DOCSLIB.ORG

Brian R. Williams Northeastern University [email protected] Department of Mathematics 360 Huntington Ave

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Brian R. Williams Northeastern University Brianwilliams.Math@Gmail.Com Department of Mathematics 360 Huntington Ave Brian R. Williams Northeastern University [email protected] Department of Mathematics https://web.northeastern.edu/brwilliams 360 Huntington Ave. Boston, MA 02115 Phone: +1 (561) 512-4903 Employment 2018{present Northeastern University Zelevinsky Research Instructor (3 year postdoctoral position). Education 2012{2018 Northwestern University Ph.D., Mathematics. Thesis: The holomorphic σ-model and its symmetries. Advisors: John Francis, Kevin Costello. 2008{2012 University of Florida B.S., summa cum laude, Mathematics and Physics. Advisors: David Groisser, Pierre Ramond. Papers · Higher Kac-Moody algebras and symmetries of holomorphic field theories. 2018. With Owen Gwilliam. Submitted. Available at arxiv:1810.06534. · Renormalization for holomorphic field theories. 2018. Submitted. Available at arxiv:1809.02661. · The holomorphic bosonic string. 2017. With Owen Gwilliam. To appear in Contemporary Mathematics. Available at arXiv:1711.05823. · Homotopy RG flow and the non-linear σ-model. 2017. With Ryan Grady. To appear in Contemporary Mathematics. Available at arxiv:1710.05973. · Asymptotic Freedom in the BV-formalism. With Chris Elliott and Philsang Yoo. Published in Journal of Geometry and Physics, 123 (C): 246{283, 2017. · Chiral differential operators via Batalin-Vilkovisky quantization. 2017. With Owen Gwilliam and Vasily Gorbounov. Submitted. Available at arxiv:1610.09657. Papers (cont.) · The Virasoro vertex algebra and factorization algebras on Riemann surfaces. Published in Letters in Mathematical Physics, 107 (12):2189{2237, 2017. Awards and National Science Foundation Graduate Research Fellowship (GRFP) Fellowships 2012{2018 Goldwater Scholar 2011{2012 Invited Talks The spooky side of factorization algebras and an index theorem. Northeastern University. \Pick my Brain" Seminar. Fall 2018. The higher dimensional Kac-Moody and Virasoro algebras Boston Univeristy. Geometry and Physics Seminar. Fall 2018. The higher dimensional Kac-Moody and Virasoro algebras MIT Geometry and Representation theory Seminar. Fall 2018. Higher dimensional Kac-Moody algebras as boundary SUSY gauge theories S´eminairede math´ematiquessup´erieures(Fields Institute): Derived Geometry and Higher Categorical Structures in Geometry and Physics. Summer 2018. The chiral algebraic index theorem. Structures sup´erieuresen Alg`ebreet Topologie: Workshop on Factorisation Algebras and Homology and the Cobordism Hypothesis. Winter 2018. Factorization algebras: axiomatizing the observables of a quantum field theory Florida Atlantic University Math Colloquium. Winter 2018. Part I: Noether's theorem and factorization; Part II: Higher dimensional Kac-Moody algebras. Notre Dame. Topology Seminar. Fall 2017. Symmetries of higher dimensional holomorphic field theories Yale University. Geometry, Symmetry, and Physics Seminar. Fall 2017. Symmetries of higher dimensional holomorphic field theories. Montana State University. Mathematics Seminar. Fall 2017 Symmetries of higher dimensional holomorphic field theories. Universit¨atHeidelberg, Mathematisches Institut. Conference "Flat Connections in Physics and Geometry". Summer 2017. Invited Talks Bulk-boundary BV-quantization for 2-1 theories. (cont.) Perimeter Institute for Theoretical Physics. Conference \Quantum Field Theory on Manifolds with Boundary and the BV Formalism". Spring 2017. Higher Kac{Moody algebras and factorization algebras. University of Berkeley. Topics in Factorization Algebras Seminar. Spring 2017 Higher dimensional chiral differential operators. Institut des Hautes Etudes´ Scientifiques (IHES), Theoretical Physics Seminar. Winter 2017. Factorization algebras and holomorphic invariants of complex manifolds. University of Aberdeen, Scotland. Mathematics Seminar. Winter 2017. Universal σ-models in the BV formalism. Montana State University. Mathematics Seminar. Fall 2016. Observables in the effective BV formalism. Oberwolfach, Germany. Conference \Factorization algebras and Functorial Field Theories". Summer 2016. The universal βγ system and CDO's. Boston University. Geometry and Physics Seminar. Winter 2016. Chiral differential operators from the curved βγ system. Institute for Basic Science (IBS) Center for Geometry and Physics. Pohang, South Korea. Conference \Homotopical Methods in Quantum Field Theory". Winter 2016. Holomorphic factorization algebras and the Virasoro. Notre Dame. Topology Seminar. Fall 2015. Fully extended two-dimensional TFT's. University of British Columbia. Conference \West Coast Algebraic Topology Seminar". Summer 2014. Visiting Montana State University, August{September 2017. Appointments Research Visitor in the Mathematics Department. Hosted by David Ayala and Ryan Grady. Perimeter Institute for Theoretical Physics, August{December 2015. Visiting Fellow. Organizational RTG Graduate Research Seminar: The Yangian and 4d gauge theory; Activities Coorganizer with Pavel Etingof and Valerio Toledano Laredo. Joint seminar between Northeastern University and MIT on the mathematics related to 4-dimensional gauge theory. Lecture series at Oberwolfach; invited to give a joint 10 hour lecture series (with Si Li and Ryan Grady) on \Observables of QFT in the BV-formalism" during the conference \Factorization Algebras and Functorial Field Theory" at Oberwolfach, Germany. May 2016. Student seminars at Northwestern University; organized and participated in various seminars on quantum field theory and homotopy theory aimed at graduate students in the math department. \ Learning seminar on string topology", Fall 2013. \Topics in conformal field theory", Fall 2014. \Instantons and the Nekrasov partition function", Spring 2015. Teaching Northeastern University Experience Calculus 1 (Honors) (Fall 2018). Topics class on \Derived deformation theory and Koszul duality" (Spring 2019). Northwestern University Calculus, Linear Algebra (MENU/Honors), Complex Variables, Partial Differential Equations. References Prof. Kevin Costello, Perimeter Institute [email protected] Prof. Mikhail Kapranov, Kavli IPMU [email protected] Prof. Si Li, Tsinghua University [email protected] Prof. Stephan Stolz, University of Notre Dame [email protected]..
Load more

Recommended publications
  • Florida Physics News University of Florida - Department of Physics Annual Alumni Newsletter 2005
    Florida Physics News University of Florida - Department of Physics Annual Alumni Newsletter 2005 University of Florida - Department of Physics 1 Contents Chair’s Corner 2 Chair’s Corner UF Teacher/Scholar Award 3 American Physical Society - Three New Fellows 5 APS Keithley Award 5 November 2005 marks the third anniversary of Professors Earn Positions in National Societies 6 my term as department chair, and I can say that the Columbia Shuttle Accident Investigation 7 Student Government Award 8 past year has been the most exciting one (“exciting” Academy Induction 8 in the sense of the ancient Chinese curse, “May you Faculty Promotions 8 Post-Doc Awarded Fellowship from L’Oreal Corporation 8 live in exciting times”). Two significant events come to Research Scholar Award 8 mind: the record 2004 hurricane season, and the July Travel Awards 9 Undergraduate Physics Newsletter - In Review 10 2004 implementation of the new Enterprise Resource Albert Einstein Institut Rewards Two Students 12 Planning so�ware from PeopleSo�, designed to Physics Teacher of the Year 12 manage UF’s financial, payroll, and human resources 25th Brandt-Ritchie Workshop 12 TannerFest 12 activities. As you know, Florida was hammered 45th Sanibel Symposium 13 by four hurricanes during last year’s season, and Faculty Retirement 13 Faculty Selected Publications 14 Hurricanes Frances and Jeanne directly hit Gainesville Davis Productivity Award 16 in September 2004. Although ultimately the damage to Staff Retirement 16 Employee Excellence Awardees 16 UF was minimal, with downed trees, power outages, Undergraduate Honors 16 and minor flooding, it was nonetheless a stressful time Outreach Program 17 Celebrating New PhD’s 18 for the many faculty, staff, and students who were Awards Made Possible By Alumni Donations 18 affected by the storms.
