two-dimensional chiral fields

We examine the non-Abelian Goldstone boson (chiral field) interaction in two dimensions. As was shown earlier, this theory strongly resembles the Yang-Mills theory in four dimensions. It is shown that dynamics of chiral fields is governed by the infinite number of the non-trivial conservation laws, which impose strong limitations on the S matrix.     

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.     

Gauge theory of the conformal and superconformal group

We show that the locally scale invariant Weyl theory of gravity is the gauge theory of the conformal group. Proper conformal transformations are gauged by a non-propagating gauge field.A gauge theory for the superconformal group is obtained which is locally scale, Lorentz, and chiral invariant but not locally supersymmetric despite remarkable cancellations.     

THE CORRESPONDENCE PRINCIPLE IN (1+1)-DIMENSIONAL FIELD THEORY AND THE COLEMAN THEOREM

The correspondence relations between a fermion field and a boson field in (1+1)-dimensional quantum field theory is discussed in general. Emphases have been laid on the renorinalization with respect.to an arbitrary mass parameter in boson version as well as the nonlocal property of currents in fermion version. After establishing the equivalence between the continuous chiral transformation in fermion version and the translational transformation in boson version, we are able to prove the Coleman theorem correspondingly.     

Dynamical symmetry breaking in the sea of the nucleon

We derive the nonanalytic chiral behavior of the flavor asymmetry d - u. Such behavior is a unique characteristic of Goldstone boson loops in chiral theories, including QCD, and establishes the unambiguous role played by the Goldstone boson cloud in the sea of the proton. Generalizing the results to the SU(3) sector, we show that strange chiral loops require that the s - s distribution be nonzero.     

Fermion propagators on a four-dimensional random-block lattice

Fermion propagators, composite boson propagators and the fermion condensate are calculated numerically on the four-dimensional random-block lattice, respectively. The ensemble-averaged fermion propagator agrees with the continuum propagator for distances greater than three average lattice spacings. The results on the fermion condensate show that the chiral symmetry of the doubled modes is broken in the continuum limit. The Goldstone boson arising from the broken symmetry is revealed by examining the composite pseudo-scalar propagator. The doubled fermion and the Goldstone boson both acquire masses of the order of inverse lattice spacing and thus decouple from the theory in the continuum limit.     

Influence of Finite Chemical Potential on Critical Boson Mass in QED3

Using the coupled Dyson-Schwinger equation for the fermion propagator at finite chemical potential μ, we investigate the fermion chiral condensate when the gauge boson mass is nonzero in QED3. We show that the chiral symmetry restores when the boson mass is large enough, and the critical boson mass depends little on μ.     

Anomalous Vector-Boson Mass Generation on a Lattice

We show the vector boson mass generation on a lattice with the Wilson's fermion formulation. By calculating explicitly the change of the effective action under chiral transformation, it is also found an arbitrariness in the solution of the chiral Schwinger model, which depends on a lattice regularization in continuum theory.     

On the character of chiral symmetry breaking and fermion vacuum structure in QED<Subscript>3</Subscript>

Equation for the Bethe-Salpeter wave function of the Goldstone boson in QED₃ is considered in the ladder approximation with the use of the Landau gauge for the photon propagator. With the help of standard simplifications, the existence of nonzero solutions for this equation is demonstrated, which testifies to the production of the above-described boson in the process of chiral symmetry breaking. At the same time, it is demonstrated that only one of the entire set of solutions describing the Goldstone boson corresponds to the stable ground state; this solution has the greatest fermion mass. In the remaining cases, the compound boson state with zero mass is excited, and all other states having smaller energies appear tachyon states and hence are unstable. The fermion condensate is calculated; it is demonstrated that in the examined case, it is finite. Based on the foregoing, conclusions are drawn about spontaneous rather than dynamic character of chiral symmetry breaking in QED₃, complex structure of fermion vacuum for the examined model, and at the same time, simple structure of the massive phase vacuum.     

The fate of the U(1) goldstone boson

In the framework of a manifestly covariant formulation of (non-Abelian) gauge theories, we analyse what the gauge invariance (BRS invariance) implies for the problem of the Goldstone boson associated with the conserved U(1) axial vector current. Based on the symmetry consideration of gauge invariance only, it is shown that the Goldstone boson does not appear as a physical particle at all, if and only if the Faddeev-Popov (FP) ghost forms a massless bound state with the gauge boson in a pseudoscalar channel. This decoupling of the Goldstone boson from the physical sector is not caused by the Goldstone dipole proposed by Kogut and Susskind, but by a Goldstone quartet including the FP ghost bound state. This decoupling mechanism by the Goldstone quartet can be shown to become equivalent to that of the Goldstone dipole, only in a special case, i.e., the Schwinger model which is an Abelian theory in two dimensions. In the Abelian gauge theory in four dimensions, the chiral U(1) Goldstone boson necessarily appears as a physical particle.     

Chiral Bosonized Versions Hidden in Chiral Schwinger Models

The left- and right-handed chiral Schwinger models are re-examined by a modified chiral bosonization. Contrary to the usual chiral bosonization, we impose the chiral constraint on the right-handed chiral Schwinger model and the antichiral constraint on the left-handed one. The resulting chiral boson and theories are gauge-invariant and equivalent to one (free) cbiral boson and one antichiral boson respectively.