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Kaluza-Klein Gravity, Concentrating on the General Rel- Ativity, Rather Than Particle Physics Side of the Subject
Kaluza-Klein Gravity J. M. Overduin Department of Physics and Astronomy, University of Victoria, P.O. Box 3055, Victoria, British Columbia, Canada, V8W 3P6 and P. S. Wesson Department of Physics, University of Waterloo, Ontario, Canada N2L 3G1 and Gravity Probe-B, Hansen Physics Laboratories, Stanford University, Stanford, California, U.S.A. 94305 Abstract We review higher-dimensional unified theories from the general relativity, rather than the particle physics side. Three distinct approaches to the subject are identi- fied and contrasted: compactified, projective and noncompactified. We discuss the cosmological and astrophysical implications of extra dimensions, and conclude that none of the three approaches can be ruled out on observational grounds at the present time. arXiv:gr-qc/9805018v1 7 May 1998 Preprint submitted to Elsevier Preprint 3 February 2008 1 Introduction Kaluza’s [1] achievement was to show that five-dimensional general relativity contains both Einstein’s four-dimensional theory of gravity and Maxwell’s the- ory of electromagnetism. He however imposed a somewhat artificial restriction (the cylinder condition) on the coordinates, essentially barring the fifth one a priori from making a direct appearance in the laws of physics. Klein’s [2] con- tribution was to make this restriction less artificial by suggesting a plausible physical basis for it in compactification of the fifth dimension. This idea was enthusiastically received by unified-field theorists, and when the time came to include the strong and weak forces by extending Kaluza’s mechanism to higher dimensions, it was assumed that these too would be compact. This line of thinking has led through eleven-dimensional supergravity theories in the 1980s to the current favorite contenders for a possible “theory of everything,” ten-dimensional superstrings. -
Thermal Evolution of the Axial Anomaly
Thermal evolution of the axial anomaly Gergely Fej}os Research Center for Nuclear Physics Osaka University The 10th APCTP-BLTP/JINR-RCNP-RIKEN Joint Workshop on Nuclear and Hadronic Physics 18th August, 2016 G. Fejos & A. Hosaka, arXiv: 1604.05982 Gergely Fej}os Thermal evolution of the axial anomaly Outline aaa Motivation Functional renormalization group Chiral (linear) sigma model and axial anomaly Extension with nucleons Summary Gergely Fej}os Thermal evolution of the axial anomaly Motivation Gergely Fej}os Thermal evolution of the axial anomaly Chiral symmetry is spontaneuously broken in the ground state: < ¯ > = < ¯R L > + < ¯L R > 6= 0 SSB pattern: SUL(Nf ) × SUR (Nf ) −! SUV (Nf ) Anomaly: UA(1) is broken by instantons Details of chiral symmetry restoration? Critical temperature? Axial anomaly? Is it recovered at the critical point? Motivation QCD Lagrangian with quarks and gluons: 1 L = − G a G µνa + ¯ (iγ Dµ − m) 4 µν i µ ij j Approximate chiral symmetry for Nf = 2; 3 flavors: iT aθa iT aθa L ! e L L; R ! e R R [vector: θL + θR , axialvector: θL − θR ] Gergely Fej}os Thermal evolution of the axial anomaly Details of chiral symmetry restoration? Critical temperature? Axial anomaly? Is it recovered at the critical point? Motivation QCD Lagrangian with quarks and gluons: 1 L = − G a G µνa + ¯ (iγ Dµ − m) 4 µν i µ ij j Approximate chiral symmetry for Nf = 2; 3 flavors: iT aθa iT aθa L ! e L L; R ! e R R [vector: θL + θR , axialvector: θL − θR ] Chiral symmetry is spontaneuously broken in the ground state: < ¯ > = < ¯R L > + < ¯L R -
Spontaneous Breaking of Conformal Invariance and Trace Anomaly
Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching ∗ A. Schwimmera and S. Theisenb a Department of Physics of Complex Systems, Weizmann Institute, Rehovot 76100, Israel b Max-Planck-Institut f¨ur Gravitationsphysik, Albert-Einstein-Institut, 14476 Golm, Germany Abstract We argue that when conformal symmetry is spontaneously broken the trace anomalies in the broken and unbroken phases are matched. This puts strong constraints on the various couplings of the dilaton. Using the uniqueness of the effective action for the Goldstone supermultiplet for broken = 1 supercon- formal symmetry the dilaton effective action is calculated. N arXiv:1011.0696v1 [hep-th] 2 Nov 2010 November 2010 ∗ Partially supported by GIF, the German-Israeli Foundation for Scientific Research, the Minerva Foundation, DIP, the German-Israeli Project Cooperation and the Einstein Center of Weizmann Institute. 1. Introduction The matching of chiral anomalies of the ultraviolet and infrared theories related by a massive flow plays an important role in understanding the dynamics of these theories. In particular using the anomaly matching the spontaneous breaking of chiral symmetry in QCD like theories was proven [1]. For supersymmetric gauge theories chiral anomaly matching provides constraints when different theories are related by “non abelian” duality in the infrared NS. The matching involves the equality of a finite number of parameters, “the anomaly coefficients” defined as the values of certain Green’s function at a very special singular point in phase space. The Green’s function themselves have very different structure at the two ends of the flow. The massive flows relate by definition conformal theories in the ultraviolet and infrared but the trace anomalies of the two theories are not matched: rather the flow has the property that the a-trace anomaly coefficient decreases along it [2]. -
Momentum-Dependent Mass and AC Hall Conductivity of Quantum Anomalous Hall Insulators and Their Relation to the Parity Anomaly
PHYSICAL REVIEW RESEARCH 2, 033193 (2020) Momentum-dependent mass and AC Hall conductivity of quantum anomalous Hall insulators and their relation to the parity anomaly Christian Tutschku, Jan Böttcher , René Meyer, and E. M. Hankiewicz* Institute for Theoretical Physics and Würzburg-Dresden Cluster of Excellence ct.qmat, Julius-Maximilians-Universität Würzburg, 97074 Würzburg, Germany (Received 9 March 2020; accepted 15 July 2020; published 4 August 2020) The Dirac mass of a two-dimensional QAH insulator is directly related to the parity anomaly of planar quantum electrodynamics, as shown initially by Niemi and Semenoff [Phys. Rev. Lett. 51, 2077 (1983)]. In this work, we connect the additional momentum-dependent Newtonian mass term of a QAH insulator to the parity anomaly. We reveal that in the calculation of the effective action, before renormalization, the Newtonian mass acts similar to a parity-breaking element of a high-energy regularization scheme. This calculation allows us to derive the finite frequency correction to the DC Hall conductivity of a QAH insulator. We predict that the leading order AC correction contains a term proportional to the Chern number. This term originates from the Newtonian mass and can be measured via electrical or magneto-optical experiments. Moreover, we prove that the Newtonian mass significantly changes the resonance structure of the AC Hall conductivity in comparison to pure Dirac systems like graphene. DOI: 10.1103/PhysRevResearch.2.033193 I. INTRODUCTION While the contribution of the Dirac mass to the effective ac- tion of a QED + systems was initially shown in Refs. [22,23], The discovery of Dirac materials, such as topological 2 1 the effective action of Chern insulator in the presence of a insulators [1–10] and Weyl or Dirac [11–16] semimetals Newtonian mass has not yet been analyzed. -
Chiral Anomaly Without Relativity Arxiv:1511.03621V1 [Physics.Pop-Ph]
Chiral anomaly without relativity A.A. Burkov Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada, and ITMO University, Saint Petersburg 197101, Russia Perspective on J. Xiong et al., Science 350, 413 (2015). The Dirac equation, which describes relativistic fermions, has a mathematically inevitable, but puzzling feature: negative energy solutions. The physical reality of these solutions is unques- tionable, as one of their direct consequences, the existence of antimatter, is confirmed by ex- periment. It is their interpretation that has always been somewhat controversial. Dirac’s own idea was to view the vacuum as a state in which all the negative energy levels are physically filled by fermions, which is now known as