Related papers: Four-Dimensional Avatars of Two-Dimensional RCFT

Meta-conformal invariance is a novel class of dynamical symmetries, with dynamical exponent $z=1$, and distinct from the standard ortho-conformal invariance. The meta-conformal Ward identities can be directly read off from the Lie algebra…

We study a simple, self-dual, rational, and $C_2$-cofinite vertex operator algebra of CFT-type whose simple current modules are graded by $\mathbb{Z}_{2k}$. Based on those simple current modules, a vertex operator algebra associated with a…

We revisit various topological issues concerning four-dimensional ungauged and gauged Wess-Zumino-Witten (WZW) terms for $SU$ and $SO$ quantum chromodynamics (QCD), from the modern bordism point of view. We explain, for example, why the…

We formulate $\lambda$-deformed $\sigma$-models as QFTs in the upper-half plane. For different boundary conditions we compute correlation functions of currents and primary operators, exactly in the deformation parameter $\lambda$ and for…

W_4 gravity is treated algebraically, represented by a set of transformations on classical fields. The Ward identities of the theory are determined by requiring the algebra to close. The general forms for the anomalies are found by looking…

We use AGT correspondence between N=2 SUSY Yang-Mills theory on ${\mathbb R}^4/{\mathbb Z}_2$ and two-dimensional CFT model with the algebra $ {\cal H} \oplus \hat{sl}(2)_2 \oplus \text{NSR}$ to obtain the explicit expressions for 4-point…

We study four-dimensional Chern-Simons theory on $D \times \mathbb{C}$ (where $D$ is a disk), which is understood to describe rational solutions of the Yang-Baxter equation from the work of Costello, Witten and Yamazaki. We find that the…

After giving some definitions for vertex operator SUPERalgebras and their modules, we construct an associative algebra corresponding to any vertex operator superalgebra, such that the representations of the vertex operator algebra are in…

We study the group properties and the similarity solutions for the constraint conditions of anti-self-dual null K\"{a}hler four-dimensional manifolds with at least a Killing symmetry vector. Specifically we apply the theory of Lie…

We study quantum cosmological models for certain classes of bang/crunch singularities, using the duality between expanding bubbles in AdS with a FRW interior cosmology and perturbed CFTs on de Sitter space-time. It is pointed out that…

The left and right zero modes of the level k SU(n) WZNW model give rise to a pair of isomorphic (left and right) mutually commuting quantum matrix algebras. For a deformation parameter q being an even (2h-th, h = k + n) root of unity each…

We derive a charged black hole solution in four dimensions described by $SL(2,R)\times SU(2)\times U(1)/U(1)^2$ WZW coset model. Using the algebraic Hamiltonian method we calculate the corresponding solution that is exact to all orders in…

Conformal symmetry underlies the mathematical description of various two-dimensional integrable models (e.g. for their Lax representation, Poisson algebra, zero curvature representation,...) or of conformal models (for the anomalous Ward…

The concept of global conformal invariance (GCI) opens the way of applying algebraic techniques, developed in the context of 2-dimensional chiral conformal field theory, to a higher (even) dimensional space-time. In particular, a system of…

We introduce a family of 3d $\mathcal{N} = 4$ superconformal field theories that have zero-dimensional Coulomb and Higgs branches and propose that the rational vertex operator algebras $W^{\text{min}}_{k -…

This is the sixth article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. It is discussed how to use localisation techniques for the calculation of expectation values of Wilson and 't Hooft…

Treating the two-dimensional Minkowski space as a Wick rotated version of the complex plane, we characterize the causal automorphisms in two-dimensional Minkowski space as the M\"{a}rzke-Wheeler maps of a certain class of observers. We also…

We consider N=1 two-dimensional (2d) dilatonic supergravity (SG), 2d dilatonic SG obtained by dimensional reduction from N=1 four-dimensional (4d) SG, N=2 2d dilatonic SG and string-inspired 4d dilatonic SG. For all the theories, the…

A phenomenon of "algebraic self-similarity" on 3d cubic lattice, providing what can be called an algebraic analogue of Kadanoff--Wilson theory, is shown to possess a 4d version as well. Namely, if there is a $4\times 4$ matrix $A$ whose…

We consider the sl(2) current algebra at level k=-4 when the sl(2) BRST operator is nilpotent. We formulate a spectral sequence converging to the cohomology of this BRST operator. At the second term of the spectral sequence, we observe an…