Related papers: Superconformal Blocks: General Theory
The representation theories of the SU(2)$_k$-extended $N$=4 superconformal algebras (SCAs) with $arbitrary$ level $k$ are developed being based on their Feigin-Fuchs representations found recently by the present author. A basic unit of the…
We construct a large new family of four-dimensional N=1 superconformal field theories by coupling Gaiotto's T_N theories to N=1 vector multiplets. In particular, we consider theories in which various T_N blocks are linked together via…
We derive closed-form expressions for all ingredients of the Zamolodchikov-like recursion relation for general spinning conformal blocks in 3-dimensional conformal field theory. This result opens a path to efficient automatic generation of…
We construct supersymmetric irregular vertex operators of arbitrary rank, appearing in the colliding limit of primary fields. We find that the structure of the supersymmetric irregular vertices differs significantly from the bosonic case:…
This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin…
We define the two-dimensional $O(n)$ conformal field theory as a theory that includes the critical dilute and dense $O(n)$ models as special cases, and depends analytically on the central charge. For generic values of $n\in\mathbb{C}$, we…
We study correlation functions in the one-dimensional $\mathcal{N}=2$ supersymmetric SYK model. The leading order 4-point correlation functions are computed by summing over ladder diagrams expanded in a suitable basis of conformal…
We revisit the higher spin extensions of the anti de Sitter algebra in four dimensions that incorporate internal symmetries and admit representations that contain fermions, classified long ago by Konstein and Vasiliev. We construct the…
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions.…
We present theories of N=2 hypermultiplets in four spacetime dimensions that are invariant under rigid or local superconformal symmetries. The target spaces of theories with rigid superconformal invariance are (4n)-dimensional {\it special}…
Any N=2 superconformal gauge theory (including N=4 SYM) contains a set of local operators made only out of fields in the N=2 vector multiplet that is closed under renormalization to all loops, namely the SU(2,1|2) sector. For planar N=4 SYM…
We show that four-dimensional superconformal algebras admit an infinite-dimensional derived enhancement after performing a holomorphic twist. The type of higher symmetry algebras we find are closely related to algebras studied by…
We present general four-loop template $\beta$-functions and anomalous field dimensions for renormalisable scalar-fermion theories in three dimensions. By imposing $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry, we obtain relations…
Within the context of Supersymmetric Quantum Mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the…
We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…
We built up a explicit realization of (0+1)-dimensional q-deformed superspace coordinates as operators on standard superspace. A q-generalization of supersymmetric transformations is obtained, enabling us to introduce scalar superfields and…
We use the manifestly N=2 supersymmetric, off-shell, harmonic (or twistor) superspace approach to solve the constraints implied by four-dimensional N=2 superconformal symmetry on the N=2 non-linear sigma-model target space, known as the…
Making use of the exact solutions of the $N=2$ supersymmetric gauge theories we construct new classes of superconformal field theories (SCFTs) by fine-tuning the moduli parameters and bringing the theories to critical points. SCFTs we have…
We study relevant deformations of conformal field theory on a cylinder using conformal perturbation theory, and in particular the one point function of the deformation operator and the energy in a system after a quench. We do the one point…
Using the worldline SU(2|1) superfield approach, we construct N=4 superconformally invariant actions for the d=1 multiplets (1, 4, 3) and (2, 4, 2). The SU(2|1) superfield framework automatically implies the trigonometric realization of the…