nLab Quantum Fields and Strings



Quantum field theory


physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics

This entry collects linked keywords for the book

on (supersymmetric) quantum field theory and (super) string theory.

Parts of this appear separately elsewhere:

on fundamental supergeometry needed for describing fermion particles (and superstrings). See also

See also:

following the chapter

While advertized as “A course for mathematicians”, experience shows that it is not really suited for pure mathematicians without previous exposition to and tolerance for physics, particularly beyond the first chapters (which show strong ambition to be mathematically precise) towards the following lectures (which are mainly standard lectures of theoretical physicists). But it is much better than the average physics text.

More in detail: this is a long collection of (in parts) long lectures by many top string theorists and also by some genuine top mathematicians. Correspondingly it covers a lot of ground, while still being introductory. Especially towards the beginning there is a strong effort towards trying to formalize or at least systematize much of the standard lore. But one can see that eventually the task of doing that throughout had been overwhelming. Nevertheless, this is probably the best source that there is out there. If you only ever touch a single book on string theory, touch this one.

See also at string theory FAQ


Volume I

Part 1: Classical fields and Supersymmetry

Classical field theory

Chapter 1. Classical mechanics
Chapter 2. Lagrangian theory of classical fields
Chapter 3. Free field theories
Chapter 4. Gauge theory
Chapter 5. σ\sigma-Models and coupled gauge theories
Chapter 6. Topological terms
Chapter 7. Wick rotation

Part 2: Formal Aspects of QFT

Volume II

Part 3: Conformal field theory and strings

Lectures on Conformal Field Theory

Lecture 1. Simple functional integrals
Lecture 2. Axiomatic approaches to conformal field theory
Lecture 3. σ\sigma-Models
Lecture 4. Constructive conformal field theory

Perturbative String Theory

Lecture 1. Point varticles and strings
Lecture 2. Spectrum of the free bosonic string
Lecture 3. String amplitudes and moduli space of curves
Lecture 4. Fadeev-Popov Ghost – BRST Quantization
Lecture 5. Moduli dependence of determinants and Green functions
Lecture 6. Strings on general manifolds
Lecture 7. Free superstrings
Lecture 8. Heterotic strings
Lecture 9. Superstring perturbation theory
Lecture 10. Supersymmetry and supergravity

Super Space Description of Super Gravity

Notes on 2d Conformal Field Theory and String Theory

Chpater 0. Introduction
Chapter 1. Chiral algebra
Chapter 2. CFT data
Chapter 3. Examples
Chapter 4. BRST and string amplitudes
Chapter 5. Further constructons
Chapter 6. The free bosonic theory

Kaluza-Klein Compactifications, Supersymmetry, and Calabi Yau Spaces

Lecture 1. Compactifications to dimension four
Lecture 2. Supersymmetry and Calabi-Yau manifolds

Part 4: Dynamical Aspects of QFT

Dynamics of Quantum Field Theory

Lecture 1. Symmetry breaking
Lecture 2. Gauge symmetry breaking and more infrared behaviour
Lecture 3. BRST quantization of gauge theories
Lecture 4. Infrared behaviour of the S-matrix of the 2-dimensional σ\sigma-model with target space S N1S^{N-1}
Lecture 5. The large NN limit of the σ\sigma-model into Grassmannians
Lecture 6. The Bose-Fermi correspondence and its applications
Lecture 7. Two-dimensional gauge theory of bosons, the Wilson line operator and confinement
Lecture 8. Abelian duality
Lecture 9. Solitons
Lecture 10. Wilson loops, ‘t Hooft loops and ‘t Hooft’s picture of confinement
Lecture 11. Quantum gauge theories in two dimensions and intersection theory on moduli space
Lecture 12. Supersymmetric field theories
Lecture 13. N=2N=2 SUSY theories in dimension two: part I
Lecture 14. N=2N=2 SUSY theories in dimension two: part II, Chiral rings and twisted theories
Lecture 15. The Landau-Ginzburg description of N=2N = 2 minimal models; Quantum cohomology and Kähler manifolds
Lecture 16. Four-dimensional gauge theories
Lecture 17. N=2N=2 supersymmetric Yang-Mills theories in dimension four: part 1
Lecture 18. N=2N=2 supersymmetric Yang-Mills theories in dimension four: part 2
Lecture 19. N=2N=2 supersymmetric Yang-Mills theories in dimension four: part 3, Topological applications

Dynamics of N=1N = 1 Supersymmetric Field Theories in Four Dimensions

category: reference

Last revised on March 9, 2024 at 03:17:43. See the history of this page for a list of all contributions to it.