Gravitational anomalies

It is shown that in certain parity-violating theories in 4k+2 dimensions, general covariance is spoiled by anomalies at the one-loop level. This occurs when Weyl fermions of $\text{spin}\text{-}\text{1}\text{2}\text{or}\text{-3}\text{2}$ or self-dual antisymmetric tensor fields are coupled to gravity. (For Dirac fermions there is no trouble.) The conditions for anomaly cancellation between fields of different spin is investigated. In six dimensions this occurs in certain theories with a fairly elaborate field content. In ten dimensions there is a unique theory with anomaly cancellation between fields of different spin. It is the chiral n = 2 supergravity theory, which is the low-energy limit of one of the superstring theories. Beyond ten dimensions there is no way to cancel anomalies between fields of different spin.     

Global anomalies in Yang-Mills theories in higher dimensions

A general method is described for finding a class of fermion representations that can lead to Z₂ anomalies. These anomalies are shown to exist in arbitrary D = 4k dimensions. Examples are given.     

Anharmonic effects of phonons with Kohn anomalies

In a quasi-one-dimensional conductor, the phonons with anomaly at the Fermi diameter, 2k_F, cause the phonons at 4k_F to soften via the three-phonon coupling, mainly due to the phonon modulation of the Coulomb interaction between tight-binding electrons on different sites. The 2k_F phonons also cause strong second-order scatterings of X-rays or neutrons. These results may explain the recent observations of phonon anomalies at 4k_F in TTF-TCNQ.     

Abelian and non-Abelian anomalies in monopole-fermion interactions

Taking an example of the standard SU(5) theory, the monopole-fermion system is reduced to an effective 2-dimensional model. This is a generalized Schwinger model containing four Abelian gauge fields interacting with N generations of massless fermions through vector and axialvector couplings. We quantize such a system exactly in the canonical operator formalism. Then, analyzing the cluster property of operators carrying various chiral charges, the roles of the Abelian and non-Abelian anomalies are studied in monopole-induced baryon decay. We demonstrate that the Abelian anomaly and the charge-mixing boundary condition are the driving forces for monopole-induced baryon decay, though the conservation law suggests the importance of the non-Abelian anomaly.     

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 anomalies and constraints on the gauge group in higher-dimensional supersymmetric Yang-Mills theories

Chiral anomalies for gauge theories in any even dimension are computed and the results applied to supersymmetric theories in D = 6, 8 and 10. For D = 8 there is an anomalous chiral U(1) invariance, just as in D = 4, except for certain special groups. For D = 6 and D = 10 there is no anomalous chiral U(1) symmetry, but the gauge current is anomalous except for certain “anomaly-free” groups. For D = 6 the group is thereby constrained to be one of {SU(2), SU(3), exceptional}, while for D = 10 it is constrained to be one of {SU(n) n ≤ 5, USp(4), E₈}.     

Space-time approach to anomalies in the W-T identities and commutators

The Ward-Takahashi identities of the axial-type n-point functions are analysed, assuming the conformal invariance and the chiral SU(3) × SU(3) symmetry to become exact at the short distance. The anomalies in the identities are obtained in a simple nonperturbative way, and the commutator anomalies are determined in connection with the pinching mechanism in taking the equal-time limit of commutators.     

Supersymmetric gauge anomalies in 2 and 4 dimensions from generalized descent-equations

Via a supersymmetric generalization of the descent-equations we derive in Wess-Zumino gauge explicit expressions for chiral anomalies inN=1 supersymmetric Yang-Mills theory for space-time dimensions 2 and 4.     

Supersymmetric gauge anomalies in 2, 4, 6, and 10 dimensions

By solving the consistency condition in Wess-Zumino gauge, we derive explicit expressions for chiral anomalies inN=1 supersymmetric Yang-Mills theories. In dimensions 2, 4, and 6 we present a unified formula for the on-shell anomalies, in 6 dimensions also the off-shell version and in 10 dimensions the complete on-shell result.     

