The Cartesian Cafe

John Baez | The Algebra of Grand Unified Theories

Listen Later

John Baez is a mathematical physicist, professor of mathematics at UC Riverside, a researcher at the Centre for Quantum Technologies in Singapore, and a researcher at the Topos Institute in Berkeley, CA. John has worked on an impressively wide range of topics, pure and applied, ranging from loop quantum gravity, applications of higher categories to physics, applied category theory, environmental issues and math related to engineering and biology, and most recently on applying network theory to scientific software.Additionally, John is a prolific writer and blogger. This first began with John’s column This Week's Finds in Mathematical Physics, which ran 300 issues between 1993 and 2010, which then continued in the form of his ongoing blog Azimuth. Last but not least, John is also a host and contributor of the popular blog The n-category Cafe.

In this episode, we dive into John Baez and John Huerta’s paper “The Algebra of Grand Unified Theories” which was awarded the Levi Conant Prize in 2013. The paper gives a crash course in the representation theory underlying the Standard Model of particle physics and its three most well known Grand Unified Theories (GUTs): the SU(5), SO(10) (aka Spin(10)), and Pati-Salam theories. The main result of Baez-Huerta is that the particle representations underlying the three GUTs can in fact be unified via a commutative diagram. We dive deep into the numerology of the standard model to see how the SU(5) theory naturally arises. We then make brief remarks about SO(10) and Pati-Salam theories in order to state the Baez-Huerta theorem about their organization into a commutative square: a unification among grand unifications!

Patreon: https://www.patreon.com/timothynguyen

Correction:

  • 1:29:01: The formula for hypercharge in the bottom right note should be Y = 2(Q-I_3) instead of Y = (Q-I_3)/2.

Notes:

  1. While we do provide a crash course on SU(2) and spin, some representation theory jargon is used at times in our discussion. Those unfamiliar should just forge ahead!
  • We work in Euclidean signature instead of Lorentzian signature. Other than keeping track of minus signs, no essential details are changed. 

    • Part I. Introduction

    • 00:00: Introduction
  • 05:50: Climate change
  • 09:40: Crackpot index
  • 14:50: Eric Weinstein, Brian Keating, Geometric Unity
  • 18:13: Overview of “The Algebra of Grand Unified Theories” paper
  • 25:40: Overview of Standard Model and GUTs
  • 34:25: SU(2), spin, isospin of nucleons 40:22: SO(4), Spin(4), double cover
  • 44:24: three kinds of spin

    • Part II. Zoology of Standard Model

    • 49:35: electron and neutrino
  • 58:40: quarks
  • 1:04:51: the three generations of the Standard Model
  • 1:08:25: isospin quantum numbers
  • 1:17:11: U(1) representations (“charge”)
  • 1:29:01: hypercharge
  • 1:34:00: strong force and color
  • 1:36:50: SU(3)
  • 1:40:45: antiparticles

    • Part III. SU(5) numerology

    • 1:41:16: 32 = 2^5 particles
  • 1:45:05: Mapping SU(3) x SU(2) x U(1) to SU(5) and hypercharge matching
  • 2:05:17: Exterior algebra of C^5 and more hypercharge matching
  • 2:37:32: SU(5) rep extends Standard Model rep

    • Part IV. How the GUTs fit together

    • 2:41:42: SO(10) rep: brief remarks
  • 2:46:28: Pati-Salam rep: brief remarks
  • 2:47:17: Commutative diagram: main result
  • 2:49:12: What about the physics? Spontaneous symmetry breaking and the Higgs mechanism

    • Twitter: @iamtimnguyen

    Webpage: http://www.timothynguyen.org

    ...more
    View all episodesView all episodes
    Download on the App Store
    The Cartesian CafeBy Timothy Nguyen
    • 4.7
    • 4.7
    • 4.7
    • 4.7
    • 4.7

    4.7

    51 ratings

    More shows like The Cartesian Cafe

    View all
    StarTalk Radio by Neil deGrasse Tyson

    StarTalk Radio

    13,994 Listeners

    The Daily by The New York Times

    The Daily

    112,758 Listeners

    Our Opinions Are Correct by Our Opinions Are Correct

    Our Opinions Are Correct

    379 Listeners

    Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas by Sean Carroll | Wondery

    Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas

    4,097 Listeners

    Theories of Everything with Curt Jaimungal by Theories of Everything

    Theories of Everything with Curt Jaimungal

    453 Listeners

    The Art of Mathematics by Carol Jacoby

    The Art of Mathematics

    21 Listeners

    The Ezra Klein Show by New York Times Opinion

    The Ezra Klein Show

    14,859 Listeners

    The Joy of Why by Steven Strogatz, Janna Levin and Quanta Magazine

    The Joy of Why

    424 Listeners

    Sherlock Holmes Short Stories by NOISER

    Sherlock Holmes Short Stories

    557 Listeners