Anomaly-Free Supergravities in Six Dimensions
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Particles-Versus-Strings.Pdf
Particles vs. strings http://insti.physics.sunysb.edu/~siegel/vs.html In light of the huge amount of propaganda and confusion regarding string theory, it might be useful to consider the relative merits of the descriptions of the fundamental constituents of matter as particles or strings. (More-skeptical reviews can be found in my physics parodies.A more technical analysis can be found at "Warren Siegel's research".) Predictability The main problem in high energy theoretical physics today is predictions, especially for quantum gravity and confinement. An important part of predictability is calculability. There are various levels of calculations possible: 1. Existence: proofs of theorems, answers to yes/no questions 2. Qualitative: "hand-waving" results, answers to multiple choice questions 3. Order of magnitude: dimensional analysis arguments, 10? (but beware hidden numbers, like powers of 4π) 4. Constants: generally low-energy results, like ground-state energies 5. Functions: complete results, like scattering probabilities in terms of energy and angle Any but the last level eventually leads to rejection of the theory, although previous levels are acceptable at early stages, as long as progress is encouraging. It is easy to write down the most general theory consistent with special (and for gravity, general) relativity, quantum mechanics, and field theory, but it is too general: The spectrum of particles must be specified, and more coupling constants and varieties of interaction become available as energy increases. The solutions to this problem go by various names -- "unification", "renormalizability", "finiteness", "universality", etc. -- but they are all just different ways to realize the same goal of predictability. -
Gravitational Anomaly and Hawking Radiation of Apparent Horizon in FRW Universe
Eur. Phys. J. C (2009) 62: 455–458 DOI 10.1140/epjc/s10052-009-1081-4 Letter Gravitational anomaly and Hawking radiation of apparent horizon in FRW universe Ran Lia, Ji-Rong Renb, Shao-Wen Wei Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, Gansu, China Received: 27 February 2009 / Published online: 26 June 2009 © Springer-Verlag / Società Italiana di Fisica 2009 Abstract Motivated by the successful applications of the have been carried out [8–28]. In fact, the anomaly analy- anomaly cancellation method to derive Hawking radiation sis can be traced back to Christensen and Fulling’s early from various types of black hole spacetimes, we further work [29], in which they suggested that there exists a rela- extend the gravitational anomaly method to investigate the tion between the Hawking radiation and the anomalous trace Hawking radiation from the apparent horizon of a FRW uni- of the field under the condition that the covariant conser- verse by assuming that the gravitational anomaly also exists vation law is valid. Imposing boundary condition near the near the apparent horizon of the FRW universe. The result horizon, Wilczek et al. showed that Hawking radiation is shows that the radiation flux from the apparent horizon of just the cancel term of the gravitational anomaly of the co- the FRW universe measured by a Kodama observer is just variant conservation law and gauge invariance. Their basic the pure thermal flux. The result presented here will further idea is that, near the horizon, a quantum field in a black hole confirm the thermal properties of the apparent horizon in a background can be effectively described by an infinite col- FRW universe. -
Chiral Currents from Anomalies