Chiral and conformal anomalies in lattice gauge theory

The continuum limit of the chiral and conformal (Weyl) Ward-Takahashi identities in the lattice Wilson action is studied. The Wilson term works for the chiral anomaly, but it gives rise to-15 times the conventional conformal anomaly for a smallr-parameter and a very sensitiver-dependence of the Λ-parameter. This shows that the strong symmetry breaking by the Wilson term by itself does not necessarily generate correct anomalies. In the lattice regularization the functional Jacobian factors becomec-numbers and do not contribute to anomalies, corresponding to the cut-off of short distance components; the naive continuum limit of lattice WT identities can thus behave differently from continuum ones. To reconstruct conventional identities from lattice relations, the lattice composite operators should be rewritten in terms of relevant continuum operators. In general, this identification of relevant operators is facilitated either by the procedure corresponding to Zimmermann's normal product algorithm or simply by the use of auxiliary regulators such as the dimensional regulator.     

Chiral supergravity and anomalies

Similarly as in the Ashtekar approach, the translational Chern-Simons term is, as a generating function, instrumental for a chiral reformulation of simple supergravity. After applying the algebraic Cartan relation between spin and torsion, the resulting canonical transformation induces not only a decomposition of the gravitational fields into selfdual and anti-selfdual modes, but also a splitting of the Rarita-Schwinger fields into their chiral parts in a natural way. In some detail, we also analyze the consequences for axial and chiral anomalies.     

Bonding anomalies in the rare earth sesquioxides

Raman and IR vibrational spectra of C-type rare earth sesquioxides exhibit anomalous wavenumber decreases for europium (f⁶) and ytterbium (f¹³) oxide which have not been previously reported. Because of the large shifts observed for the Raman spectra, the IR band positions have been re-examined. Smaller, but definite decreases have been observed in the IR spectra as well. Scatter in the literature data had obscured these anomalies. The anomalies correlate with thermodynamic properties and indicate weaker bonding for these two oxides. It is suggested that these anomalies are caused by electron-phonon interaction, involving low-lying f-states which are below the Fermi level for europium and ytterbium. Therefore, these data provide another example of a system in which 4f electronic structure significantly influences chemical bonding. We suggest that it is due to the presence of the unique, low-lying electronic energy levels in these two elements, and not simply the result of the number of f electrons (half-full or full). Literature results suggest the anomalies are not due to “mixed valence” for Eu₂O₃ and Yb₂O₃; however, further research is needed to explain the origin more completely. Raman band positions are reported for the first time for several of the oxides.     

Ward identities and chiral anomalies in stochastic quantization

We derive the Ward identities (WI) for vector and axial currents in stochastic quantization at any given fictitious time t. This is achieved through a functional integral representation of the fermionic Langevin equations. The currents for this effective field theory differ in general from the naive ones; if stochastic regularization is used they are both conserved. We establish the connection between those WI and the field theory ones. The physical source of chiral anomalies is identified: these result from the quantum fluctuations in the fictitious time evolution of the system. In this context, both a traditional regularization method (Pauli-Villars) and stochastic regularization are considered.     

Dynamical supersymmetry breaking and gauge anomalies

Some aspects of supersymmetric gauge theories and discussed. It is shown that dynamical supersymmetry breaking does not occur in supersymmetric QED in higher dimensions. The cancellation of both local (perturbative) and global (non-perturbative) gauge anomalies are also discussed in supersymmetric gauge theories. We argue that there is no dynamical supersymmetry breaking in higher dimensions in any supersymmetric gauge theories free of gauge anomalies. It is also shown that for supersymmetric gauge theories in higher dimensions with a compact connected simple gauge group, when the local anomaly-free condition is satisfied, there can be at most a possibleZ ₂ global gauge anomaly in extended supersymmetricSO(10) (or spin (10)) gauge theories inD=10 dimensions containing additional Weyl fermions in a spinor representation ofSO(10) (or spin (10)). In four dimensions with local anomaly-free condition satisfied, the only possible global gauge anomalies in supersymmetric gauge theories areZ ₂ global gauge anomalies for extended supersymmetricSP(2N) (N=rank) gauge theories containing additional Weyl fermions in a representation ofSP(2N) with an odd 2nd-order Dynkin index.     

