Related papers: Superconformal field theory and Jack superpolynomi…
This work initiates the study of {\it orthogonal} symmetric polynomials in superspace. Here we present two approaches leading to a family of orthogonal polynomials in superspace that generalize the Jack polynomials. The first approach…
We extend the superembedding formalism for 4D N=1 superconformal field theory (SCFT) to the case of fields in arbitrary representations of the superconformal group SU(2,2|1). As applications we obtain manifestly superconformally covariant…
We present subsingular vectors of the N=2 superconformal algebras other than the ones which become singular in chiral Verma modules, reported recently by Gato-Rivera and Rosado. We show that two large classes of singular vectors of the…
We review some recent results on the Calogero-Sutherland model with emphasis upon its algebraic aspects. We give integral formulae for excited states (Jack polynomials) of this model and their relations with W_n singular vectors and…
The classification of one parameter local Coulomb branch solution of theories with eight supercharges is given by assuming that it is given by a genus $g$ fiberation of Riemann surfaces. The crucial point is the fact that certain conjugacy…
We use the Jack symmetric functions as a basis of the Fock space, and study the action of the Virasoro generators $L_n$. We calculate explicitly the matrix elements of $L_n$ with respect to the Jack-basis. A combinatorial procedure which…
In this paper, we explore supersymmetric and 2d analogs of the SYK model. We begin by working out a basis of (super)conformal eigenfunctions appropriate for expanding a four-point function. We use this to clarify some details of the 1d…
We generalize, in a manifestly Weyl-invariant way, our previous expressions for irregular singularity wave functions in two-dimensional SU(2) q-deformed Yang-Mills theory to SU(N). As an application, we give closed-form expressions for the…
A well-established organisational principle for Argyres--Douglas-type $\mathcal{N}=2$ superconformal field theories in four dimensions is to characterise such theories by the data defining a(n irregular) Hitchin system on $\mathbb{CP}^1$.…
AGT allows one to compute conformal blocks of d = 2 CFT for a large class of chiral CFT algebras. This is related to the existence of a certain orthogonal basis in the module of the (extended) chiral algebra. The elements of the basis are…
It is shown that the previously known $N=3$ and $N=4$ superconformal algebras can be contracted consistently by singular scaling of some of the generators. For the later case, by a contraction which depends on the central term, we obtain a…
This is the 8th article in the collection of reviews "Exact results in N=2 supersymmetric gauge theories", ed. J. Teschner. The article reviews the superconformal index. It is often simpler to calculate than instanton partition functions,…
We study N = 2 supersymmetric gauge theories with gauge group SU(2) coupled to fundamental flavours, covering all asymptotically free and conformal cases. We re-derive, from the conformal field theory perspective, the differential equations…
In this work we uncover a connection that relates the 1-form and the 2-group symmetries of 5D SCFTs derived from geometric engineering methods to monodromies of the corresponding B-models via mirror symmetry. Viewing defects as branes…
A Birch and Swinnerton-Dyer conjecture for number fields $K / \mathbb{Q}$ would assert that $dim V_K = ord_{s = 1/2} \zeta_K (s)$ for some vector space functorially attached to $K$. Presently there is no natural candidate for the $V_K$'s.…
Motivated by Stanley's conjecture on the multiplication of Jack symmetric functions, we prove a couple of identities showing that skew Jack symmetric functions are semi-invariant up to translation and rotation of a $\pi$ angle of the skew…
We classify nontrivial deformations of the standard embedding of the Lie algebra $\Vect(S^1)$ of smooth vector fields on the circle, into the Lie algebra~$\PD(S^1)$ of pseudodifferential symbols on $S^1$. This approach leads to deformations…
In this thesis, we obtain the formula for the Kac determinant of the algebra arising from the level $N$ representation of the Ding-Iohara-Miki algebra. This formula can be proved by decomposing the level $N$ representation into the deformed…
We exhibit an infinite family of supersymmetric phases in the three-dimensional ABJM superconformal field theory and the dual asymptotically AdS$_4$ gravity. They are interpreted as partially deconfined phases which generalize the…
At an extremely low-energy scale, it is believed that the two-dimensional $\mathcal{N}=2$ Wess--Zumino model becomes an $\mathcal{N}=2$ superconformal field theory (SCFT). We study this theoretical conjecture of the Landau--Ginzburg (LG)…