    [Show full text]
  • Renormalization and Effective Field Theory
    Mathematical Surveys and Monographs Volume 170 Renormalization and Effective Field Theory Kevin Costello American Mathematical Society surv-170-costello-cov.indd 1 1/28/11 8:15 AM http://dx.doi.org/10.1090/surv/170 Renormalization and Effective Field Theory Mathematical Surveys and Monographs Volume 170 Renormalization and Effective Field Theory Kevin Costello American Mathematical Society Providence, Rhode Island EDITORIAL COMMITTEE Ralph L. Cohen, Chair MichaelA.Singer Eric M. Friedlander Benjamin Sudakov MichaelI.Weinstein 2010 Mathematics Subject Classification. Primary 81T13, 81T15, 81T17, 81T18, 81T20, 81T70. The author was partially supported by NSF grant 0706954 and an Alfred P. Sloan Fellowship. For additional information and updates on this book, visit www.ams.org/bookpages/surv-170 Library of Congress Cataloging-in-Publication Data Costello, Kevin. Renormalization and effective fieldtheory/KevinCostello. p. cm. — (Mathematical surveys and monographs ; v. 170) Includes bibliographical references. ISBN 978-0-8218-5288-0 (alk. paper) 1. Renormalization (Physics) 2. Quantum field theory. I. Title. QC174.17.R46C67 2011 530.143—dc22 2010047463 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294 USA.
    [Show full text]
  • Inside the Perimeter Is Published by Perimeter Institute for Theoretical Physics
    the Perimeter fall/winter 2014 Skateboarding Physicist Seeks a Unified Theory of Self The Black Hole that Birthed the Big Bang The Beauty of Truth: A Chat with Savas Dimopoulos Subir Sachdev's Superconductivity Puzzles Editor Natasha Waxman [email protected] Contributing Authors Graphic Design Niayesh Afshordi Gabriela Secara Erin Bow Mike Brown Photographers & Artists Phil Froklage Tibra Ali Colin Hunter Justin Bishop Robert B. Mann Amanda Ferneyhough Razieh Pourhasan Liz Goheen Natasha Waxman Alioscia Hamma Jim McDonnell Copy Editors Gabriela Secara Tenille Bonoguore Tegan Sitler Erin Bow Mike Brown Colin Hunter Inside the Perimeter is published by Perimeter Institute for Theoretical Physics. www.perimeterinstitute.ca To subscribe, email us at [email protected]. 31 Caroline Street North, Waterloo, Ontario, Canada p: 519.569.7600 f: 519.569.7611 02 IN THIS ISSUE 04/ Young at Heart, Neil Turok 06/ Skateboarding Physicist Seeks a Unified Theory of Self,Colin Hunter 10/ Inspired by the Beauty of Math: A Chat with Kevin Costello, Colin Hunter 12/ The Black Hole that Birthed the Big Bang, Niayesh Afshordi, Robert B. Mann, and Razieh Pourhasan 14/ Is the Universe a Bubble?, Colin Hunter 15/ Probing Nature’s Building Blocks, Phil Froklage 16/ The Beauty of Truth: A Chat with Savas Dimopoulos, Colin Hunter 18/ Conference Reports 22/ Back to the Classroom, Erin Bow 24/ Finding the Door, Erin Bow 26/ "Bright Minds in Their Life’s Prime", Colin Hunter 28/ Anthology: The Portraits of Alioscia Hamma, Natasha Waxman 34/ Superconductivity Puzzles, Colin Hunter 36/ Particles 39/ Donor Profile: Amy Doofenbaker, Colin Hunter 40/ From the Black Hole Bistro, Erin Bow 42/ PI Kids are Asking, Erin Bow 03 neil’s notes Young at Heart n the cover of this issue, on the initial singularity from which everything the lip of a halfpipe, teeters emerged.
