Related papers: Generalised 4d Partition Functions and Modular Dif…
We construct modular linear differential equations (MLDEs) w.r.t. subgroups of the modular group whose solutions are Virasoro conformal blocks appearing in the expansion of a crossing symmetric 4-point correlator on the sphere. This uses a…
We obtain the brane setup describing 3d $\mathcal{N}=2$ dualities for $USp(2N_c)$ and $U(N_c)$ SQCD with monopole superpotentials. This classification follows from a complete analysis of affine and twisted affine compactifications from 4d.…
We find closed-form expressions for the Schur indices of 4d $\mathcal{N}=2^{*}$ super Yang-Mills theory with unitary gauge groups for arbitrary ranks via the Fermi-gas formulation. They can be written as a sum over the Young diagrams…
We study the supersymmetric partition function of 4d supersymmetric gauge theories with a U(1) R-symmetry on Euclidean $S^3\times S_\beta^1$, with $S^3$ the unit-radius squashed three-sphere, and $\beta$ the circumference of the circle. For…
Exact results are derived for 5d SCFTs with holographic duals in Type IIB supergravity. These theories have relevant deformations that flow to linear quiver gauge theories, with the number of nodes large in the large-$N$ limits described by…
Simplest examples of AdS/CFT duality correspond to free CFTs in d dimensions with fields in vector or adjoint representation of an internal symmetry group dual in the large N limit to a theory of massless or massless plus massive higher…
A general class of W-algebras can be constructed from the affine sl(N) algebra by (quantum) Drinfeld-Sokolov reduction and are classified by partitions of N. Surface operators in an N=2 SU(N) 4d gauge theory are also classified by…
We prove a duality, recently conjectured in arXiv:1103.5726, which relates the F-terms of supersymmetric gauge theories defined in two and four dimensions respectively. The proof proceeds by a saddle point analysis of the four-dimensional…
Let $F$ be a non-archimedean local field with residue field $\mathbb{F}_q$ and let $G = GL_{2/F}$. Let $\mathbf{q}$ be an indeterminate and let $H^{(1)}(\mathbf{q})$ be the generic pro-p Iwahori-Hecke algebra of the group $G(F)$. Let…
The 6d (2,0) theory of $N$ M5 branes compactified on the product geometry $T^2\times S$, where $S$ is a K\"ahler 4-manifold, can be studied in two different limits. In one limit, the size of $T^2$ is taken to zero and together with a…
We construct the duality groups for N=2 Supersymmetric QCD with gauge group SU(2n+1) and N_f=4n+2 hypermultiplets in the fundamental representation. The groups are generated by two elements $S$ and $T$ that satisfy a relation…
We study the non-perturbative properties of N=2 super conformal field theories in four dimensions using localization techniques. In particular we consider SU(2) gauge theories, deformed by a generic epsilon-background, with four fundamental…
We introduce the notion of standard multipartitions and establish a one-to-one correspondence between standard multipartitions and irreducible representations with integral weights for the affine Hecke algebra of type A with a parameter q…
We show that the full matrix algebra Mat_p(C) is a U-module algebra for U = U_q sl(2), a 2p^3-dimensional quantum sl(2) group at the 2p-th root of unity. Mat_p(C) decomposes into a direct sum of projective U-modules P^+_n with all odd n,…
In this work, first, we discuss the connections between various low-dimensional quantum gravity models, including 3d Chern-Simons, 2d JT, 2d BF theory, 2d Liouville, 2d WZW, and 1d Schwarzian, which are related through holography and…
The irreducible modules over quiver Hecke superalgebras $R_\theta$ can be classified in terms of cuspidal modules. To an indivisible positive root $\alpha$ and a non-negative integer $d$, one associates a quotient $\bar R_{d\alpha}$ of…
In our recent work [Phys. Rev. Lett. 102, 230502 (2009)] we showed that the partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), can be…
We study various duality webs involving the 3d FT[SU(N)] theory, a close relative of the T[SU(N)] quiver tail. We first map the partition functions of FT[SU(N)] and its 3d spectral dual to a pair of spectral dual q-Toda conformal blocks.…
In this note, we explore the relation between crossing symmetry and modular invariance in conformal field theory and S-duality in gauge theory. It is shown that partition functions of different S dual theories of N=2 SU(2) gauge theory with…
We show that canonical bases in $\dot{U}(\mathfrak{sl}_n)$ and the Schur algebra are compatible; in fact we extend this result to $p$-canonical bases. This follows immediately from a fullness result from a functor categorifying this map. In…