Related papers: On non-relativistic integrable models and 4d SCFTs
We conjecture a precise relationship between the Schur limit of the superconformal index of four-dimensional $\mathcal{N}=2$ field theories, which counts local operators, and the spectrum of BPS particles on the Coulomb branch. We verify…
We conjecture that decoupling relations in the operator product expansion of a 4d $\mathcal{N}=2$ superconformal field theory (SCFT) are encoded by an algebro-geometric object: a bifiltered affine scheme. We demonstrate how this scheme…
We review and present new studies on the relation between the partition functions of integrable lattice models and symmetric polynomials, and its combinatorial representation theory based on the correspondence, including our work. In…
An all orders formula for the $S$-matrix for 2 $\rightarrow$ 2 scattering in large N Chern-Simons theory coupled to a fundamental scalar has recently been conjectured. We find a scaling limit of the theory in which the pole in this…
One can derive a large class of new $\mathcal{N}=1$ SCFTs by turning on $\mathcal{N}=1$ preserving deformations for $\mathcal{N}=2$ Argyres-Dougals theories. In this work, we use $\mathcal{N}=2$ superconformal indices to get indices of…
We propose that a certain $4d$ $\mathcal{N}=1$ $SU(4)$ gauge theory flows in the IR to the rank $1$ $\mathcal{N}=2$ strongly coupled SCFT with $E_6$ global symmetry and $25$ free chiral fields. This proposal is tested by comparing various…
We introduce and investigate a family of tau-functions of the 2D Toda hierarchy, which is a natural generalization of the hypergeometric family associated with Hurwitz numbers. For this family we prove a skew Schur function expansion…
Invariance under modular transformations and spectral flow restrict the possible spectra of superconformal field theories (SCFT). This paper presents a technique to calculate the number of constraints on the polar spectra of N=(2,2) and…
We revisit 6d (2,0) SCFTs of type $D_N$ and their realization in M-theory, focusing on absolute variants of these theories and on their global finite 0- and 2-form symmetries. We derive the 7d SymTFT capturing these global symmetries from…
The multi-component nonlinear Schrodinger equation related to C.I=Sp(2p)/U(p) and D.III=SO(2p)/U(p)-type symmetric spaces with non-vanishing boundary conditions is solvable with the inverse scattering method (ISM). As Lax operator L we use…
Joint distribution function of N eigenvalues of U(N) invariant random-matrix ensemble can be interpreted as a probability density to find N fictitious non-interacting fermions to be confined in a one-dimensional space. Within this picture a…
Conformal theories with a global symmetry may be studied in the double scaling regime where the interaction strength is reduced while the global charge increases. Here, we study generic 4d $\mathcal N=2$ $SU(N)$ gauge theories with…
We investigate multi-field multicritical scalar theories using CFT constraints on two- and three-point functions combined with the Schwinger-Dyson equation. This is done in general and without assuming any symmetry for the models, which we…
Recently, Maulik and Okounkov proposed an integrable lattice model where the degree of freedom at each site is identical to the Hilbert space of free boson in two dimensions. We give a brief review of their construction and explain the…
We investigate Stein-Malliavin approximations for nonlinear functionals of geometric interest of Gaussian random eigenfunctions on the unit $d$ -dimensional sphere ${\mathbb{S}}^{d},$ $d\geq 2.$ All our results are established in the high…
We define the gauge-equivariant index of a family of elliptic operators invariant with respect to the free action of a family $\GR \to B$ of Lie groups (these families are called ``gauge-invariant families'' in what follows). If the fibers…
The 4-dimensional Sklyanin algebras are a well-studied 2-parameter family of non-commutative graded algebras, often denoted A(E,tau), that depend on a quartic elliptic curve E in P^3 and a translation automorphism tau of E. They are graded…
A dynamical $r$-matrix is associated with every self-dual Lie algebra $\A$ which is graded by finite-dimensional subspaces as $\A=\oplus_{n \in \cZ} \A_n$, where $\A_n$ is dual to $\A_{-n}$ with respect to the invariant scalar product on…
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. In the case of…
Most of the work done in the past on the integrability structure of the Classical Heisenberg Spin Chain (CHSC) has been devoted to studying the $su(2)$ case, both at the continuous and at the discrete level. In this paper we address the…