Composite Anomaly in Supergravity and String Amplitude Comparison Soumya Sasmal
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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. -
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. -
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) . -
Nonperturbative Definition of the Standard Models
PHYSICAL REVIEW RESEARCH 2, 023356 (2020) Nonperturbative definition of the standard models Juven Wang 1,2,* and Xiao-Gang Wen3 1School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA 2Center of Mathematical Sciences and Applications, Harvard University, Cambridge, Massachusetts 02138, USA 3Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA (Received 14 June 2019; accepted 21 May 2020; published 17 June 2020) The standard models contain chiral fermions coupled to gauge theories. It has been a longstanding problem to give such gauged chiral fermion theories a quantum nonperturbative definition. By classification of quantum anomalies (including perturbative local anomalies and nonperturbative global anomalies) and symmetric interacting invertible topological orders via a mathematical cobordism theorem for differentiable and triangulable manifolds, and by the existence of a symmetric gapped boundary (designed for the mirror sector) on the trivial symmetric invertible topological orders, we propose that Spin(10) chiral fermion theories with Weyl fermions in 16-dimensional spinor representations can be defined on a 3 + 1D lattice without fermion doubling, and subsequently dynamically gauged to be a Spin(10) chiral gauge theory. As a result, the standard models from the 16n-chiral fermion SO(10) grand unification can be defined nonperturbatively via a 3 + 1D local lattice model of bosons or qubits. Furthermore, we propose that standard models from the 15n-chiral fermion -
U(1) Gauge Extensions of the Standard Model
U(1) Gauge Extensions of the Standard Model Ernest Ma Physics and Astronomy Department University of California Riverside, CA 92521, USA U(1) Gauge Extensions of the Standard Model (int08) back to start 1 Contents • Anomaly Freedom of the Standard Model • B − L • Le − Lµ and B − 3Lτ • U(1)Σ • Supersymmetric U(1)X • Some Remarks U(1) Gauge Extensions of the Standard Model (int08) back to start 2 Anomaly Freedom of the Standard Model Gauge Group: SU(3)C × SU((2)L × U(1)Y . Consider the fermion multiplets: (u, d)L ∼ (3, 2, n1), uR ∼ (3, 1, n2), dR ∼ (3, 1, n3), (ν, e)L ∼ (1, 2, n4), eR ∼ (1, 1, n5). Bouchiat/Iliopolous/Meyer(1972): The SM with n1 = 1/6, n2 = 2/3, n3 = −1/3, n4 = −1/2, n5 = −1, is free of axial-vector anomalies, i.e. 2 [SU(3)] U(1)Y : 2n1 − n2 − n3 = 0. 2 [SU(2)] U(1)Y : 3n1 + n4 = 0. 3 3 3 3 3 3 [U(1)Y ] : 6n1 − 3n2 − 3n3 + 2n4 − n5 = 0. U(1) Gauge Extensions of the Standard Model (int08) back to start 3 It is also free of the mixed gravitational-gauge anomaly, U(1)Y : 6n1 − 3n2 − 3n3 + 2n4 − n5 = 0. Geng/Marshak(1989), Minahan/Ramond/Warner(1990) : Above 4 equations ⇒ n1(4n1 − n2)(2n1 + n2) = 0. n2 = 4n1 ⇒ SM; n2 = −2n1 ⇒ SM (uR ↔ dR); n1 = 0 ⇒ n4 = n5 = n2 + n3 = 0. Here eR ∼ (1, 1, 0) may be dropped. (u, d)L, (ν, e)L have charges (1/2, −1/2) and (uR, dR) have charges (n2, −n2). -
Boundary and Defect CFT: Open Problems and Applications
Boundary and Defect CFT: Open Problems and rspa.royalsocietypublishing.org Applications Research N. Andrei1, A. Bissi2, M. Buican3, J. Cardy4;5, P. Dorey6, N. Drukker7, Article submitted to journal J. Erdmenger8, D. Friedan1;9, D. Fursaev10, A. Konechny11;12, C. Kristjansen13, Subject Areas: Theoretical Physics, Mathematical I. Makabe7, Y. Nakayama14, A. O’Bannon15, Physics R. Parini16, B. Robinson15, S. Ryu17, Keywords: C. Schmidt-Colinet18, V. Schomerus19, Conformal Field Theory, Boundaries and Defects, Non-Perturbative C. Schweigert20, and G.M.T. Watts7 Effects, Holographic Duality, 1 Supersymmetry Dept. of Phys., Rutgers Univ., Piscataway, NJ, USA. 2Dept. of Phys. and Astro., Uppsala Univ., SE 3 Author for correspondence: CRST and SPA, Queen