Conformal Field Theory

… yet to be updated.

• 2014: Bosonic ghost system of central charge 2 was addressed by Ridout and Wood
• 2008: Grumiller and Johansson suggested that the conformal field theories dual to certain topological gravity theories on $AdS_3$ are logarithmic.
• 1998: Guruswamy and Ludwig realized the $c=-1$ bosonic ghost systems (also known as $\beta\gamma$ systems; a logarithimic CFT) exhibits an $\hat{\mathfrak{sl}}(2)_{-1/2}$ symmetry.
• 1998: Verlinde showed fusion coefficient is related to modular S-matrices of character which is now known as Verlinde’s formula. It connects the local and global properties of CFT.
• 1996: Gaberdiel and Kausch applied Nahm algorithm to explicitly construct (chiral) representations upon which the energy operator acts non-diagonalisably
• 1994: Nahm introduced a method for computing the fusion product of representations
• 1993: Link between the non-diagonalisability of the energy operator (i.e. Virasoro zero-mode $L_0$) and logarithmic singularities in correlators by Gurarie. He first coined “Logarithmic CFT“
• 1992: Rozensky and Saleur noted in the study of the $U(1|1)$ Wess-Zumino-Witten model that some correlation functions will possess logarithmic branch-cuts and reducible representation
• 1990: The importance of topological excitation was shown in 2D quantum gravity (or 2D CFT) by Witten 1988.
• 1987: Knizhnik noted that the correlation function can have logarithmic singularities.
• 1986: First introduced the concept of ghost system by Friedan, Martinee, and Shenker
• 1984: Formally introduced by Belavin, Polyakov and Zamolodchikov
• 1974: Proposed Conformal bootstrap program by Polyakov and to a large extend realized by Belavin, Polyakov and Zamolodchikovn in 1984.
• 1970: Polyakov demonstrated that the conformal invariance arises at the critical points
• 1969: The short-distance expansion of the product of fields known as the Operator product expansion (OPE) was originally proposed in the context of standard quantum field theory (QFT) by Wilson . It’s a useful tool in CFT.

Boris Feigin (M), Dmitry Fuchs (M), Israel Gelfand (M), Edward Frenkel (MP), Edward Witten (MP)$^\dagger$, Miguel Ángel Virasoro (P), David Ridout (MP), Justine Fasquel (M), Zachary Fehily (M), Christopher Raymond (MP), Leszek Hadasz (P/MP), Paulina Suchanek (P/MP), … yet to be updated.

Note: P = Physicist, M = Mathematician, MP = Mathematical Physicist