QCD, Strings and Black Holes
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Compactifying M-Theory on a G2 Manifold to Describe/Explain Our World – Predictions for LHC (Gluinos, Winos, Squarks), and Dark Matter
Compactifying M-theory on a G2 manifold to describe/explain our world – Predictions for LHC (gluinos, winos, squarks), and dark matter Gordy Kane CMS, Fermilab, April 2016 1 OUTLINE • Testing theories in physics – some generalities - Testing 10/11 dimensional string/M-theories as underlying theories of our world requires compactification to four space-time dimensions! • Compactifying M-theory on “G2 manifolds” to describe/ explain our vacuum – underlying theory - fluxless sector! • Moduli – 4D manifestations of extra dimensions – stabilization - supersymmetry breaking – changes cosmology first 16 slides • Technical stuff – 18-33 - quickly • From the Planck scale to EW scale – 34-39 • LHC predictions – gluino about 1.5 TeV – also winos at LHC – but not squarks - 40-47 • Dark matter – in progress – surprising – 48 • (Little hierarchy problem – 49-51) • Final remarks 1-5 2 String/M theory a powerful, very promising framework for constructing an underlying theory that incorporates the Standard Models of particle physics and cosmology and probably addresses all the questions we hope to understand about the physical universe – we hope for such a theory! – probably also a quantum theory of gravity Compactified M-theory generically has gravity; Yang- Mills forces like the SM; chiral fermions like quarks and leptons; softly broken supersymmetry; solutions to hierarchy problems; EWSB and Higgs physics; unification; small EDMs; no flavor changing problems; partially observable superpartner spectrum; hidden sector DM; etc Simultaneously – generically Argue compactified M-theory is by far the best motivated, and most comprehensive, extension of the SM – gets physics relevant to the LHC and Higgs and superpartners right – no ad hoc inputs or free parameters Take it very seriously 4 So have to spend some time explaining derivations, testability of string/M theory Don’t have to be somewhere to test theory there – E.g. -
Quantum Field Theory*
Quantum Field Theory y Frank Wilczek Institute for Advanced Study, School of Natural Science, Olden Lane, Princeton, NJ 08540 I discuss the general principles underlying quantum eld theory, and attempt to identify its most profound consequences. The deep est of these consequences result from the in nite number of degrees of freedom invoked to implement lo cality.Imention a few of its most striking successes, b oth achieved and prosp ective. Possible limitation s of quantum eld theory are viewed in the light of its history. I. SURVEY Quantum eld theory is the framework in which the regnant theories of the electroweak and strong interactions, which together form the Standard Mo del, are formulated. Quantum electro dynamics (QED), b esides providing a com- plete foundation for atomic physics and chemistry, has supp orted calculations of physical quantities with unparalleled precision. The exp erimentally measured value of the magnetic dip ole moment of the muon, 11 (g 2) = 233 184 600 (1680) 10 ; (1) exp: for example, should b e compared with the theoretical prediction 11 (g 2) = 233 183 478 (308) 10 : (2) theor: In quantum chromo dynamics (QCD) we cannot, for the forseeable future, aspire to to comparable accuracy.Yet QCD provides di erent, and at least equally impressive, evidence for the validity of the basic principles of quantum eld theory. Indeed, b ecause in QCD the interactions are stronger, QCD manifests a wider variety of phenomena characteristic of quantum eld theory. These include esp ecially running of the e ective coupling with distance or energy scale and the phenomenon of con nement. -
Zero-Point Energy in Bag Models
