QFT Anomalies and Applications

Graduate course given at the Beijing Institute of Mathematical Sciences and Applications (BIMSA) in the fall of 2021

Dates: Every Monday & Wednesday 2021-09-13 ~ 12-03, 13:30-15:05 (UTC +8:00)
Venue: BIMSA Rm 1110
Zoom ID: 388 528 9728，Password: BIMSA

Description:
Perturbative calculation of anomalies, Wess-Zumino conditions and BRST algebra, anomaly descent, anomaly inflow, topological aspects of anomalies, anomalies in supersymmetric theories, anomalies and defects, Hawking radiation

Prerequisites:
a) Basic Quantum Field Theory (Feynman path integral and diagrams, one-loop calculations)
b) Basic differential geometry (manifolds, forms, de Rham cohomology, Riemannian geometry)
c) Lie algebras and groups

References:

  1. R. Bertlmann, Anomalies in quantum field theory. Oxford University Press, 1996.
  2. Fiorenzo Bastianelli and Peter Van Nieuwenhuizen, Path Integrals and Anomalies in Curved Space. Cambridge University Press, 2006.
  3. Kazuo Fujikawa and Hiroshi Suzuki, Path Integrals and Quantum Anomalies. Oxford University Press, 2007.
  4. Adel Bilal, Lectures on Anomalies, [arXiv:0802.0634]
  5. Jeffrey A. Harvey, TASI 2003 Lectures on Anomalies, [arXiv:hep-th/0509097]
  6. C.A. Scrucca, M. Serone, Anomalies in field theories with extra dimensions, [arXiv:hep-th/0403163]
  7. J. Zinn-Justin, Chiral Anomalies and Topology, [arXiv:hep-th/0201220]
  8. M. J. Duff, Twenty Years of the Weyl Anomaly, [arXiv:hep-th/9308075]
  9. Edward Witten, Fermion Path Integrals And Topological Phases, [arXiv:1508.04715]
  10. Kazuya Yonekura, Dai-Freed theorem and topological phases of matter, [arXiv:1607.01873]
  11. Edward Witten, Kazuya Yonekura, Anomaly Inflow and the η-Invariant, [arXiv:1909.08775]
  12. Samuel Monnier, A Modern Point of View on Anomalies, [arXiv:1903.02828]
  13. Shun K. Kobayashi, Kazuya Yonekura, The Atiyah–Patodi–Singer index theorem from the axial anomaly, [arXiv:2103.10654]

Lecture Notes:
Lecture 1: Symmetries, Ward identities and quantum anomalies
Lecture 2: Perturbative calculation of anomalies, ABJ anomaly
Lecture 3: Point-splitting regularization, non-Abelian anomalies
Lecture 4: Path integral approach to anomalies, Fujikawa’s derivation of the ABJ anomaly
Lecture 5: Fujikawa’s derivation of the non-Abelian anomaly, consistent and covariant anomalies
Lecture 6: Heat kernel and zeta function regularization
Lecture 7: Topology of gauge bundles and physics
Lecture 8: Invariant polynomials and characteristic classes
Lecture 9: Cartan homotopy formula and BRS transformations
Lecture 10: Wess-Zumino conditions and anomaly descent
Lecture 11: Geometry of Faddeev-Popov ghosts, covariant anomaly
Lecture 12: Atiyah-Singer index theorem (singlet anomaly)
Lecture 13: Family index theorem (non-Abelian anomaly)
Lecture 14: Riemannian geometry as a GL(d) or SO(d) gauge theory
Lecture 15: Gravitational anomalies
Lecture 16: Mixed axial anomaly, supersymmetric quantum mechanics
Lecture 17: Mixed axial anomaly from supersymmetric quantum mechanics
Lecture 18: Green-Schwarz mechanism, anomaly inflow
Lecture 19: Anomaly inflow, non-perturbative anomalies
Lecture 20: Atiyah-Patodi-Singer index theorem, η-invariant, Dai-Freed partition function
Lecture 21: Weyl anomalies and the renormalization group
Lecture 22: Anomalies in supersymmetric theories

Problem Sets:
[1] [2] [3]