2d theories

[blefloch]

Tabulate properties of well-known 2d CFTs. This should include central charge, chiral algebra, operator content, structure constant. The list of CFTs should include:

• Liouville,
• generalized minimal models,
• minimal models (unitary or not) (http://arxiv.org/abs/math/9902064 The Cappelli-Itzykson-Zuber A-D-E classification) see also Runkel on A series and D series minimal models
• super Liouville
• super generalized minimal models?
• super minimal models (unitary N=2 classified in http://arxiv.org/abs/0812.1318, see also http://arxiv.org/abs/hep-th/9211097)
• Toda, super Toda
• boundary CFT (BCFT)
• W_N minimal models (partial classification http://arxiv.org/abs/1004.1205 claims about N=2 susy http://arxiv.org/abs/hep-th/9612071)
• Logarithmic CFTs
• 2d Quaternionic/Octonionic SCFTs
• non-compact WZW (coset model) http://arxiv.org/abs/hep-th/9110076 includes H_3^+ (for SL(2,C)/SU(2))
• http://arxiv.org/abs/1509.07516 construct theories intermediate between Toda CFT and SL_N(C)/SU(N) coset model, which have W-algebra symmetry

[blefloch]

2d (0,2):

• For notations see Phases of N=2 paper by Witten
• Silverstein Witten Global U(1) R-symmetry and Conformal Invariance of (0,2) Models: left-moving conformal algebra (in cohomology of \bar Q_+) requires J-term to have total charge 1 (for E-term, flip sign of Fermi's charge), and sum_fermions (charge x chirality) = 0. Also give c_L in (2.10). Also consider left-moving U(1) symmetry.
• (0,2) duality (mirror symmetry, quantum sheaf cohomology)
• Quantum sheaf cohomology http://arxiv.org/abs/1101.1305 http://arxiv.org/abs/1110.3751
• The superconformal manifold of a 2d (0,2) SCFT is Kähler-Hodge (see http://arxiv.org/abs/1509.08511) and its Kähler class is expected to vanish (same paper).
• (0,2) trialities (Gadde Gukov Putrov)
• Bertolini Melnikov Plesser accidental symmetries and aspects of (0,2) conformal perturbation theory.
• U(1)_R mixes with global symmetries, need c-extremization Benini-Bobev
• spectral flow

[blefloch]

2d (2,2):

• Obviously Phases of N=2 paper by Witten
• Chiral rings in N = 2 superconformal theories (Lerche, Vafa, Warner)
• http://arxiv.org/abs/1509.08511 The superconformal manifold of a 2d (2,2) SCFT is Kähler-Hodge and its Kähler class is expected to vanish and the sphere partition function is the exponential of the Kähler potential.
• Gaiotto, Moore, Witten: http://arxiv.org/abs/1506.04086 (45 pages) http://arxiv.org/abs/1506.04087 (429 pages)
• Cremonesi Closset classify (2,2) curved backgrounds also explain well supermultiplets (chiral, twisted chiral, linear, twisted linear, vector, twisted vector,...), see also http://arxiv.org/abs/0705.3201 ; also "constrained semichiral vector multiplet" exist.