Ooa/ea/oHsnif- ^*7 ( 4*0 0 1 5 4 3 - m . Zero-Point Energy in Bag Models by Kimball A. Milton* Department of Physics The Ohio State University Columbus, Ohio 43210 A b s t r a c t The zero-point (Casimir) energy of free vector (gluon) fields confined to a spherical cavity (bag) is computed. With a suitable renormalization the result for eight gluons is This result is substantially larger than that for a spher ical shell (where both interior and exterior modes are pre sent), and so affects Johnson's model of the QCD vacuum. It is also smaller than, and of opposite sign to the value used in bag model phenomenology, so it will have important implications there. * On leave ifrom Department of Physics, University of California, Los Angeles, CA 90024. I. Introduction Quantum chromodynamics (QCD) may we 1.1 be the appropriate theory of hadronic matter. However, the theory is not at all well understood. It may turn out that color confinement is roughly approximated by the phenomenologically suc cessful bag model [1,2]. In this model, the normal vacuum is a perfect color magnetic conductor, that iis, the color magnetic permeability n is infinite, while the vacuum.in the interior of the bag is characterized by n=l. This implies that the color electric and magnetic fields are confined to the interior of the bag, and that they satisfy the following boundary conditions on its surface S: n.&jg= 0, nxBlg= 0, (1) where n is normal to S. Now, even in an "empty" bag (i.e., one containing no quarks) there will be non-zero fields present because of quantum fluctua tions. -
18. Lattice Quantum Chromodynamics
18. Lattice QCD 1 18. Lattice Quantum Chromodynamics Updated September 2017 by S. Hashimoto (KEK), J. Laiho (Syracuse University) and S.R. Sharpe (University of Washington). Many physical processes considered in the Review of Particle Properties (RPP) involve hadrons. The properties of hadrons—which are composed of quarks and gluons—are governed primarily by Quantum Chromodynamics (QCD) (with small corrections from Quantum Electrodynamics [QED]). Theoretical calculations of these properties require non-perturbative methods, and Lattice Quantum Chromodynamics (LQCD) is a tool to carry out such calculations. It has been successfully applied to many properties of hadrons. Most important for the RPP are the calculation of electroweak form factors, which are needed to extract Cabbibo-Kobayashi-Maskawa (CKM) matrix elements when combined with the corresponding experimental measurements. LQCD has also been used to determine other fundamental parameters of the standard model, in particular the strong coupling constant and quark masses, as well as to predict hadronic contributions to the anomalous magnetic moment of the muon, gµ 2. − This review describes the theoretical foundations of LQCD and sketches the methods used to calculate the quantities relevant for the RPP. It also describes the various sources of error that must be controlled in a LQCD calculation. Results for hadronic quantities are given in the corresponding dedicated reviews. 18.1. Lattice regularization of QCD Gauge theories form the building blocks of the Standard Model. While the SU(2) and U(1) parts have weak couplings and can be studied accurately with perturbative methods, the SU(3) component—QCD—is only amenable to a perturbative treatment at high energies. -
Deformations of G2-Structures, String Dualities and Flat Higgs Bundles Rodrigo De Menezes Barbosa University of Pennsylvania, [email protected]
University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 2019 Deformations Of G2-Structures, String Dualities And Flat Higgs Bundles Rodrigo De Menezes Barbosa University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Mathematics Commons, and the Quantum Physics Commons Recommended Citation Barbosa, Rodrigo De Menezes, "Deformations Of G2-Structures, String Dualities And Flat Higgs Bundles" (2019). Publicly Accessible Penn Dissertations. 3279. https://repository.upenn.edu/edissertations/3279 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/3279 For more information, please contact [email protected]. Deformations Of G2-Structures, String Dualities And Flat Higgs Bundles Abstract We study M-theory compactifications on G2-orbifolds and their resolutions given by total spaces of coassociative ALE-fibrations over a compact flat Riemannian 3-manifold Q. The afl tness condition allows an explicit description of the deformation space of closed G2-structures, and hence also the moduli space of supersymmetric vacua: it is modeled by flat sections of a bundle of Brieskorn-Grothendieck resolutions over Q. Moreover, when instanton corrections are neglected, we obtain an explicit description of the moduli space for the dual type IIA string compactification. The two moduli spaces are shown to be isomorphic for an important example involving A1-singularities, and the result is conjectured to hold in generality. We also discuss an interpretation of the IIA moduli space in terms of "flat Higgs bundles" on Q and explain how it suggests a new approach to SYZ mirror symmetry, while also providing a description of G2-structures in terms of B-branes. -
