Instantons in Particle Physics
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D-Instanton Perturbation Theory
D-instanton Perturbation Theory Ashoke Sen Harish-Chandra Research Institute, Allahabad, India Sao Paolo, June 2020 1 Plan: 1. Overview of the problem and the solution 2. Review of basic aspects of world-sheet string theory and string field theory 3. Some explicit computations A.S., arXiv:1908.02782, 2002.04043, work in progress 2 The problem 3 String theory began with Veneziano amplitude – tree level scattering amplitude of four tachyons in open string theory World-sheet expression for the amplitude (in α0 = 1 unit) Z 1 dy y2p1:p2 (1 − y)2p2:p3 0 – diverges for 2p1:p2 ≤ −1 or 2p2:p3 ≤ −1. Our convention: a:b ≡ −a0b0 + ~a:~b Conventional viewpoint: Define the amplitude for 2p1:p2 > −1, 2p2:p3 > −1 and then analytically continue to the other kinematic regions. 4 However, analytic continuation does not always work It may not be possible to move away from the singularity by changing the external momenta Examples: Mass renormalization, Vacuum shift – discussed earlier In these lectures we shall discuss another situation where analytic continuation fails – D-instanton contribution to string amplitudes 5 D-instanton: A D-brane with Dirichlet boundary condition on all non-compact directions including (euclidean) time. D-instantons give non-perturbative contribution to string amplitudes that are important in many situations Example: KKLT moduli stabilization uses non-perturbative contribution from D-instanton (euclidean D3-brane) Systematic computation of string amplitudes in such backgrounds will require us to compute amplitudes in the presence of D-instantons Problem: Open strings living on the D-instanton do not carry any continuous momenta ) we cannot move away from the singularities by varying the external momenta 6 Some examples: Let X be the (euclidean) time direction Since the D-instanton is localized at some given euclidean time, it has a zero mode that translates it along time direction 4-point function of these zero modes: Z 1 A = dy y−2 + (y − 1)−2 + 1 0 Derivation of this expression will be discussed later. -
Holography Principle and Topology Change in String Theory 1 Abstract
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server SNUTP 98-089 hep-th/9807241 Holography Principle and Topology Change in String Theory 1 Soo-Jong Rey Physics Department, Seoul National University, Seoul 151-742 KOREA abstract D-instantons of Type IIB string theory are Ramond-Ramond counterpart of Giddings-Strominger wormholes connecting two asymptotic regions of spacetime. Such wormholes, according to Coleman, might lead to spacetime topology change, third-quantized baby universes and prob- abilistic determination of fundamental coupling parameters. Utilizing correspondence between AdS5 × M5 Type IIB supergravity and d = 4 super Yang-Mills theory, we point out that topol- ogy change and sum over topologies not only take place in string theory but also are required for consistency with holography. Nevertheless, we argue that the effects of D-instanton wormholes remain completely deterministic, in sharp contrast to Coleman’s scenario. 1Work supported in part by KOSEF SRC-Program, Ministry of Education Grant BSRI 98-2418, SNU Re- search Fund and Korea Foundation for Advanced Studies Faculty Fellowship. One of the most vexing problems in quantum gravity has been the issue of spacetime topol- ogy change: whether topology of spacetime can fluctuate and, if so, spacetime of different topologies should be summed over. Any positive answer to this question would bear profound implications to the fundamental interactions of Nature. For example, in Coleman’s scenario [1] of baby universes [2], fluctuation of spacetime topology induce effective lon-local interactions and third quantization of the universe thereof 2. As a result, the cosmological constant is no longer a calculable, deterministic parameter but is turned into a quantity of probabilistic dis- tribution sharply peaked around zero. -
SHELDON LEE GLASHOW Lyman Laboratory of Physics Harvard University Cambridge, Mass., USA