    [Show full text]
  • Fermilab Theory Group
    Fermilab Theory Group Christopher T. Hill DOE Annual Program Review Fermilab, May 17, 2006 Scale of Effort(s) Program Review FY05 FY06 FY07 FY08 Particle Theory (SWF+M&S+G&V) $3,598 $3,531 $3,731 $3,899 Lattice $1,451 $2,782 $2,733 $3,035 The support for the Lattice gauge is increasing; some of the funds come from SciDAC, some from the core budget. Scientists (12) Associate Scientists (1) Research Associates (9) Bill Bardeen Thomas Becher (9/04) Mu-Chun Chen Marcela Carena Richard Hill Estia Eichten Jay Hubicz Keith Ellis Jim Laiho Walter Giele Olga Mena Christopher Hill Senior Guest Scientist(1) Enrico Lunghi Andreas Kronfeld Jose Santiago Boris Kayser Joe Lykken Peter Skands Paul Mackenzie Ruth van de Water Bogdan Dobrescu* Emeritus Scientist (1) Regular Users Stephen Parke Leon M. Lederman C. Albright (NIU) Chris Quigg S. Mrenna (Fermilab, Computing) Y. Keung (UIC) *Promoted, 10/01/05 S.P. Martin (NIU) Ulrich Baur (Buffalo) Departures: Associate Scientist Search: Ayres Freitas Zurich ETH Babis Anastasiou (offered and declined) Giulia Zanderighi CERN Uli Haisch Zurich ETH History of the Post-Docs, Associate Masataka Okamoto KEK Scientists and Frontier Fellows is Ulrich Nierste Karlsruhe (Professor) posted on the web: http://theory.fnal.gov/people/ellis/alumni.html New Postdoc Hires arrived Fall 2005: http://theory.fnal.gov/people/ellis/Assoc.html Mu-Chun Chen (from BNL),(*) http://theory.fnal.gov/people/ellis/frontier.html Richard Hill (from SLAC), Jay Hubicz (from Cornell) Enrico Lunghi (from ETH) Ruth van de Water (from Seattle) (*) just received Jr. Faculty offer from Irvine New Postdoc Hires to arrive Fall 2006: K.
    [Show full text]
  • The Early Years of String Theory: a Personal Perspective
    CALT-68-2657 THE EARLY YEARS OF STRING THEORY: A PERSONAL PERSPECTIVE John H. Schwarz California Institute of Technology Pasadena, CA 91125, USA Abstract arXiv:0708.1917v3 [hep-th] 3 Apr 2009 This article surveys some of the highlights in the development of string theory through the first superstring revolution in 1984. The emphasis is on topics in which the author was involved, especially the observation that critical string theories provide consistent quantum theories of gravity and the proposal to use string theory to construct a unified theory of all fundamental particles and forces. Based on a lecture presented on June 20, 2007 at the Galileo Galilei Institute 1 Introduction I am happy to have this opportunity to reminisce about the origins and development of string theory from 1962 (when I entered graduate school) through the first superstring revolution in 1984. Some of the topics were discussed previously in three papers that were written for various special events in 2000 [1, 2, 3]. Also, some of this material was reviewed in the 1985 reprint volumes [4], as well as the string theory textbooks [5, 6]. In presenting my experiences and impressions of this period, it is inevitable that my own contributions are emphasized. Some of the other early contributors to string theory have presented their recollections at the Galileo Galilei Institute meeting on “The Birth of String Theory” in May 2007. Since I was unable to attend that meeting, my talk was given at the GGI one month later. Taken together, the papers in this collection should
    [Show full text]
  • STRING THEORY in the TWENTIETH CENTURY John H