Energy level crossing and magnetic anomalies in PrVO4 in strong fields

The magnetic anomalies due to the interaction of the energy levels of a rare-earth ion in a strong magnetic field are studied experimentally and theoretically for the van-Vleck paramagnet PrVO₄. A maximum is discovered in the differential susceptibility dM/dH in a field H _c ≈ 45 T, where the lower energy levels cross. The magnetocaloric effect in pulsed fields is calculated assuming the magnetization process to be adiabatic. This effect is characterized by the absence of initial heating of the sample when the field is turned on and strong cooling as H _c is approached. It is shown that in PrVO₄, which is an enhanced nuclear magnet, the hyperfine interaction plays an extremely important role for the magnetic anomalies associated with crossover. For another van-Vleck paramagnet, HoVO₄, it is shown that a second crossover occurs near 310 T and the magnetocaloric effect is calculated.     

The topological meaning of non-abelian anomalies

We show how the non-abelian anomaly for gauge fields coupled to Weyl fermions in 2n dimensions is related to the non-trivial topology of gauge orbit space. The form of the anomaly and its normalization are shown to follow from a familiar index theorem for a certain (2n + 2)-dimensional Dirac operator. We are thus able to recover and give topological meaning to a variety of results concerning anomalies in 4- and higher-dimensional theories.     

Classification of two-shell nanotubes with commensurate structures of shells

A classification of two-shell carbon nanotubes with commensurate structures of shells is proposed. The classification is based on the concept of equivalence classes as a set of shells with chiral indices of the (kf, kg) type, where f and g are the chiral indices of the equivalence class and k is the index of the shell diameter. All two-shell nanotubes with commensurate shells that are characterized by the chiral indices (k₁f₁, k₁g₁) and (k₂f₂, k₂g₂), where k₁ and k₂ are integral numbers, make up a family of nanotubes of different radii but with equal geometric parameters (such as the intershell distance, the unit cell length of the nanotube, and the difference between the chiral angles of the shells). The geometric parameters of nanotubes are calculated for a number of families, the distribution of different types of two-shell nanotubes with commensurate shells over the outer-shell radii is determined, and the threshold forces required to induce relative motion of nanotube shells are evaluated. The possible use of two-shell nanotubes with commensurate shells in nanostructures is discussed.     

Superconformal anomalies and the effective lagrangian for pure supersymmetric QCD

We discuss the extent to which the superconformal anomalies constrain the effective lagrangian for pure N = 1 Yang-Mills theory. Assuming that the order parameter describing the model is a single chiral superfield (and allowing its derivatives) we find a larger class of possible models than had been previously noted. We give a detailed analysis of a particularly interesting example and find that it leads to the possibility of spontaneous breakdown of supersymmetry. Thus we conclude that the anomaly constraints by themselves are not sufficient to protect supersymmetry. Some unusual features which seem characteristic of such higher derivative theories are noted. A number of related topics, including the question of gluon condensation, are discussed.     

Auxiliary-field anomalies

In general, quantum corrections to matter-supergravity couplings uniquely determine what are acceptable auxiliary fields for N = 1 supergravity, and partially determine those for N = 2. This is because one-loop corrections produce anomalies in not only the local superscale transformations, but also in the local (Poincaré) supersymmetry transformations themselves, except for special cases: in particular, for N = 1 the $\text{n =}\text{1}\text{3}$ minimimal set of auxiliary fields is uniquely chosen.     

Anomalies in Conductance and Localization Length of Disordered Ladders

We discuss the conditions under which an anomaly occurs in conductance and localization length of Anderson model on a lattice. Using the ladder Hamiltonian and analytical calculation of average conductance we find the set of resonance conditions which complements the π-coupling rule for anomalies. We identify those anomalies that might vanish due to the symmetry of the lattice or the distribution of the disorder. In terms of the dispersion relation it is known from strictly one-dimensional model that the lowest order (i.e., the most strong) anomalies satisfy the equation E(k)=E(3k). We show that the anomalies of the generalized model studied here are also the solutions of the same equation with modified dispersion relation.