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Home > MAM4001W > Applied Mathematics Modules > Topics in String Theory

Topics in String Theory

Professor Jeff Murugan
2nd semester 2020
20 credits / 30 lectures

String theory is one of the most exciting fields in theoretical physics today and offers the potential of unifying gravity and all of the other forces of nature together with all forms of matter into one unified conceptual framework. Consequently, it has, over the past 40 years evolved into a truly interdisciplinary field assimilating knowledge ranging from differential equations to algebraic geometry (and everything in between). This course offers a pedagogical introduction to various contemporary topics in the field (and related areas) depending largely on the interests of the class. It will be broken up into three parts:

Part I: String Theory as a Conformal Field Theory 

  1. The Conformal Group
  2. Conformal field theory - primary fields, energy momentum tensor and radial quantisatio
  3. The operator product expansion
  4. Normal ordering and the CFT Hilbert space
  5. Free bosons and fermions
  6. Bosonisation and conformal correlators
  7. Virasoro representation theory

Part II: Superconformal field theory

  1. Introduction to superspace
  2. N = 1 superconformal field theories
  3. N = 2 superconformal field theories
  4. Chiral rings and spectral flow

Part III: (optional) Advanced topics I - The 2-dimensional Ising model

  1. A review of statistical mechanics and critical phenomena
  2. The renormalisation group
  3. Ising model correlators and bosonization revisited

Part IV: (optional) Advanced topics II - The shadow formalism

  1. Superconformal symmetry in D=1 and the Casimir equation
  2. Shadow representations in D=1
  3. Shadow representations in D=2

Prerequisites:

A basic knowledge of quantum mechanics, linear algebra and group theory would be useful.