TOWARDS A UNIFIED THEORY - THREADS IN A TAPESTRY Nobel Lecture, 8 December, 1979 by SHELDON LEE GLASHOW Lyman Laboratory of Physics Harvard University Cambridge, Mass., USA INTRODUCTION In 1956, when I began doing theoretical physics, the study of elementary particles was like a patchwork quilt. Electrodynamics, weak interactions, and strong interactions were clearly separate disciplines, separately taught and separately studied. There was no coherent theory that described them all. Developments such as the observation of parity violation, the successes of quantum electrodynamics, the discovery of hadron resonances and the appearance of strangeness were well-defined parts of the picture, but they could not be easily fitted together. Things have changed. Today we have what has been called a “standard theory” of elementary particle physics in which strong, weak, and electro- magnetic interactions all arise from a local symmetry principle. It is, in a sense, a complete and apparently correct theory, offering a qualitative description of all particle phenomena and precise quantitative predictions in many instances. There is no experimental data that contradicts the theory. In principle, if not yet in practice, all experimental data can be expressed in terms of a small number of “fundamental” masses and cou- pling constants. The theory we now have is an integral work of art: the patchwork quilt has become a tapestry. Tapestries are made by many artisans working together. The contribu- tions of separate workers cannot be discerned in the completed work, and the loose and false threads have been covered over. So it is in our picture of particle physics. Part of the picture is the unification of weak and electromagnetic interactions and the prediction of neutral currents, now being celebrated by the award of the Nobel Prize. -
Gravity, Scale Invariance and the Hierarchy Problem
Motivation Setup Warm-up: Dilaton+Gravity One example: Higgs+Gravity Further Examples: Higgs+Dilaton+Gravity Discussion and Outlook Backups Gravity, Scale Invariance and the Hierarchy Problem M. Shaposhnikov, A. Shkerin EPFL & INR RAS Based on arXiv:1803.08907, arXiv:1804.06376 QUARKS-2018 Valday, May 31, 2018 1 / 39 Motivation Setup Warm-up: Dilaton+Gravity One example: Higgs+Gravity Further Examples: Higgs+Dilaton+Gravity Discussion and Outlook Backups Overview 1 Motivation 2 Setup 3 Warm-up: Dilaton+Gravity 4 One example: Higgs+Gravity 5 Further Examples: Higgs+Dilaton+Gravity 6 Discussion and Outlook 2 / 39 Motivation Setup Warm-up: Dilaton+Gravity One example: Higgs+Gravity Further Examples: Higgs+Dilaton+Gravity Discussion and Outlook Backups Drowning by numbers The fact is that G 2 F ~ ∼ 1033, where G | Fermi constant, G | Newton constant 2 F N GN c Two aspects of the hierarchy problem (G. F. Giudice'08): \classical" \quantum": Let MX be some heavy mass scale. Then one expects 2 2 δmH;X ∼ MX : Even if one assumes that there are no heavy thresholds beyond the EW scale, then, naively, 2 2 δmH;grav: ∼ MP : 3 / 39 Motivation Setup Warm-up: Dilaton+Gravity One example: Higgs+Gravity Further Examples: Higgs+Dilaton+Gravity Discussion and Outlook Backups EFT approach and beyond A common approach to the hierarchy problem lies within the effective field theory framework: Low energy description of Nature, provided by the SM, can be affected by an unknown UV physics only though a finite set of parameters This \naturalness principle" is questioned now in light of the absence of signatures of new physics at the TeV scale. -
Some Comments on Physical Mathematics
Preprint typeset in JHEP style - HYPER VERSION Some Comments on Physical Mathematics Gregory W. Moore Abstract: These are some thoughts that accompany a talk delivered at the APS Savannah meeting, April 5, 2014. I have serious doubts about whether I deserve to be awarded the 2014 Heineman Prize. Nevertheless, I thank the APS and the selection committee for their recognition of the work I have been involved in, as well as the Heineman Foundation for its continued support of Mathematical Physics. Above all, I thank my many excellent collaborators and teachers for making possible my participation in some very rewarding scientific research. 1 I have been asked to give a talk in this prize session, and so I will use the occasion to say a few words about Mathematical Physics, and its relation to the sub-discipline of Physical Mathematics. I will also comment on how some of the work mentioned in the citation illuminates this emergent field. I will begin by framing the remarks in a much broader historical and philosophical context. I hasten to add that I am neither a historian nor a philosopher of science, as will become immediately obvious to any expert, but my impression is that if we look back to the modern era of science then major figures such as Galileo, Kepler, Leibniz, and New- ton were neither physicists nor mathematicans. Rather they were Natural Philosophers. Even around the turn of the 19th century the same could still be said of Bernoulli, Euler, Lagrange, and Hamilton. But a real divide between Mathematics and Physics began to open up in the 19th century. -
