Conformal Field Theory

Contents

→ Causal Dynamical Triangulations

Highlights

• Formalism and Reviews
• 2D CFT
• Connection to Maths
• Ideas from Standard QFT
• Noting “Yellow Book”

This webpage is dedicated to curating papers on (the mathematical aspect of) conformal field theory (CFT). For Lie algebra and its representation, visit here. I will only add the papers that are relevant to me.

Formalism and Reviews

• 1998 - Applied Conformal Field Theory - Ginsparg $\mid$ Lecture Note $\mid$ Good introduction to the subject $\mid$ Paul Ginsparg developed the arXiv.org e-print archive.
• 1995 - Conformal Field Theory - Schellekens
• 2009 - Introducing Conformal Field Theory - Tong $\mid$ Part of “Lectures on String Theory”

2D CFT

• 1992 - Meromorphic $c=24$ Conformal Field Theories - Schellekens
• 1986 - Operator content of two-dimensional conformally invariant theories - Cardy $\mid$ First pointed out the mathematical implications of modular invariance for CFTs $\mid$ Modular invariance of the partition function (character of reps.) poses constraints on the operator content. These constraints can be useful for the classification of CFTs.
• 1984 - Infinite conformal symmetry in two-dimensional quantum field theory - Belavin, Polyakov, Zamolodchikov $\mid$ CFT became popular in physics with their seminal paper $\mid$ Laid the mathematical foundations of axiomatic CFT $\mid$ Showed the physical significance in statistical physics.
• 1970 - Subsidiary Conditions and Ghosts in Dual-Resonance Models - Virasoro

Connection to Maths

• 1992 - Monstrous moonshine and monstrous Lie superalgebras - Borcherds $\mid$ Proved the moonshine conjecture $\mid$ He was awarded the 1998 Fields medal for this work.
• 1986 - Vertex algebras, Kac-Moody algebras, and the Monster - Borcherds $\mid$ Introduced vertex operator algebras $\mid$ Motivated by the construction of an infinite-dimensional Lie algebra due to Igor Frenkel $\mid$ This algebraic structure that plays an important role in 2D CFT and string theory. $\mid$ Wiki
• 1979 - Monstrous Moonshine - Conway, Norton $\mid$ Introduced Monstrous Moonshine (finite) group $\mid$ Conjectured the bridge between finite groups and modular forms; the (monstrous) moonshine conjecture $\mid$ Wiki $\mid$ Videos from 3Blue1Brown , Numberphile

Ideas from Standard QFT

• 1969 - Non-Lagrangian Models of Current Algebra - Wilson $\mid$ Introduced operator product expansion (OPE) $\mid$ Wiki

Noting “Yellow Book”

• Virasoro modes $L_n$ have $L^{\dagger}_n = L_{-n}$ which is true in most CFTs. For eg. the free boson. YB stated on page 202 to be a general result. $\mid$ Note