Related papers: Four-dimensional Lens Space Index from Two-dimensi…
In four spacetime dimensions, the classically integrable self-dual sectors of gauge theory and gravity have associated chiral algebras, which emerge naturally from their description in twistor space. We show that there are similar chiral…
Six-dimensional conformal field theories with $(2,0)$ supersymmetry are shown to possess a protected sector of operators and observables that are isomorphic to a two-dimensional chiral algebra. We argue that the chiral algebra associated to…
We discuss orbifold version of the Schur index defined as the supersymmetric partition function in S^3/Z_n x S^1. We first give a general formula for Lagrangian theories obtained by localization technique, and then suggest a generalization…
The supersymmetric Lagrangian compatible with the presence of torsion in the background spacetime requires, in addition to the minimal coupling, an interaction between the spin and the torsion of the form ${1/2}…
We study partition function of four-dimensional $\mathcal{N}=1$ supersymmetric field theory on $T^2 \times S^2$. By applying supersymmetry localization, we show that the $T^2 \times S^2$ partition function is given by elliptic genus of…
In this note we study four dimensional theories with N=3 superconformal symmetry, that do not also have N=4 supersymmetry. No examples of such theories are known, but their existence is also not ruled out. We analyze several properties that…
In this letter, we propose a 4d mirror symmetry for the class-$\mathcal{S}$ theories which relates the representation theory of the chiral quantization of the Higgs branch and the geometry of the Coulomb branch. We study the representation…
We provide a formula for the partition function of five-dimensional $\mathcal{N}=1$ gauge theories on $\mathcal{M}_4 \times S^1$, topologically twisted along $\mathcal{M}_4$ in the presence of general background magnetic fluxes, where…
We study three-dimensional ${\mathcal N}=2$ supersymmetric gauge theories on ${\Sigma_g \times S^1}$ with a topological twist along $\Sigma_g$, a genus-$g$ Riemann surface. The twisted supersymmetric index at genus $g$ and the correlation…
We review the calculation and properties of the supersymmetric index for four dimensional N=1 theories, illustrating its physical significance in several examples.
The Schur index is a powerful tool to probe the spectrum and dualities of 4d $\mathcal{N}=2$ superconformal field theories (SCFTs), deeply related to 2d vertex operator algebras (VOAs). In this paper, we compute the Schur index in closed…
We construct examples of isometric M-theory backgrounds which preserve a different amount of supersymmetry depending on the choice of spin structure. These examples are of the form AdS_4 x L, where L is a seven-dimensional lens space whose…
We discover a modular property of supersymmetric partition functions of supersymmetric theories with R-symmetry in four dimensions. This modular property is, in a sense, the generalization of the modular invariance of the supersymmetric…
The 6d $(2,0)$ theory has codimension-one symmetry defects associated to the outer-automorphism group of the underlying ADE Lie algebra. These symmetry defects give rise to twisted sectors of codimension-two defects that are either regular…
An exact formula for partition functions in 3d field theories was recently suggested by Jafferis, and Hama, Hosomichi, and Lee. These functions are expressed in terms of specific $q$-hypergeometric integrals whose key building block is the…
We describe a new correspondence between four-dimensional conformal field theories with extended supersymmetry and two-dimensional chiral algebras. The meromorphic correlators of the chiral algebra compute correlators in a protected sector…
We consider two-dimensional $\mathcal{N}=(2,2)$ supersymmetric field theories living on a weighted projective space $\mathbb{WCP}_{[n_1,n_2]}^1$, often referred to as a spindle. Starting from the spindle solution of five-dimensional minimal…
The chiral algebra of a 4D $N\geq2$ superconformal field theory is a vertex operator algebra generated by the Schur subsector of the 4D theory and its rigid (yet rich) structure has been useful in constraining and classifying 4D N=2 SCFTs.…
We propose a new fermionic sum formula for the Macdonald index of a class of Argyres-Douglas theories. The formula arises naturally from a three-dimensional topological field theory obtained via a twisted dimensional reduction of the 4d…
A relation between the 4d superconformal index and the S^3 partition function is studied with focus on the 4d and 3d actions used in localization. In the case of vanishing Chern-Simons levels and round S^3 we explicitly show that the 3d…