Particle & Nuclear Physics Quantum Field Theory
Particle & Nuclear Physics Quantum Field Theory NOW AVAILABLE New Books & Highlights in 2019-2020 ON WORLDSCINET World Scientific Lecture Notes in Physics - Vol 83 Lectures of Sidney Coleman on Quantum Field Field Theory Theory A Path Integral Approach Foreword by David Kaiser 3rd Edition edited by Bryan Gin-ge Chen (Leiden University, Netherlands), David by Ashok Das (University of Rochester, USA & Institute of Physics, Derbes (University of Chicago, USA), David Griffiths (Reed College, Bhubaneswar, India) USA), Brian Hill (Saint Mary’s College of California, USA), Richard Sohn (Kronos, Inc., Lowell, USA) & Yuan-Sen Ting (Harvard University, “This book is well-written and very readable. The book is a self-consistent USA) introduction to the path integral formalism and no prior knowledge of it is required, although the reader should be familiar with quantum “Sidney Coleman was the master teacher of quantum field theory. All of mechanics. This book is an excellent guide for the reader who wants a us who knew him became his students and disciples. Sidney’s legendary good and detailed introduction to the path integral and most of its important course remains fresh and bracing, because he chose his topics with a sure application in physics. I especially recommend it for graduate students in feel for the essential, and treated them with elegant economy.” theoretical physics and for researchers who want to be introduced to the Frank Wilczek powerful path integral methods.” Nobel Laureate in Physics 2004 Mathematical Reviews 1196pp Dec 2018 -
Supersymmetry and the Multi-Instanton Measure
View metadata, citation and similar papers at core.ac.uk brought to you by CORE hep-th/9708036provided by CERN Document Server Supersymmetry and the Multi-Instanton Measure Nicholas Dorey Physics Department, University of Wales Swansea Swansea SA2 8PP UK [email protected] Valentin V. Khoze Department of Physics, Centre for Particle Theory, University of Durham Durham DH1 3LE UK [email protected] and Michael P. Mattis Theoretical Division T-8, Los Alamos National Laboratory Los Alamos, NM 87545 USA [email protected] We propose explicit formulae for the integration measure on the moduli space of charge-n ADHM multi-instantons in N = 1 and N =2super- symmetric gauge theories. The form of this measure is fixed by its (su- per)symmetries as well as the physical requirement of clustering in the limit of large spacetime separation between instantons. We test our proposals against known expressions for n ≤ 2. Knowledge of the measure for all n al- lows us to revisit, and strengthen, earlier N = 2 results, chiefly: (1) For any number of flavors NF , we provide a closed formula for Fn, the n-instanton contribution to the Seiberg-Witten prepotential, as a finite-dimensional col- lective coordinate integral. This amounts to a solution, in quadratures, of the Seiberg-Witten models, without appeal to electric-magnetic duality. (2) In the conformal case NF =4,this means reducing to quadratures the previously unknown finite renormalization that relates the microscopic and effective coupling constants, τmicro and τeff. (3) Similar expressions are given for the 4-derivative/8-fermion term in the gradient expansion of N = 2 supersymmetric QCD. -
Gustaaj C. Cornelis It States the Question Why the Universe Seems To