the Dirac sea. This idea seems to directly contradict a common-sense view of the vacuum as a state in which matter is absent and is thus generally disliked among high-energy physicists, who prefer to regard the Dirac sea as not much more than a useful metaphor. On the other hand, the Dirac sea is a very natural concept from the point of view of a condensed matter physicist, since there is a direct and simple analogy: filled valence bands of an insulating crystal. There exists, however, a phenomenon within the con- arXiv:1511.03621v1 [physics.pop-ph] 26 Oct 2015 text of the relativistic quantum field theory itself, whose satisfactory understanding seems to be hard to achieve without assigning physical reality to the Dirac sea. This phenomenon is the chiral anomaly, a quantum-mechanical violation of chiral symmetry, which was first observed experimentally in the particle physics setting as a decay of a neutral pion into two photons. -
Real-Time Dynamics of Chern-Simons Fluctuations Near a Critical Point
PHYSICAL REVIEW D 103, L071502 (2021) Letter Real-time dynamics of Chern-Simons fluctuations near a critical point † ‡ Kazuki Ikeda ,1,* Dmitri E. Kharzeev ,2,3,4, and Yuta Kikuchi 3, 1Research Institute for Advanced Materials and Devices, Kyocera Corporation, Soraku, Kyoto 619-0237, Japan 2Center for Nuclear Theory, Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA 3Department of Physics, Brookhaven National Laboratory, Upton, New York 11973-5000 4RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000 (Received 16 December 2020; accepted 22 March 2021; published 21 April 2021) The real-time topological susceptibility is studied in ð1 þ 1Þ-dimensional massive Schwinger model with a θ-term. We evaluate the real-time correlation function of electric field that represents the topological Chern-Pontryagin number density in (1 þ 1) dimensions. Near the parity-breaking critical point located at θ ¼ π and fermion mass m to coupling g ratio of m=g ≈ 0.33, we observe a sharp maximum in the topological susceptibility. We interpret this maximum in terms of the growth of critical fluctuations near the critical point, and draw analogies between the massive Schwinger model, QCD near the critical point, and ferroelectrics near the Curie point. DOI: 10.1103/PhysRevD.103.L071502 I. INTRODUCTION Coleman [59] that the line of the first order phase transition terminates at some critical value mÃ, where the phase The Schwinger model [1] is quantum electrodynamics in transition is second order. The position of this critical point ð1 þ 1Þ space-time dimensions. -
Effective Lagrangian for Axial Anomaly and Its Applications in Dirac And
www.nature.com/scientificreports OPEN Efective lagrangian for axial anomaly and its applications in Dirac and Weyl semimetals Received: 25 April 2018 Chih-Yu Chen, C. D. Hu & Yeu-Chung Lin Accepted: 9 July 2018 A gauge invariant efective lagrangian for the fermion axial anomaly is constructed. The dynamical Published: xx xx xxxx degree of freedom for fermion feld is preserved. Using the anomaly lagrangian, the scattering cross section of pair production γγ → e−e+ in Dirac or Weyl semimetal is computed. The result is compared with the corresponding result from Dirac lagrangian. It is found that anomaly lagrangain and Dirac lagrangian exhibit the same E B pattern, therefore the E B signature may not serve a good indicator of the existence of axial anomaly. Because anomaly generates excessive right-handed electrons and positrons, pair production can give rise to spin current by applying gate voltage and charge current with depositing spin flters. These experiments are able to discern genuine anomaly phenomena. Axial anomaly1,2, sometimes referred to as chiral anomaly in proper context, arises from the non-invariance of fermion measure under axial γ5 transformation3, it is a generic property of quantum fermion feld theory, massive or massless. Te realization of axial anomaly in condensed matter is frst explored by Nielsen and Ninomiya4. It is argued that in the presence of external parallel electric and magnetic felds, there is net production of chiral charge and electrons move from lef-handed (LH) Weyl cone to right-handed (RH) Weyl cone, the induced anomaly current causes magneto-conductivity prominent. Aji5 investigated pyrochlore iridates under magnetic feld. -