ω2 α 2 ω1 α1 Michael Stone (ICMT ) Chiral Currents Santa-Fe July 18 2018 1 Chiral currents from Anomalies Michael Stone Institute for Condensed Matter Theory University of Illinois Santa-Fe July 18 2018 Michael Stone (ICMT ) Chiral Currents Santa-Fe July 18 2018 2 Michael Stone (ICMT ) Chiral Currents Santa-Fe July 18 2018 3 Experiment aims to verify: k ρσαβ r T µν = F µνJ − p r [F Rνµ ]; µ µ 384π2 −g µ ρσ αβ k µνρσ k µνρσ r J µ = − p F F − p Rα Rβ ; µ 32π2 −g µν ρσ 768π2 −g βµν αρσ Here k is number of Weyl fermions, or the Berry flux for a single Weyl node. Michael Stone (ICMT ) Chiral Currents Santa-Fe July 18 2018 4 What the experiment measures Contribution to energy current for 3d Weyl fermion with H^ = σ · k µ2 1 J = B + T 2 8π2 24 Simple explanation: The B field makes B=2π one-dimensional chiral fermions per unit area. These have = +k Energy current/density from each one-dimensional chiral fermion: Z 1 d 1 µ2 1 J = − θ(−) = 2π + T 2 β(−µ) 2 −∞ 2π 1 + e 8π 24 Could even have been worked out by Sommerfeld in 1928! Michael Stone (ICMT ) Chiral Currents Santa-Fe July 18 2018 5 Are we really exploring anomaly physics? Michael Stone (ICMT ) Chiral Currents Santa-Fe July 18 2018 6 Yes! Michael Stone (ICMT ) Chiral Currents Santa-Fe July 18 2018 7 Energy-Momentum Anomaly k ρσαβ r T µν = F µνJ − p r [F Rνµ ]; µ µ 384π2 −g µ ρσ αβ Michael Stone (ICMT ) Chiral Currents Santa-Fe July 18 2018 8 Origin of Gravitational Anomaly in 2 dimensions Set z = x + iy and use conformal coordinates ds2 = expfφ(z; z¯)gdz¯ ⊗ dz Example: non-chiral scalar field '^ has central charge c = 1 and energy-momentum operator is T^(z) =:@z'@^ z'^: Actual energy-momentum tensor is c T = T^(z) + @2 φ − 1 (@ φ)2 zz 24π zz 2 z c T = T^(¯z) + @2 φ − 1 (@ φ)2 z¯z¯ 24π z¯z¯ 2 z¯ c T = − @2 φ zz¯ 24π zz¯ z z¯ Now Γzz = @zφ, Γz¯z¯ = @z¯φ, all others zero. -
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. -
Scientists Observe Gravitational Anomaly on Earth 21 July 2017
Scientists observe gravitational anomaly on Earth 21 July 2017 strange that they named this phenomenon an "anomaly." For most of their history, these quantum anomalies were confined to the world of elementary particle physics explored in huge accelerator laboratories such as Large Hadron Collider at CERN in Switzerland. Now however, a new type of materials, the so-called Weyl semimetals, similar to 3-D graphene, allow us to put the symmetry destructing quantum anomaly to work in everyday phenomena, such as the creation of electric current. In these exotic materials electrons effectively behave in the very same way as the elementary Prof. Dr. Karl Landsteiner, a string theorist at the particles studied in high energy accelerators. These Instituto de Fisica Teorica UAM/CSIC and co-author of particles have the strange property that they cannot the paper made this graphic to explain the gravitational be at rest—they have to move with a constant speed anomaly. Credit: IBM Research at all times. They also have another property called spin. It is like a tiny magnet attached to the particles and they come in two species. The spin can either point in the direction of motion or in the opposite Modern physics has accustomed us to strange and direction. counterintuitive notions of reality—especially quantum physics which is famous for leaving physical objects in strange states of superposition. For example, Schrödinger's cat, who finds itself unable to decide if it is dead or alive. Sometimes however quantum mechanics is more decisive and even destructive. Symmetries are the holy grail for physicists. -
On the Trace Anomaly of a Weyl Fermion in a Gauge Background
On the trace anomaly of a Weyl fermion in a gauge background Fiorenzo Bastianelli,a;b;c Matteo Broccoli,a;c aDipartimento di Fisica ed Astronomia, Universit`adi Bologna, via Irnerio 46, I-40126 Bologna, Italy bINFN, Sezione di Bologna, via Irnerio 46, I-40126 Bologna, Italy cMax-Planck-Institut f¨ur Gravitationsphysik (Albert-Einstein-Institut) Am M¨uhlenberg 1, D-14476 Golm, Germany E-mail: [email protected], [email protected] Abstract: We study the trace anomaly of a Weyl fermion in an abelian gauge background. Although the presence of the chiral anomaly implies a breakdown of gauge invariance, we find that the trace anomaly can be cast in a gauge invariant form. In particular, we find that it does not contain any