Philosophica 63 (1999, 1) pp. 7-17 INFLATION. WHERE DID THAT COME FROM? GustaaJ C. Cornelis 1. Introduction It would have been perfect. Empirical data generate theoretical problems (the so-called cosmological paradoxes) and induce a crisis in scientific thinking, i.e. cosmology. A revolution occurs and a new paradigm, in casu big bang cosmology annex inflation theory (the idea that the universe grew exponentially in a split second) emerges. Did the search for dark matter generate the flatness problem, and, subsequently, did the flatness problem lead to inflation theory, did inflation theory solve the flatness paradox, and did it become the new paradigm? Unfortunately, this train of thought cannot be substantiated. So where did the 'ridiculous' idea of iIiflation come from? 2. The paradoxes During the sixties and seventies the so-called cosmological paradoxes came forth, known as the horizon-problem, the flatness-problem and the smoothness-problem. The last one originated out of the first. In literature, these problems were treated as genuine cosmological paradoxes, although - as will be shown - only one can be proven to be a genuine paradox. 2.1. The horizon-problem In 1969 Charles Misner presented the horizon-paradox (Misner, 1969). It states the question why the universe seems to be more uniform than can be explained through thermodynamical processes. Misner acknowledged 8 GUSTAAF C. CORNELIS the fact that the universe could only have a more or less equal distribution of matter and temperature if all parts could 'communicate' with each other at a certain time in the past - given, of course, that the universe did not originate out of a 'perfect' singularity. -
Instanton Operators in Five-Dimensional Gauge
MTH-KCL/2014-20 QMUL-PH-14-25 Instanton Operators in Five-Dimensional Gauge Theories N. Lambert a,∗, C. Papageorgakis b,† and M. Schmidt-Sommerfeld c,d,‡ aDepartment of Mathematics King’s College London, WC2R 2LS, UK bCRST and School of Physics and Astronomy Queen Mary University of London, E1 4NS, UK cArnold-Sommerfeld-Center f¨ur Theoretische Physik, LMU M¨unchen Theresienstraße 37, 80333 M¨unchen, Germany dExcellence Cluster Universe, Technische Universit¨at M¨unchen Boltzmannstraße 2, 85748 Garching, Germany Abstract We discuss instanton operators in five-dimensional Yang-Mills gauge theo- ries. These are defined as disorder operators which create a non-vanishing arXiv:1412.2789v3 [hep-th] 4 Jun 2015 second Chern class on a four-sphere surrounding their insertion point. As such they may be thought of as higher-dimensional analogues of three- dimensional monopole (or ‘t Hooft) operators. We argue that they play an important role in the enhancement of the Lorentz symmetry for maximally supersymmetric Yang-Mills to SO(1, 5) at strong coupling. ∗E-mail address: [email protected] †E-mail address: [email protected] ‡E-mail address: [email protected] 1 Introduction One of the more dramatic results to come out of the study of strongly coupled string theory and M-theory was the realisation that there exist UV-complete quantum super- conformal field theories (SCFTs) in five and six dimensions [1–5]. These theories then provide UV completions to a variety of perturbatively non-renormalisable five-dimensional (5D) Yang-Mills theories. In this paper we will consider the notion of ‘instanton operators’ (or Yang operators) and explore their role in five-dimensional Yang-Mills. -
Einstein and the Kaluza-Klein Particle
ITFA-99-28 Einstein and the Kaluza-Klein particle Jeroen van Dongen1 Institute for Theoretical Physics, University of Amsterdam Valckeniersstraat 65 1018 XE Amsterdam and Joseph Henry Laboratories, Princeton University Princeton NJ 08544 Abstract In his search for a unified field theory that could undercut quantum mechanics, Einstein considered five dimensional classical Kaluza-Klein theory. He studied this theory most intensively during the years 1938-1943. One of his primary objectives was finding a non-singular particle solution. In the full theory this search got frustrated and in the x5-independent theory Einstein, together with Pauli, argued it would be impossible to find these structures. Keywords: Einstein; Unified Field Theory; Kaluza-Klein Theory; Quantization; Soli- tons 1 Introduction After having formulated general relativity Albert Einstein did not immediately focus on the unification of electromagnetism and gravity in a classical field theory - the issue that would characterize much of his later work. It was still an open question to him whether arXiv:gr-qc/0009087v1 26 Sep 2000 relativity and electrodynamics together would cast light on the problem of the structure of matter [18]. Rather, in a 1916 paper on gravitational waves he anticipated a different development: since the electron in its atomic orbit would radiate gravitationally, something that cannot “occur in reality”, he expected quantum theory would have to change not only the ”Maxwellian electrodynamics, but also the new theory of gravitation” [19]2. Einstein’s position, however, gradually changed. From about 1919 onwards, he took a strong interest in the unification programme3. In later years, after about 1926, he hoped that he would find a particular classical unified field theory that could undercut quantum theory. -