    STRING THEORY IN THE TWENTIETH CENTURY John H. Schwarz Strings 2016 { August 1, 2016 ABSTRACT String theory has been described as 21st century sci- ence, which was discovered in the 20th century. Most of you are too young to have experienced what happened. Therefore, I think it makes sense to summarize some of the highlights in this opening lecture. Since I only have 25 minutes, this cannot be a com- prehensive history. Important omitted topics include 2d CFT, string field theory, topological string theory, string phenomenology, and contributions to pure mathematics. Even so, I probably have too many slides. 1 1960 { 68: The analytic S matrix The goal was to construct the S matrix that describes hadronic scattering amplitudes by assuming • Unitarity and analyticity of the S matrix • Analyticity in angular momentum and Regge Pole The- ory • The bootstrap conjecture, which developed into Dual- ity (e.g., between s-channel and t-channel resonances) 2 The dual resonance model In 1968 Veneziano found an explicit realization of duality and Regge behavior in the narrow resonance approxima- tion: Γ(−α(s))Γ(−α(t)) A(s; t) = g2 ; Γ(−α(s) − α(t)) 0 α(s) = α(0) + α s: The motivation was phenomenological. Incredibly, this turned out to be a tree amplitude in a string theory! 3 Soon thereafter Virasoro proposed, as an alternative, g2 Γ(−α(s))Γ(−α(t))Γ(−α(u)) T = 2 2 2 ; −α(t)+α(u) −α(s)+α(u) −α(s)+α(t) Γ( 2 )Γ( 2 )Γ( 2 ) which has similar virtues.
    [Show full text]
  • Superfluous Physics
    Superfluous Physics Evan Berkowitz,1, ∗ William Donnelly,2 and Sylvia Zhu3, 4 (Scientists Undertaking Preposterous Etymological Research Collaboration) 1Institut f¨ur Kernphysik and Institute for Advanced Simulation, Forschungszentrum J¨ulich, 54245 J¨ulich Germany 2Perimeter Institute for Theoretical Physics, 31 Caroline St. N. Waterloo, ON, N2L 2Y5, Canada 3Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Callinstraße 38, 30167 Hannover Germany 4Leibniz Universit¨at Hannover, D-30167 Hannover, Germany (Dated: April 1, 2019) A superweapon of modern physics superscribes a wide superset of phenomena, ranging from supernumerary rainbows to superfluidity and even possible supermultiplets. I. INTRODUCTION The questions run too deep For such a simple man Won’t you please, Please tell me what we’ve learned? Supertramp, The Logical Song Supermassive black holes have nonzero supermass, the quantity that couples to N = 1 supergravity, while in theories with more supercharges one may have superdupermassive black holes, and so on. Just as the no-hair theorem tells us that non-rotating black holes can be described as massive and charged, the no-hair supertheorem tell us that non-rotating superheavy black holes can be described as supermassive and supercharged. String theory provides hope to understand how to go beyond the semiclassical limit to describe in detail if and how black holes preserve unitarity, while superstring theory provides hope to understand the unitarity of supermassive black holes. With the recent observation of normal black hole [1–5] and neutron star[6] mergers via gravitational waves by the super-sensitive Advanced LIGO and VIRGO detectors, it is not unreasonable to expect gravitational-wave detections of supernovae of collapsing superstars or violent supermassive black hole astrophysical phenomena are on the horizon or, if you’ll forgive the absurd pun, superhorizon.