Parity Anomaly and Duality
Parity Anomaly and Duality Web Chen-Te Ma 1 Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 10617, Taiwan, R.O.C. Abstract We review the parity anomaly and a duality web in 2+1 dimensions. An odd di- mensional non-interacting Dirac fermion theory is not parity invariant at quantum level. We demonstrate the parity anomaly in a three dimensional non-interacting Dirac fermion theory and a one dimensional non-interacting Dirac fermion theory. These theories can generate non-gauge invariant Abelian Chern-Simons terms at a finite temperature through an effective action. The parity anomaly also leads us to study the duality web in 2+1 dimensions, in which the 2+1 dimensional duality web begins from the conjecture of a duality between a three dimensional Dirac fermion theory and a three dimensional interacting scalar field theory at the Wilson-Fisher arXiv:1802.08959v3 [hep-th] 2 Jul 2018 fixed point. We first review the duality web for the flat background, then we discuss its extension to the spinc manifold to avoid inconsistency from the spin structure. This also leads a global effect. We discuss that the composite fermions approach of the quantum Hall system also suffers from the same issue of the global description. Finally, we use perspective of the electric-magnetic duality of the Abelian gauge theory in 3+1 dimensions to study the 2+1 dimensional duality web. 1e-mail address: [email protected] 1 Introduction Symmetry can be seen as an operation that maps an object to itself. The symmetry can be built from a mathematical group. -
A Note on the Chiral Anomaly in the Ads/CFT Correspondence and 1/N 2 Correction
NEIP-99-012 hep-th/9907106 A Note on the Chiral Anomaly in the AdS/CFT Correspondence and 1=N 2 Correction Adel Bilal and Chong-Sun Chu Institute of Physics, University of Neuch^atel, CH-2000 Neuch^atel, Switzerland [email protected] [email protected] Abstract According to the AdS/CFT correspondence, the d =4, =4SU(N) SYM is dual to 5 N the Type IIB string theory compactified on AdS5 S . A mechanism was proposed previously that the chiral anomaly of the gauge theory× is accounted for to the leading order in N by the Chern-Simons action in the AdS5 SUGRA. In this paper, we consider the SUGRA string action at one loop and determine the quantum corrections to the Chern-Simons\ action. While gluon loops do not modify the coefficient of the Chern- Simons action, spinor loops shift the coefficient by an integer. We find that for finite N, the quantum corrections from the complete tower of Kaluza-Klein states reproduce exactly the desired shift N 2 N 2 1 of the Chern-Simons coefficient, suggesting that this coefficient does not receive→ corrections− from the other states of the string theory. We discuss why this is plausible. 1 Introduction According to the AdS/CFT correspondence [1, 2, 3, 4], the =4SU(N) supersymmetric 2 N gauge theory considered in the ‘t Hooft limit with λ gYMNfixed is dual to the IIB string 5 ≡ theory compactified on AdS5 S . The parameters of the two theories are identified as 2 4 × 4 gYM =gs, λ=(R=ls) and hence 1=N = gs(ls=R) . -
Screening in Two-Dimensional Qcd
IC/96/51 hep-th /9604063 INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS lllllfilllllllllllll XA9743416 SCREENING IN TWO-DIMENSIONAL QCD E. Abdalla R. Mohayaee and A. Zadra MIRAMARE-TRIESTE IC/96/51 hep-th/9604063 United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS SCREENING IN TWO-DIMENSIONAL QCD E. Abdalla 1 , R. Mohayaee2 and A. Zadra 3 International Centre for Theoretical Physics, Trieste, Italy. ABSTRACT We discuss the issue of screening and confinement of external colour charges in bosonised two-dimensional quantum chromodynamics. Our computation relies on the static solu tions of the semi-classical equations of motion. The significance of the different repre sentations of the matter field is explicitly studied. We arrive at the conclusion that the screening phase prevails, even in the presence of a small mass term for