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Title: Non-standard symmetries and quantum anomalies

Abstract

Quantum anomalies are investigated on curved spacetimes. The intimate relation between Killing-Yano tensors and non-standard symmetries is pointed out. The gravitational anomalies are absent if the hidden symmetry is associated to a Killing-Yano tensor. The axial anomaly in a background gravitational field is directly related with the index of the Dirac operator. In the Dirac theory on curved spaces, Killing-Yano tensors generate Dirac-type operators involved in interesting algebraic structures. The general results are applied to the 4-dimensional Euclidean Taub-NUT space.

Authors:
;  [1]
  1. Depart. Theoretical Physics National Institute for Physics and Nuclear Engineering P.O. Box MG-6, Magurele, Bucharest (Romania)
Publication Date:
OSTI Identifier:
21149172
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1030; Journal Issue: 1; Conference: SCADRON70: Workshop on scalar mesons and related topics honoring Michael Scadron's 70. birthday, Lisbon (Portugal), 11-16 Feb 2008; Other Information: DOI: 10.1063/1.2973504; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CHIRAL SYMMETRY; DIRAC EQUATION; DIRAC OPERATORS; EUCLIDEAN SPACE; FIELD ALGEBRA; FOUR-DIMENSIONAL CALCULATIONS; GRAVITATIONAL FIELDS; QUANTUM CHROMODYNAMICS; SPACE-TIME; SYMMETRY BREAKING; TENSORS

Citation Formats

Visinescu, Anca, and Visinescu, Mihai. Non-standard symmetries and quantum anomalies. United States: N. p., 2008. Web. doi:10.1063/1.2973504.
Visinescu, Anca, & Visinescu, Mihai. Non-standard symmetries and quantum anomalies. United States. doi:10.1063/1.2973504.
Visinescu, Anca, and Visinescu, Mihai. 2008. "Non-standard symmetries and quantum anomalies". United States. doi:10.1063/1.2973504.
@article{osti_21149172,
title = {Non-standard symmetries and quantum anomalies},
author = {Visinescu, Anca and Visinescu, Mihai},
abstractNote = {Quantum anomalies are investigated on curved spacetimes. The intimate relation between Killing-Yano tensors and non-standard symmetries is pointed out. The gravitational anomalies are absent if the hidden symmetry is associated to a Killing-Yano tensor. The axial anomaly in a background gravitational field is directly related with the index of the Dirac operator. In the Dirac theory on curved spaces, Killing-Yano tensors generate Dirac-type operators involved in interesting algebraic structures. The general results are applied to the 4-dimensional Euclidean Taub-NUT space.},
doi = {10.1063/1.2973504},
journal = {AIP Conference Proceedings},
number = 1,
volume = 1030,
place = {United States},
year = 2008,
month = 8
}
  • Investigating the Dirac equation in curved backgrounds we point out the role of the Killing-Yano tensors in the construction of the Dirac-type operators. The gravitational and axial anomalies are studied for generalized Euclidean Taub-Newman-Unti-Tamburino (Taub-NUT) metrics, which admit hidden symmetries analogous to the Runge-Lenz vector of the Kepler-type problem. The generalized Taub-NUT metrics exhibit in general gravitational anomalies. Using the Atiyah-Patodi-Singer index theorem for manifolds with boundaries, it is shown that these metrics make no contribution to the axial anomaly.
  • We present a survey of all possible scalar particles that can couple at the tree level to the standard fermions in the standard model. We discuss the phenomenology of such scalars. In particular, we examine the influence of exotic scalars on {ital g}{minus}2 measurements, flavor-changing neutral currents, and {ital CP} violation. We also comment briefly upon decays and production of these particles.
  • Lie groups with the same Lie algebra as the standard model but different global topology are considered, and the possibilities are reduced to four viable alternatives for the true symmetry group of the standard model: SU(3){times}SU(2){times}U(1), U(3){times}SU(2), SU(3){times}U(2), and S(U(3){times}U(2)). It is demonstrated that the last three groups require hypercharge quantization for their allowable representations, and that S(U(3){times}U(2)) is the most likely candidate for the true symmetry group of the standard model because it offers the best explanation of the observed hypercharges of the elementary fermions. Explicit S(U(3){times}U(2)) tensor representations of the quarks and leptons are given and are comparedmore » to the standard SU(5) assignments. The spontaneous symmetry breaking of S(U(3){times}U(2)) to an electrostrong U(3) is briefly discussed, and electric charge quantization follows from weak hypercharge quantization and the existence of the standard Higgs doublet with nonzero vacuum expectation value. Lastly, it is shown that combining the conditions imposed by anomaly cancellation with the S(U(3){times}U(2)) hypercharge quantization condition uniquely determines the ratios of the hypercharges in a standard quark-lepton family.« less
  • The uniqueness of the Weyl representations of the standard gauge group is reexamined. We find that, prior to spontaneous breaking of the electroweak subgroup, the minimal Weyl representations and their charges are uniquely determined by insisting on all three known chiral gauge anomaly-free conditions in four dimensions: (1) cancellation of triangular anomalies; (2) absence of the global SU(2) anomaly; and (3) cancellation of the mixed-gauge-gravitational anomaly. The uniqueness question for the left-right-symmetric group and the simple (grand-unified-theory) group are discussed from the anomalies viewpoint.
  • The standard model SU(2){sub L}xU(1){sub Y} gauging of the Wess-Zumino-Witten term requires a modified counterterm when background fields, needed to generate the full set of currents, are introduced. The modified counterterm plays an essential role in properly defining covariant global currents and their anomalies. For example, it is required in order to correctly derive the gauge-invariant baryon number current and its anomalous divergence. The background fields can also be promoted to a description of the physical spin-1 vector and axial-vector mesons in QCD and the counterterm leads to novel interactions. These are (pseudo)Chern-Simons terms, such as {epsilon}{sup {mu}}{sup {nu}}{sup {rho}}{supmore » {sigma}}{omega}{sub {mu}}Z{sub {nu}}{partial_derivative}{sub {rho}}A{sub {sigma}} and {epsilon}{sup {mu}}{sup {nu}}{sup {rho}}{sup {sigma}}{rho}{sub {mu}}{sup {+-}}W{sub {nu}}{sup {+-}}{partial_derivative}{sub {rho}}A{sub {sigma}} that mediate new interactions between neutrinos and photons at finite baryon density.« less