    [Show full text]
  • The Birth of String Theory
    The Birth of String Theory Edited by Andrea Cappelli INFN, Florence Elena Castellani Department of Philosophy, University of Florence Filippo Colomo INFN, Florence Paolo Di Vecchia The Niels Bohr Institute, Copenhagen and Nordita, Stockholm Contents Contributors page vii Preface xi Contents of Editors' Chapters xiv Abbreviations and acronyms xviii Photographs of contributors xxi Part I Overview 1 1 Introduction and synopsis 3 2 Rise and fall of the hadronic string Gabriele Veneziano 19 3 Gravity, unification, and the superstring John H. Schwarz 41 4 Early string theory as a challenging case study for philo- sophers Elena Castellani 71 EARLY STRING THEORY 91 Part II The prehistory: the analytic S-matrix 93 5 Introduction to Part II 95 6 Particle theory in the Sixties: from current algebra to the Veneziano amplitude Marco Ademollo 115 7 The path to the Veneziano model Hector R. Rubinstein 134 iii iv Contents 8 Two-component duality and strings Peter G.O. Freund 141 9 Note on the prehistory of string theory Murray Gell-Mann 148 Part III The Dual Resonance Model 151 10 Introduction to Part III 153 11 From the S-matrix to string theory Paolo Di Vecchia 178 12 Reminiscence on the birth of string theory Joel A. Shapiro 204 13 Personal recollections Daniele Amati 219 14 Early string theory at Fermilab and Rutgers Louis Clavelli 221 15 Dual amplitudes in higher dimensions: a personal view Claud Lovelace 227 16 Personal recollections on dual models Renato Musto 232 17 Remembering the `supergroup' collaboration Francesco Nicodemi 239 18 The `3-Reggeon vertex' Stefano Sciuto 246 Part IV The string 251 19 Introduction to Part IV 253 20 From dual models to relativistic strings Peter Goddard 270 21 The first string theory: personal recollections Leonard Susskind 301 22 The string picture of the Veneziano model Holger B.
    [Show full text]
  • Mathematisches Forschungsinstitut Oberwolfach Topologie
    Mathematisches Forschungsinstitut Oberwolfach Report No. 42/2014 DOI: 10.4171/OWR/2014/42 Topologie Organised by Thomas Schick, G¨ottingen Peter Teichner, Bonn Nathalie Wahl, Copenhagen Michael Weiss, M¨unster 14 September – 20 September 2014 Abstract. The Oberwolfach conference “Topologie” is one of only a few opportunities for researchers from many different areas in algebraic and geo- metric topology to meet and exchange ideas. The program covered new de- velopments in fields such as automorphisms of manifolds, applications of alge- braic topology to differential geometry, quantum field theories, combinatorial methods in low-dimensional topology, abstract and applied homotopy theory and applications of L2-cohomology. We heard about new results describ- ing the cohomology of the automorphism spaces of some smooth manifolds, progress on spaces of positive scalar curvature metrics, a variant of the Segal conjecture without completion, advances in classifying topological quantum field theories, and a new undecidability result in combinatorial group theory, to mention some examples. As a special attraction, the conference featured a series of three talks by Dani Wise on the combinatorics of CAT(0)-cube complexes and applications to 3-manifold topology. Mathematics Subject Classification (2010): 55-xx, 57-xx, 18Axx, 18Bxx. Introduction by the Organisers This conference was the third topology conference in Oberwolfach organized by Thomas Schick, Peter Teichner, Nathalie Wahl and Michael Weiss. About 50 mathematicians participated, working in many different areas of algebraic and geometric topology. 2354 Oberwolfach Report 42/2014 The talks were of three types. There were 14 regular one-hour talks, 3 one-hour talks by keynote speaker Dani Wise and a “gong show” where 12 young speak- ers had the opportunity to present their research in 10 minutes each, including question time.
    [Show full text]
  • E6, Strings, Branes, and the Standard Model
    CERN-CDS-EXT-2004-031 TS-04-4 April 2004 E6, Strings, Branes, and the Standard Model Frank D. (Tony) Smith, Jr. e-mail: [email protected] P. O. Box 370, Cartersville, GA 30120 USA WWW URL: http://www.innerx.net/personal/tsmith/TShome.html Abstract E6,anexceptional Lie algebra, contains generators with spinor fermionic characteristics, providing a way to include fermions in string theory without 1-1 boson-fermion supersymmetry. E6 graded structure E6 = g(−2) + g(−1) + g(0) + g(1) + g(2) can be used to construct a physically realistic representation of the 26-dimensions of string theory in which strings are interpreted as world-lines in a Many-Worlds quantum picture. This paper describes the construction step-by-step. The resulting physical interpretation is consistent with the physics model described in physics/0207095 [8] . Contents 1 String Theory, Exceptional Lie Algebra E6 and Fermions 2 1.1 26-dim Traceless Jordan J3(O)o and Exceptional Lie algebra E6 2 1.2 E6 as a 5-graded Lie algebra . .................. 4 1.3 E6 and 28 gauge bosons, 8-dim spacetime and 8 sets of fermion particles and antiparticles . .................. 5 1.4 4-dim Internal Symmetry Space and 4-dim Physical Spacetime 6 2 Strings, Branes, and the Standard Model 7 2.1 Step 1 - 26-dim J3(O)o ...................... 12 2.2 Step 2 - D3 of Quaternionic substructure of Octonionic space . 12 2.3 Step 3 - Compactify 4-dim Internal Symmetry Space and make D7 ................................. 12 2.4 Step 4 - Orbifold to discretize time and make D8 .