the fermions. To confirm this result further, we outline the construction of operators corresponding to screened quarks. MIRAMARE - TRIESTE April 1996 iPermanent address: Institute de Ffsica-USP, C.P. 20516, Sao Paulo, Brazil. E-mail address: [email protected] 2E-mail address: [email protected]; ^Permanent address: Institute de Fisica, Universidade de Sao Paulo, Caixa Postal 66 318, Cidade Universitaria, Sao Paulo, Brazil. E-mail address: [email protected] 1 Introduction Theissue of confinement of fundamental constituents of matter is a long-standing prob lem of theoretical physics whose solution has evaded full comprehension up to now. How ever, significant progress has been made towards making a clear distinction between the apparently related phenomena of screening and confinement. -
Numerical Investigations of the Schwinger Model and Selected Quantum Spin Models
Adam Mickiewicz University Faculty of Physics Poznań, Poland Master’s Thesis Numerical investigations of the Schwinger model and selected quantum spin models Marcin Szyniszewski Supervisors: prof. UAM dr hab. Piotr Tomczak dr Krzysztof Cichy Quantum Physics Division, Faculty of Physics, UAM Poznań 2012 Abstract Numerical investigations of the XY model, the Heisenberg model and the 퐽 − 퐽′ Heisenberg model are conducted, using the exact diagonalisation, the numerical renormalisation and the density matrix renormalisation group approach. The low-lying energy levels are obtained and finite size scaling is performed to estimate the bulk limit value. The results are found to be consistent with the exact values. The DMRG results are found to be most promising. The Schwinger model is also studied using the exact diagonalisation and the strong coupling expansion. The massless, the massive model and the model with a background electric field are explored. Ground state energy, scalar and vector particle masses and order parameters are examined. The achieved values areobserved to be consistent with previous results and theoretical predictions. Path to the future studies is outlined. 2 Table of contents Introduction ...................................................................................................................5 1 Theoretical background ................................................................................................7 1.1 Basics of statistical physics and quantum mechanics ............................................... -
Π0 Decay Precision-Tests the Chiral Anomaly Harvey B
NUCLEAR PHYSICS p0 decay precision-tests the chiral anomaly More precise neutral pion lifetime measurements probe quantum symmetry breaking By Harvey B. Meyer point, it was assumed that a symmetry of the errors in quadrature, this amounts to a classical Lagrangian would protect p0 from tension of 1.8 standard deviations versus ost subatomic particles are decaying in the limit of massless up and the combined result of the PrimEx-I and strongly interacting composites down quarks and lead to a longer lifetime. -II experiments, 8.34 (60.13) × 10−17 s. Al- called hadrons. Most hadrons are However, it turns out to be impossible to reg- though this difference could be a statisti- unstable and decay on extremely ularize quantum chromodynamics without cal fluctuation, it provides motivation to short time scales (10−22 s) to lighter breaking that symmetry. Therefore, the latter revisit the theory prediction. The gp pp hadrons. The electrically neutral is not respected by the quantum fluctuations reaction also has a sharp low-energy pre- Mpion, p0, is the lightest hadron and decays of the quantum chromodynamics fields and diction based on the chiral anomaly (6, 7) on a time scale of 10−16 s in 98.8% of cases does not protect p0 from decaying. and is being investigated by the COMPASS into two photons, gg, through the electro- The quantum origin of the symmetry experiment (8). magnetic interaction. Historically, under- breaking leads to an exact prediction for the The gg decay width of p0 has recently standing this time scale presented a major strength of p0 coupling to gg and hence the been evaluated from first principles using Downloaded from challenge to theoreticians.