Dark Energy and Inflation from Gravitational Waves
universe Article Dark Energy and Inflation from Gravitational Waves Leonid Marochnik Department of Physics, East-West Space Science Center, University of Maryland, College Park, MD 20742, USA; [email protected] Received: 2 July 2017; Accepted: 10 October 2017; Published: 18 October 2017 Abstract: In this seven-part paper, we show that gravitational waves (classical and quantum) produce the accelerated de Sitter expansion at the start and at the end of the cosmological evolution of the Universe. In these periods, the Universe contains no matter fields but contains classical and quantum metric fluctuations, i.e., it is filled with classical and quantum gravitational waves. In such evolution of the Universe, dominated by gravitational waves, the de Sitter state is the exact solution to the self-consistent equations for classical and quantum gravitational waves and background geometry for the empty space-time with FLRW metric. In both classical and quantum cases, this solution is of the instanton origin since it is obtained in the Euclidean space of imaginary time with the subsequent analytic continuation to real time. The cosmological acceleration from gravitational waves provides a transparent physical explanation to the coincidence, threshold and “old cosmological constant” paradoxes of dark energy avoiding recourse to the anthropic principle. The cosmological acceleration from virtual gravitons at the start of the Universe evolution produces inflation, which is consistent with the observational data on CMB anisotropy. Section 1 is devoted to cosmological acceleration from classical gravitational waves. Section 2 is devoted to the theory of virtual gravitons in the Universe. Section 3 is devoted to cosmological acceleration from virtual gravitons. -
3-Forms, Axions and D-Brane Instantons
3-Forms, Axions and D-brane Instantons Eduardo Garc´ıa-Valdecasas Tenreiro Instituto de F´ısica Teorica´ UAM/CSIC, Madrid Based on 1605.08092 by E.G. & A. Uranga V Postgradute Meeting on Theoretical Physics, Oviedo, 18th November 2016 Axions, Monodromy and 3-Forms String Theory, D-Branes and Instantons Backreacting Instantons Motivation & Outline Motivation Axions have very flat potentials ) Good for Inflation. Axions with non-perturbative (instantons) potential can always be described as a 3-Form eating up the 2-Form dual to the axion. There is no candidate 3-Form for stringy instantons. We will look for it in the geometry deformed by the instanton. Outline 1 Axions, Monodromy and 3-Forms. 2 String Theory, D-Branes and Instantons. 3 Backreacting Instantons. Eduardo Garc´ıa-Valdecasas Tenreiro 3-Forms, Axions and D-brane Instantons 2 / 20 2 / 20 Axions, Monodromy and 3-Forms String Theory, D-Branes and Instantons Backreacting Instantons Axions and Monodromy. Axions are periodic scalar fields. This shift symmetry can be broken to a discrete symmetry by non-perturbative effects ! Very flat potential, good for inflation. The discrete shift symmetry gives periodic potentials, but non-periodic ones can be used by endowing them with a monodromy structure. For instance: jφj2 + µ2φ2 (1) Superplanckian field excursions in Quantum Gravity are under pressure due to the Weak Gravity Conjecture (Arkani-Hamed et al., 2007). Monodromy may provide a workaround (Silverstein & Westphal, 2008; Marchesano et al., 2014). This mechanism can be easily realized in string theory. Eduardo Garc´ıa-Valdecasas Tenreiro 3-Forms, Axions and D-brane Instantons 3 / 20 3 / 20 Axions, Monodromy and 3-Forms String Theory, D-Branes and Instantons Backreacting Instantons Kaloper-Sorbo Monodromy A quadratic potential with monodromy can be described by a Kaloper-Sorbo lagrangian (Kaloper & Sorbo, 2009), 2 2 j dφj + nφF4 + jF4j (2) Where the monodromy is given by the vev of F4, different fluxes correspond to different branches of the potential.