CFT

Books and Notes

• conformal field theroy-“the yellow book”
• Introduction to conformal field theory with application to string theory
• String theory_Polchinski
• String theory_D.Tong

Reviews

• Applied conformal field theory_Ginsparg
• An introduction to conformal field theory_Gaberdiel

These two reviews are good, the former is more physical, the later contain more formal aspects of 2d CFT, and the references are important.

Lecture notes

• Conformal field theroy_Alday
• Supersymmetry and conformal field theory_Herzog
• Conformal field theory for string theorists_Herzog
• Lectures on conformal field theory_Qualls

I don’t have enough time to study all these, these will be used as just reference, the main materials for study will be [Ginsparg],[Gaberdiel],[Yellow book],[Tong], and the important papers especially about [BPZ] and [MS]

Zhihu notes

• [https://zhuanlan.zhihu.com/p/473536902]
• [https://zhuanlan.zhihu.com/p/392768986]

Online lectures

• 2020 Introduction to Topological Field Theory-Prof. M. Marino [https://www.bilibili.com/video/BV1Ji4y187pH/?spm_id_from=333.999.0.0&vd_source=a5a8460500e2a3b8256e6de946ff552f]
• Introduction to conformal field theory by Tobias Osborne [https://www.bilibili.com/video/BV1xW411F7jn/?spm_id_from=333.999.0.0&vd_source=a5a8460500e2a3b8256e6de946ff552f]
• RCFT 孔良 [https://www.bilibili.com/video/BV1t44y1g7e8/?spm_id_from=333.999.0.0&vd_source=a5a8460500e2a3b8256e6de946ff552f]
• Conformal Field Theory (PSI 11-12, Core) - Jaume Gomis [https://www.bilibili.com/video/BV1u4411E7Uj/?spm_id_from=333.337.search-card.all.click&vd_source=a5a8460500e2a3b8256e6de946ff552f]

Important original papers

• BPZ
• Moore,Seiberg
• Segel
• …

Important notions

• Scale invariance, conformal invariance, trace anomaly, universality, consistent conditions.
• Witt algebra, OPE, VOA, Virasoro algebra, central charge
• Verma module and representation
• Meromorphic CFT(chiral algebra,VOA)
• Moore Seiberg: MTC, quantum groups

TQFT

More physical

• Tong_Quantum Hall Effect
• Gauge theory_Tong
• Aspects of Chern-Simons Theory_Dune
• Chapters on FQHE_Wen
• Topological investigations of gauge theory_Jackiw
• References on Instantons: Zee, WeinbergII,…
• Topological quantum_H.Simons
• Chapter 9 of Altland&B.Simons
• Topology,geometry and quantum interference in condensed matter physics
• Three Lectures On Topological Phases Of Matter_Witten
• Fermion path integral and Fermion path integrals and topological phases_Witten
• Many other papers and reviews on topological field theoretical approach to I/FQHE,SPT,SET states(May follow the reference of some lectures on topological order)

More mathematical

• On characteristic classes
• On supersymmetric TQFT…