odd-parity contribution proportional to the Chern-Pontryagin density, which would be allowed by the con- sistency conditions. We perform our calculations using Pauli-Villars regularization and heat kernel methods. The issue is analogous to the one recently discussed in the literature about the trace anomaly of a Weyl fermion in curved backgrounds. Keywords: Anomalies in Field and String Theories, Conformal Field Theory arXiv:1808.03489v2 [hep-th] 7 May 2019 Contents 1 Introduction1 2 Actions and symmetries3 2.1 The Weyl fermion3 2.1.1 Mass terms5 2.2 The Dirac fermion8 2.2.1 Mass terms9 3 Regulators and consistent anomalies 10 4 Anomalies 13 4.1 Chiral and trace anomalies of a Weyl fermion 13 4.1.1 PV regularization with Majorana mass 14 4.1.2 PV regularization with Dirac mass 15 4.2 Chiral and trace anomalies of a Dirac fermion 16 4.2.1 PV regularization with Dirac mass 16 4.2.2 PV regularization with Majorana mass 17 5 Conclusions 18 A Conventions 19 B The heat kernel 21 C Sample calculations 22 1 Introduction In this paper we study the trace anomaly of a chiral fermion coupled to an abelian gauge field in four dimensions. -
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]. -
Chiral Gauge Theories Revisited
CERN-TH/2001-031 Chiral gauge theories revisited Lectures given at the International School of Subnuclear Physics Erice, 27 August { 5 September 2000 Martin L¨uscher ∗ CERN, Theory Division CH-1211 Geneva 23, Switzerland Contents 1. Introduction 2. Chiral gauge theories & the gauge anomaly 3. The regularization problem 4. Weyl fermions from 4+1 dimensions 5. The Ginsparg–Wilson relation 6. Gauge-invariant lattice regularization of anomaly-free theories 1. Introduction A characteristic feature of the electroweak interactions is that the left- and right- handed components of the fermion fields do not couple to the gauge fields in the same way. The term chiral gauge theory is reserved for field theories of this type, while all other gauge theories (such as QCD) are referred to as vector-like, since the gauge fields only couple to vector currents in this case. At first sight the difference appears to be mathematically insignificant, but it turns out that in many respects chiral ∗ On leave from Deutsches Elektronen-Synchrotron DESY, D-22603 Hamburg, Germany 1 νµ ν e µ W W γ e Fig. 1. Feynman diagram contributing to the muon decay at two-loop order of the electroweak interactions. The triangular subdiagram in this example is potentially anomalous and must be treated with care to ensure that gauge invariance is preserved. gauge theories are much more complicated. Their definition beyond the classical level, for example, is already highly non-trivial and it is in general extremely difficult to obtain any solid information about their non-perturbative properties. 1.1 Anomalies Most of the peculiarities in chiral gauge theories are related to the fact that the gauge symmetry tends to be violated by quantum effects. -
Prospects from Strings and Branes
Prospects from strings and branes Alexander Sevrin Vrije Universiteit Brussel and The International Solvay Institutes for Physics and Chemistry http://tena4.vub.ac.be/ Moriond 2004 Strings and branes… Moriond, March 24, 2004 1 References Not-too-technical review paper, including numerous references: Strings, Gravity and Particle Physics by Augusto Sagnotti and AS In the proceedings of 37th Rencontres de Moriond on Electroweak Interactions and Unified Theories, 2002. e-Print Archive: hep-ex/0209011 Strings and branes… Moriond, March 24, 2004 2 Contents • Dirichlet-branes • D-branes and gauge theories - Worldvolume point of view -AdS/CFT • D-branes and black holes •Cosmology • Some conclusions Strings and branes… Moriond, March 24, 2004 3 Branes Solitons: solutions of the equations of motion with a finite energy(-density) and a mass inversely proportional to the coupling constant. E.g. Scalar field in d = 1 + 1: kink. 12m3 mass = λ Other example in d = 3 + 1: magnetic monopole: 1 mass ∝ 2 gYM Strings and branes… Moriond, March 24, 2004 4 Solitons in string theory: Dirichlet branes Besides the “conventional” fields, such as e.g., gµν (x)=gνµ(x): metric = graviton Φ(x): dilaton, one has RR- potentials as well. E.g. vector potential, A µ : Fµν = ∂µAν − ∂ν Aµ, Aµ → Aµ − ∂µf, Fµν → Fµν . Couples to particles: µ S = q dτ x˙ (τ)Aµ(x(τ)). Z Strings and branes… Moriond, March 24, 2004 5 E.g. 2-form potential, A µ ν = − A ν µ : Fµνρ = ∂µAνρ + ∂ν Aρµ + ∂ρAµν , Aµν → Aµν − ∂µfν + ∂ν fµ,Fµνρ → Fµνρ. Couples to strings: µ ν S = q dτdσ x˙(τ, σ) x0(τ, σ) Aµν (x(τ, σ)). -
