Related papers: $\mathcal{N} = 2$ Schur index and line operators
Integrable $su(2\vert2)_{c}$ symmetric models have integrable boundaries with $osp(2\vert2)$ symmetries, which can be embedded into $su(2\vert2)_{c}$ in two different ways. We dualize the previously obtained asymptotic overlap formulas for…
We consider the $\mathcal{N}=4$ SYM theory with gauge group $Sp(N)$ and the $\mathcal{N}=2$ superconformal field theory consisting of four hypermultiplets in the fundamental representation and one hypermultiplet in the rank-two…
We develop techniques to study the correlation functions of "large operators" whose bare dimension grows parametrically with N, in SO(N) gauge theory. We build the operators from a single complex matrix. For these operators, the large N…
The Coulomb and Higgs indices of the 3d $\mathcal{N}=4$ $U(N)$ ADHM theories can be decorated by line defect operators as the line defect correlators. We obtain exact closed-form expressions and various non-trivial algebraic relations for…
There are two major ways of constructing 4d $\mathcal{N}=2$ superconformal field theories (SCFTs): the first one is putting a 6d $(2,0)$ theory on a punctured Riemann surface (class-S theory), and the second one is putting type IIB string…
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 present a rigorous but elementary index theory for a class of one-dimensional systems of interacting (and possibly disordered) fermions with $\Uone\rtimes\bbZ_2$ symmetry defined on the infinite chain. The class includes the…
It has recently been argued by Alday et al that the inclusion of surface operators in 4d N=2 SU(2) quiver gauge theories should correspond to insertions of certain degenerate operators in the dual Liouville theory. So far only the insertion…
We generalize S-duality to N=2 superconformal field theories (SCFTs) with Coulomb branch operators of non-integer scaling dimension. As simple examples, we find minimal generalizations of the S-dualities discovered in SU(2) gauge theory…
The study of exactly marginal deformations of superconformal field theories is a topic that has received considerable attention due to their rich properties. We investigate the $\mathcal{N}=2$ preserving exactly marginal operators of 3d…
We investigate the deformed Schur index in four dimensional N=4 super Yang-Mills theories with $SO$ and $Sp$ gauge groups, generalizing Hatsuda's recent calculations. We express the deformed Schur index as integrals of Koornwinder…
The so-called 2d/4d correspondences connect two-dimensional conformal field theory (2d CFT), N=2 supersymmetric gauge theories and quantum integrable systems. The latter in the simplest case of the SU(2) gauge group are nothing but the…
We consider the defect CFT defined by a 't Hooft line embedded in N=4 super Yang-Mills theory. By explicitly quantizing around the given background we exactly reproduce a prediction from S-duality for the correlators between the 't Hooft…
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 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…
Large N duality conjecture between U(N) Chern-Simons gauge theory on $S^3$ and A-model topological string theory on the resolved conifold was verified at the level of partition function and Wilson loop observables. As a consequence, the…
The Witten index counts the difference in the number of bosonic and fermionic states of a quantum mechanical system. The Schur index, which can be defined for theories with at least $\mathcal{N}=2$ supersymmetry in four dimensions is a…
We undertake a systematic study of the $4$-dimensional $SU(N)$ $2$-index chiral gauge theories and investigate their faithful global symmetries and dynamics. These are a finite set of theories with fermions in the $2$-index symmetric and…
We derive explicit formulae to compute the $a$ and $c$ central charges of four dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also…
We study strings associated with minimal 6d SCFTs, which by definition have only one string charge and no Higgs branch. These theories are labelled by a number n with 1 <= n <= 8 or n = 12. Quiver theories have previously been proposed…