Non-Holomorphic Cycles and Non-BPS Black Branes Arxiv
Non-Holomorphic Cycles and Non-BPS Black Branes Cody Long,1;2 Artan Sheshmani,2;3;4 Cumrun Vafa,1 and Shing-Tung Yau2;5 1Jefferson Physical Laboratory, Harvard University Cambridge, MA 02138, USA 2Center for Mathematical Sciences and Applications, Harvard University Cambridge, MA 02139, USA 3Institut for Matematik, Aarhus Universitet 8000 Aarhus C, Denmark 4 National Research University Higher School of Economics, Russian Federation, Laboratory of Mirror Symmetry, Moscow, Russia, 119048 5Department of Mathematics, Harvard University Cambridge, MA 02138, USA We study extremal non-BPS black holes and strings arising in M-theory compactifica- tions on Calabi-Yau threefolds, obtained by wrapping M2 branes on non-holomorphic 2-cycles and M5 branes on non-holomorphic 4-cycles. Using the attractor mechanism we compute the black hole mass and black string tension, leading to a conjectural for- mula for the asymptotic volumes of connected, locally volume-minimizing representa- tives of non-holomorphic, even-dimensional homology classes in the threefold, without arXiv:2104.06420v1 [hep-th] 13 Apr 2021 knowledge of an explicit metric. In the case of divisors we find examples where the vol- ume of the representative corresponding to the black string is less than the volume of the minimal piecewise-holomorphic representative, predicting recombination for those homology classes and leading to stable, non-BPS strings. We also compute the central charges of non-BPS strings in F-theory via a near-horizon AdS3 limit in 6d which, upon compactification on a circle, account for the asymptotic entropy of extremal non- supersymmetric 5d black holes (i.e., the asymptotic count of non-holomorphic minimal 2-cycles). -
Modular Invariance of Characters of Vertex Operator Algebras
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Volume 9, Number 1, January 1996 MODULAR INVARIANCE OF CHARACTERS OF VERTEX OPERATOR ALGEBRAS YONGCHANG ZHU Introduction In contrast with the finite dimensional case, one of the distinguished features in the theory of infinite dimensional Lie algebras is the modular invariance of the characters of certain representations. It is known [Fr], [KP] that for a given affine Lie algebra, the linear space spanned by the characters of the integrable highest weight modules with a fixed level is invariant under the usual action of the modular group SL2(Z). The similar result for the minimal series of the Virasoro algebra is observed in [Ca] and [IZ]. In both cases one uses the explicit character formulas to prove the modular invariance. The character formula for the affine Lie algebra is computed in [K], and the character formula for the Virasoro algebra is essentially contained in [FF]; see [R] for an explicit computation. This mysterious connection between the infinite dimensional Lie algebras and the modular group can be explained by the two dimensional conformal field theory. The highest weight modules of affine Lie algebras and the Virasoro algebra give rise to conformal field theories. In particular, the conformal field theories associated to the integrable highest modules and minimal series are rational. The characters of these modules are understood to be the holomorphic parts of the partition functions on the torus for the corresponding conformal field theories. From this point of view, the role of the modular group SL2(Z)ismanifest. In the study of conformal field theory, physicists arrived at the notion of chi- ral algebras (see e.g. -
On Mirror Maps for Manifolds of Exceptional Holonomy JHEP10(2019)204 ]) 2 and 2 G ] (See Also [ 1 21 31 ]