Mary Univ. of London, UK B. Robinson 4Dept. of Phys., Univ. of California, Berkeley, CA, USA e-mail: [email protected] 5All Souls College, Oxford, UK 6Dept. of Math. Sci., Durham Univ., UK 7Dept. of Maths, King’s College London, UK 8Julius-Maximilians-Univ. Würzburg, DE 9 Natural Science Inst., Univ. of Iceland, IS 10Dubna State Univ., Dubna, RU 11Dept. of Maths, Heriot-Watt Univ., Edinburgh, UK 12Maxwell Inst. for Math. Sci., Edinburgh, UK 13Niels Bohr Inst., Copenhagen Univ., , DK 14Dept. of Phys., Rikkyo Univ., Tokyo, JP 15STAG Research Centre, Univ. of Southampton, UK 16Department of Mathematics, University of York, UK 17J. Franck Inst. & KCTP., Univ. of Chicago, IL, USA 18Arnold Sommerfeld Center, Univ. München, DE arXiv:1810.05697v1 [hep-th] 12 Oct 2018 19DESY Theory Group, DESY Hamburg, Hamburg, DE 20Fachbereich Math., Univ. Hamburg, Hamburg, DE Proceedings of the workshop “Boundary and Defect Conformal Field Theory: Open Problems and Applications,” Chicheley Hall, Buckinghamshire, UK, 7-8 Sept. -
Conformal Anomaly Actions for Dilaton Interactions
EPJ Web of Conferences 80, 00015 (2014) DOI: 10.1051/epj conf/20140001580 C Owned by the authors, published by EDP Sciences, 2014 Conformal anomaly actions for dilaton interactions Luigi Delle Rose1,a, Carlo Marzo1,b, Mirko Serino1,c 1Dipartimento di Matematica e Fisica "Ennio De Giorgi" Universitá del Salento and INFN Lecce Via per Arnesano 73100 Lecce, Italy Abstract. We discuss, in conformally invariant field theories such as QCD with massless fermions, a possible link between the perturbative signature of the conformal anomaly, in the form of anomaly poles of the 1-particle irreducible effective action, and its descrip- tion in terms of Wess-Zumino actions with a dilaton. The two descriptions are expected to capture the UV and IR behaviour of the conformal anomaly, in terms of fundamental and effective degrees of freedom respectively, with the dilaton effective state appearing in a nonlinear realization. As in the chiral case, conformal anomalies seem to be related to the appearance of these effective interactions in the 1PI action in all the gauge-invariant sectors of the Standard Model. We show that, as a consequence of the underlying anoma- lous symmetry, the infinite hierarchy of recurrence relations involving self-interactions of the dilaton is entirely determined only by the first four of them. This relation can be generalized to any even space-time dimension. 1 Introduction Conformal anomalies play a significant role in theories which are classically scale invariant, such as QCD. This type of anomaly manifests as a non-vanishing trace of the vacuum expectation value (vev) of the energy momentum tensor in a metric (gμν) and gauge field (Aμ) background. -
The Beryllium Anomaly and New Physics
THE BERYLLIUM ANOMALY AND NEW PHYSICS New Physics at the Intensity Frontier CERN-EPFL-Korea Theory Institute Jonathan Feng, University of California, Irvine 21 February 2017 21 Feb 2017 Feng 1 OUTLINE A. J. Krasznhorkay et al., “Observation of Anomalous Internal Pair Creation in 8Be: A Possible Indication of a Light, Neutral Boson,” 1504.01527 [nucl-ex], PRL 116, 042501 (2016) J. Feng et al., “Protophobic Fifth Force Interpretation of the Observed Anomaly in 8Be Nuclear Transitions,” 1604.07411 [hep-ph], PRL 117, 071803 (2016) J. Feng et al., “Particle Physics Models for the 17 MeV Anomaly in Beryllium Nuclear Decays,” 1608.03591 [hep-ph], PRD 95, 035017 (2017) Jonathan Bart Iftah Susan Jordan Tim Flip Feng Fornal Galon Gardner Smolinsky Tait Tanedo 21 Feb 2017 Feng 2 NEW PHYSICS AT THE INTENSITY FRONTIER • There are currently many outstanding puzzles: neutrino masses, gauge hierarchy, strong CP, flavor, dark matter, baryogenesis, dark energy,... • Some of these motivate searches for new particles and forces at high energies: the energy frontier • But some also motivate searches for new physics that is light, but weakly coupled: the intensity frontier • Of particular interest here are connections to dark matter 21 Feb 2017 Feng 3 DARK MATTER AT THE INTENSITY FRONTIER !!! 21 Feb 2017 Feng 4 DARK SECTORS • All evidence for dark matter is gravitational. Perhaps it’s in a hidden sector, composed of particles with no SM gauge interactions (electromagnetic, weak, strong) Visible Dark Sector Sector • The dark sector may have a rich structure with matter and forces of its own Lee, Yang (1956); Kobsarev, Okun, Pomeranchuk (1966); Blinnikov, Khlopov (1982); Foot, Lew, Volkas (1991); Hodges (1993); Berezhiani, Dolgov, Mohapatra (1995); Pospelov, Ritz, Voloshin (2007); Feng, Kumar (2008);.. -