    [Show full text]
  • On Cohomological Algebras in Supersymmetric Quantum Field Theories
    On Cohomological Algebras in Supersymmetric Quantum Field Theories by Nafiz Ishtiaque A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Physics Waterloo, Ontario, Canada, 2019 c Nafiz Ishtiaque 2019 Examining Committee Membership The following served on the Examining Committee for this thesis. The decision of the Examining Committee is by majority vote. External Examiner: Erich Poppitz Professor, Dept. of Physics, University of Toronto Supervisor: Jaume Gomis Faculty, Perimeter Institute for Theoretical Physics Adjunct Professor, Dept. of Physics and Astronomy, University of Waterloo Internal Member: Davide Gaiotto Faculty, Perimeter Institute for Theoretical Physics Adjunct Professor, Dept. of Physics and Astronomy, University of Waterloo Internal Member: Niayesh Afshordi Associate Faculty, Perimeter Institute for Theoretical Physics Associate Professor, Dept. of Physics and Astronomy, University of Waterloo Internal-External Member: Ruxandra Moraru Associate Professor, Dept. of Pure Mathematics, University of Waterloo ii Author's Declaration This thesis consists of material all of which I authored or co-authored: see Statement of Contributions included in the thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. iii Statement of Contributions This thesis is based on the following papers: 1. Jaume Gomis and Nafiz Ishtiaque. K¨ahlerpotential and ambiguities in 4d N = 2 SCFTs. JHEP, 04:169, 2015, 1409.5325. 2. Efrat Gerchkovitz, Jaume Gomis, Nafiz Ishtiaque, Avner Karasik, Zohar Komar- godski, and Silviu S. Pufu. Correlation Functions of Coulomb Branch Operators.
    [Show full text]
  • Factorization Algebras in Quantum Field Theory Volume 2 (28 April 2016)
    Factorization algebras in quantum field theory Volume 2 (28 April 2016) Kevin Costello and Owen Gwilliam Contents Chapter 1. Overview1 1.1. Classical field theory and factorization algebras1 1.2. Quantum field theory and factorization algebras2 1.3. The quantization theorem3 1.4. The rigid quantization conjecture4 Chapter 2. Structured factorization algebras and quantization7 2.1. Structured factorization algebras7 2.2. Commutative factorization algebras9 2.3. The P0 operad9 2.4. The Beilinson-Drinfeld operad 13 Part 1. Classical field theory 17 Chapter 3. Introduction to classical field theory 19 3.1. The Euler-Lagrange equations 19 3.2. Observables 20 3.3. The symplectic structure 20 3.4. The P0 structure 21 Chapter 4. Elliptic moduli problems 23 4.1. Formal moduli problems and Lie algebras 24 4.2. Examples of elliptic moduli problems related to scalar field theories 28 4.3. Examples of elliptic moduli problems related to gauge theories 30 4.4. Cochains of a local L¥ algebra 34 4.5. D-modules and local L¥ algebras 36 Chapter 5. The classical Batalin-Vilkovisky formalism 45 5.1. The classical BV formalism in finite dimensions 45 5.2. The classical BV formalism in infinite dimensions 47 5.3. The derived critical locus of an action functional 50 5.4. A succinct definition of a classical field theory 55 5.5. Examples of field theories from action functionals 57 5.6. Cotangent field theories 58 Chapter 6. The observables of a classical field theory 63 iii iv CONTENTS 6.1. The factorization algebra of classical observables 63 6.2.
    [Show full text]