Published for SISSA by Springer Received: August 23, 2019 Accepted: October 2, 2019 Published: October 21, 2019 On mirror maps for manifolds of exceptional holonomy JHEP10(2019)204 Andreas P. Braun,a Suvajit Majumdera and Alexander Ottob;c aMathematical Institute, University of Oxford Woodstock Road, Oxford, OX2 6GG, U.K. bPerimeter Institute for Theoretical Physics, 31 Caroline St N, Waterloo, ON N2L 2Y5, Canada cDepartment of Physics, University of Waterloo, Waterloo, ON N2L 3G1, Canada E-mail: [email protected], [email protected], [email protected] Abstract: We study mirror symmetry of type II strings on manifolds with the exceptional holonomy groups G2 and Spin(7). Our central result is a construction of mirrors of Spin(7) manifolds realized as generalized connected sums. In parallel to twisted connected sum G2 manifolds, mirrors of such Spin(7) manifolds can be found by applying mirror symmetry to the pair of non-compact manifolds they are glued from. To provide non-trivial checks for such geometric mirror constructions, we give a CFT analysis of mirror maps for Joyce orbifolds in several new instances for both the Spin(7) and the G2 case. For all of these models we find possible assignments of discrete torsion phases, work out the action of mirror symmetry, and confirm the consistency with the geometrical construction. A novel feature appearing in the examples we analyse is the possibility of frozen singularities. Keywords: String Duality, Conformal Field Models in String Theory, Superstring Vacua ArXiv ePrint: 1905.01474 Open Access, c The Authors. https://doi.org/10.1007/JHEP10(2019)204 Article funded by SCOAP3. -
From String Theory and Moonshine to Vertex Algebras
Preample From string theory and Moonshine to vertex algebras Bong H. Lian Department of Mathematics Brandeis University [email protected] Harvard University, May 22, 2020 Dedicated to the memory of John Horton Conway December 26, 1937 – April 11, 2020. Preample Acknowledgements: Speaker’s collaborators on the theory of vertex algebras: Andy Linshaw (Denver University) Bailin Song (University of Science and Technology of China) Gregg Zuckerman (Yale University) For their helpful input to this lecture, special thanks to An Huang (Brandeis University) Tsung-Ju Lee (Harvard CMSA) Andy Linshaw (Denver University) Preample Disclaimers: This lecture includes a brief survey of the period prior to and soon after the creation of the theory of vertex algebras, and makes no claim of completeness – the survey is intended to highlight developments that reflect the speaker’s own views (and biases) about the subject. As a short survey of early history, it will inevitably miss many of the more recent important or even towering results. Egs. geometric Langlands, braided tensor categories, conformal nets, applications to mirror symmetry, deformations of VAs, .... Emphases are placed on the mutually beneficial cross-influences between physics and vertex algebras in their concurrent early developments, and the lecture is aimed for a general audience. Preample Outline 1 Early History 1970s – 90s: two parallel universes 2 A fruitful perspective: vertex algebras as higher commutative algebras 3 Classification: cousins of the Moonshine VOA 4 Speculations The String Theory Universe 1968: Veneziano proposed a model (using the Euler beta function) to explain the ‘st-channel crossing’ symmetry in 4-meson scattering, and the Regge trajectory (an angular momentum vs binding energy plot for the Coulumb potential). -
Super-Higgs in Superspace
Article Super-Higgs in Superspace Gianni Tallarita 1,* and Moritz McGarrie 2 1 Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ibáñez, Santiago 7941169, Chile 2 Deutsches Elektronen-Synchrotron, DESY, Notkestrasse 85, 22607 Hamburg, Germany; [email protected] * Correspondence: [email protected] or [email protected] Received: 1 April 2019; Accepted: 10 June 2019; Published: 14 June 2019 Abstract: We determine the effective gravitational couplings in superspace whose components reproduce the supergravity Higgs effect for the constrained Goldstino multiplet. It reproduces the known Gravitino sector while constraining the off-shell completion. We show that these couplings arise by computing them as quantum corrections. This may be useful for phenomenological studies and model-building. We give an example of its application to multiple Goldstini. Keywords: supersymmetry; Goldstino; superspace 1. Introduction The spontaneous breakdown of global supersymmetry generates a massless Goldstino [1,2], which is well described by the Akulov-Volkov (A-V) effective action [3]. When