Mixed Anomalies of Chiral Algebras Compactified to Smooth Quasi
MIXED ANOMALIES OF CHIRAL ALGEBRAS COMPACTIFIED TO SMOOTH QUASI-PROJECTIVE SURFACES MAKOTO SAKURAI Abstract. Some time ago, the chiral algebra theory of Beilinson- Drinfeld[BD] was expected to play a central role in the conver- gence of divergence in mathematical physics of superstring theory for quantization of gauge theory and gravity. Naively, this al- gebra plays an important role in a holomorphic conformal field theory with a non-negative integer graded conformal dimension, whose target space does not necessarily have the vanishing first Chern class. This algebra has two definitions until now: one is that by Malikov-Schechtman-Vaintrob by gluing affine patches, and the other is that of Kapranov-Vasserot by gluing the formal loop spaces. I will use the new definition of Nekrasov by simplifying Malikov-Schechtman-Vaintrob in order to compute the obstruction classes of gerbes of chiral differential operators. In this paper, I will examine the two independent Ans¨atze (or working hypotheses) of Witten’s = (0, 2) heterotic strings and Nekrasov’s generalized complex geometry,N after Hitchin and Gualtieri, are consistent in the case of CP2, which has 3 affine patches and is expected to have the “first Pontryagin anomaly”. I also scrutinized the physical meanings of 2 dimensional toric Fano manifolds, or rather toric del Pezzo surfaces, obtained by blowing up the non-colinear 1, 2, 3 points of CP2. The obstruction classes of gerbes of them coincide with the second Chern char- acters obtained by the Riemann-Roch theorem and in particular vanishes for 1 point blowup, which means that one of the gravita- tional anomalies vanishes for a non-Calabi-Yau manifold compact- arXiv:0712.2318v5 [hep-th] 25 Feb 2015 ification. -
Global Anomalies in M-Theory
CERN-TH/97-277 hep-th/9710126 Global Anomalies in M -theory Mans Henningson Theory Division, CERN CH-1211 Geneva 23, Switzerland [email protected] Abstract We rst consider M -theory formulated on an op en eleven-dimensional spin-manifold. There is then a p otential anomaly under gauge transforma- tions on the E bundle that is de ned over the b oundary and also under 8 di eomorphisms of the b oundary. We then consider M -theory con gura- tions that include a ve-brane. In this case, di eomorphisms of the eleven- manifold induce di eomorphisms of the ve-brane world-volume and gauge transformations on its normal bundle. These transformations are also po- tentially anomalous. In b oth of these cases, it has previously b een shown that the p erturbative anomalies, i.e. the anomalies under transformations that can be continuously connected to the identity, cancel. We extend this analysis to global anomalies, i.e. anomalies under transformations in other comp onents of the group of gauge transformations and di eomorphisms. These anomalies are given by certain top ological invariants, that we explic- itly construct. CERN-TH/97-277 Octob er 1997 1. Intro duction The consistency of a theory with gauge- elds or dynamical gravity requires that the e ective action is invariant under gauge transformations and space-time di eomorphisms, usually referred to as cancelation of gauge and gravitational anomalies. The rst step towards establishing that a given theory is anomaly free is to consider transformations that are continuously connected to the identity. -
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) .