Anomalous Supersymmetry George Katsianis STAG Research Centre, Mathematical Sciences, University of Southampton
Anomalous Supersymmetry George Katsianis STAG Research Centre, Mathematical Sciences, University of Southampton 1. Symmetries 3. Anomalies 6. Results (for the experts) A symmetry of a physical system is any set of transformations that Sometimes classical symmetries fail to survive the quantization We consider the free massless Wess-Zumino model leave some properties of that system invariant. A simple example is procedure. This means that the original symmetries of the classical Z 1 S = d4x −∂ φ∗∂µφ − (ψγ¯ µ∂ ψ) that of the reflection symmetry of a picture, where the left and theory are not actual symmetries of the full quantum theory. We µ 2 µ right sides look like mirror images of each other. call this phenomenon a quantum anomaly. Since the discovery of the axial anomaly by Adler, Bell and Jackiw in 1969, the anomalies which is invariant under supersymmetry transformations of the form played a central role in theoretical physics. In some cases the δψ ∼ φ , δφ ∼ ψ existence of (gauge) anomalies lead to inconsistencies, so their and U(1) field transformations. The corresponding conserved cancellation help us build viable physical models. In other cases currents are the supercurrent Sµ and the R-current Rµ. (global) anomalies are linked to observable effects and explain We compute the 4-point correlation function of two supercurrents experimental data, since they allow classically forbidden processes and two R-currents T (Sµ(x )S¯ν(x )Rκ (x ) Rλ (x )i. to occur. One such example is the pion decay into two photons. 1 2 3 4 The Feynman diagrams for the connected part of this correlation function have the following form: Source: wild.maths.org 4. -
Ads/CFT Correspondence and Differential Geometry Johanna
. AdS/CFT Correspondence and Differential Geometry Johanna Erdmenger Max Planck–Institut fur¨ Physik, Munchen¨ 1 Outline 1. Introduction: The AdS/CFT correspondence 2. Conformal Anomaly 3. AdS/CFT for field theories with = 1 Supersymmetry N 4. Example: Sasaki-Einstein manifolds 2 AdS/CFT Correspondence (Maldacena 1997, AdS: Anti de Sitter space, CFT: conformal field theory) Witten; Gubser, Klebanov, Polyakov Duality Quantum Field Theory Gravity Theory ⇔ Arises from String Theory in a particular low-energy limit Duality: Quantum field theory at strong coupling Gravity theory at weak coupling ⇔ Conformal field theory in four dimensions Supergravity Theory on AdS S5 ⇔ 5 × 3 Anti-de Sitter space Anti de Sitter space: Einstein space with constant negative curvature has a boundary which is the upper half of the Einstein static universe (locally this may be conformally mapped to four-dimensional Minkowski space ) Isometry group of AdS5: SO(4, 2) AdS/CFT: relates conformal field theory at the boundary of AdS5 to gravity theory on AdS S5 5 × Isometry group of S5: SO(6) ( SU(4)) ∼ 4 AdS/CFT correspondence Anti-de Sitter space: Einstein space with constant negative curvature AdS space has a boundary 2 2r/L µ ν 2 Metric: ds = e ηµνdx dx + dr Isometry group of (d + 1)-dimensional AdS space coincides with conformal group in d dimensions (SO(d, 2)). AdS/CFT correspondence provides dictionary between field theory opera- tors and supergravity fields 2 φ , ∆ = d + d + L2m2 O∆ ↔ m 2 4 ! Items in the same dictionary entry have the same quantum numbers under superconformal symmetry SU(2, 2 4).