supersymmetry is made local, the Gravitino “eats” the Goldstino of the A-V action to become massive: The super-Higgs mechanism [4,5]. In terms of superfields, the constrained Goldstino multiplet FNL [6–12] is equivalent to the A-V formulation (see also [13–17]). It is, therefore, natural to extend the description of supergravity with this multiplet, in superspace, to one that can reproduce the super-Higgs mechanism. In this paper we address two issues—first we demonstrate how the Gravitino, Goldstino, and multiple Goldstini obtain a mass. Secondly, by using the Spurion analysis, we write down the most minimal set of new terms in superspace that incorporate both supergravity and the Goldstino multiplet in order to reproduce the super-Higgs mechanism of [5,18] at lowest order in M¯ Pl. -
Quantum Mechanics Quantum Chromodynamics (QCD)
Quantum Mechanics_quantum chromodynamics (QCD) In theoretical physics, quantum chromodynamics (QCD) is a theory ofstrong interactions, a fundamental forcedescribing the interactions between quarksand gluons which make up hadrons such as the proton, neutron and pion. QCD is a type of Quantum field theory called a non- abelian gauge theory with symmetry group SU(3). The QCD analog of electric charge is a property called 'color'. Gluons are the force carrier of the theory, like photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of Particle physics. A huge body of experimental evidence for QCD has been gathered over the years. QCD enjoys two peculiar properties: Confinement, which means that the force between quarks does not diminish as they are separated. Because of this, when you do split the quark the energy is enough to create another quark thus creating another quark pair; they are forever bound into hadrons such as theproton and the neutron or the pion and kaon. Although analytically unproven, confinement is widely believed to be true because it explains the consistent failure of free quark searches, and it is easy to demonstrate in lattice QCD. Asymptotic freedom, which means that in very high-energy reactions, quarks and gluons interact very weakly creating a quark–gluon plasma. This prediction of QCD was first discovered in the early 1970s by David Politzer and by Frank Wilczek and David Gross. For this work they were awarded the 2004 Nobel Prize in Physics. There is no known phase-transition line separating these two properties; confinement is dominant in low-energy scales but, as energy increases, asymptotic freedom becomes dominant. -
Black Brane Evaporation Through D-Brane Bubble Nucleation
HIP-2021-20/TH Black brane evaporation through D-brane bubble nucleation Oscar Henriksson∗ Department of Physics and Helsinki Institute of Physics P.O. Box 64, FI-00014 University of Helsinki, Finland Abstract We study the process of black brane evaporation through the emission of D-branes. Gravi- tational solutions describing black branes in asymptotically anti-de Sitter spacetimes, which are holographically dual to field theory states at finite temperature and density, have previously been found to exhibit an instability due to brane nucleation. Working in the setting of D3-branes on the conifold, we construct static Euclidean solutions describing this nucleation to leading order | D3-branes bubbling off the horizon. Furthermore, we analyze the late-time dynamics of such a D3-brane bubble as it expands and find a steady-state solution including the wall profile and its speed. CONTENTS I. Introduction 2 II. Gravity solutions and field theory dual 3 III. The D3-brane effective action 4 IV. Bubble nucleation 6 arXiv:2106.13254v1 [hep-th] 24 Jun 2021 V. Late time expansion 8 VI. Discussion 11 Acknowledgments 12 References 12 ∗ oscar.henriksson@helsinki.fi 1 I. INTRODUCTION Black holes are unstable to evaporation due to Hawking radiation. Though this fact is on firm theoretical footing, there are still many open questions regarding the precise details of this evaporation, some of which may require a complete theory of quantum gravity to settle. String theory is a strong candidate for such a theory. Besides strings, this framework also introduces other extended objects known as branes. These dynamical objects also gravitate, and a large number of them can be described in the supergravity limit of string theory as a black brane.