Related papers: Four-dimensional Lens Space Index from Two-dimensi…
The chiral space of local fields in Sine-Gordon or the SU(2)-invariant Thirring model is studied as a module over the commutative algebra D of local integrals of motion. Using the recent construction of form factors by means of quantum…
Higher spin fields in four dimensions, and more generally conformal fields in arbitrary dimensions, can be described by spinning particle models with a gauged SO(N) extended supergravity on the worldline. We consider here the one-loop…
We study the properties of 4d N=3 superconformal field theories whose rank is one, i.e. those that reduce to a single vector multiplet on their moduli space of vacua. We find that the moduli space can only be of the form C^3/Z_k for…
We provide the geometrical meaning of the ${\cal N}=4$ superconformal index. With this interpretation, the ${\cal N}=4$ superconformal index can be realized as the partition function on a Scherk-Schwarz deformed background. We apply the…
We introduce the analytic superspace formalism for six-dimensional $(N,0)$ superconformal field theories. Concentrating on the $(2,0)$ theory we write down the Ward identities for correlation functions in the theory and show how to solve…
Within a four dimensional manifestly N = 1 supersymmetric action, we show that Wess-Zumino-Novikov-Witten (WZNW) terms can be embedded in an extraordinarily simple manner into a purely chiral superaction. In order to achieve this result it…
Classical harmonic analysis says that the spaces of homogeneous harmonic polynomials (solutions of Laplace equation) are irreducible modules of the corresponding orthogonal Lie group (algebra) and the whole polynomial algebra is a free…
We propose a new program for computing a certain integrand of scattering amplitudes of four-dimensional gauge theories which we call the \textit{form factor integrand}, starting from 6d holomorphic theories on twistor space. We show that…
We explore the geometric interpretation of the twisted index of 3d ${\mathcal N} =4$ gauge theories on $S^1\times \Sigma$ where $\Sigma$ is a closed Riemann surface. We focus on a rich class of supersymmetric quiver gauge theories that have…
We derive the component Lagrangian for the free $N$-extended on-shell massless higher spin supermultiplets in four-dimensional anti-de Sitter space. The construction is based on frame-like description of massless integer and half-integer…
We present a new duality between the F-terms of supersymmetric field theories defined in two- and four-dimensions respectively. The duality relates N=2 supersymmetric gauge theories in four dimensions, deformed by an Omega-background in one…
We derive a general integral formula on an embedded hypersurface for general relativistic space-times. Suppose the hypersurface is foliated by two-dimensional compact ``sections'' $S_s$. Then the formula relates the rate of change of the…
We reformulate self-dual supersymmetric theories directly in conformal chiral superspace, where superconformal invariance is manifest. The superspace can be interpreted as the generalization of the usual Atiyah-Drinfel'd-Hitchin-Manin…
We prove that the near-horizon geometries of minimal gauged five-dimensional supergravity preserve at least half of the supersymmetry. If the near-horizon geometries preserve a larger fraction, then they are locally isometric to $AdS_5$.…
We study briefly some properties of real Clifford algebras and identify them as matrix algebras. We then show that the representation space on which Clifford algebras act are spinors and we study in details matrix representations. The…
Superconformal indices (SCIs) of 4d ${\mathcal N}=4$ SYM theories with simple gauge groups are described in terms of elliptic hypergeometric integrals. For $F_4, E_6, E_7, E_8$ gauge groups this yields first examples of integrals of such…
We study a rich set of four-dimensional superconformal field theories (SCFTs) with both central charges identical: $a = c$. These are constructed via the diagonal $\mathcal{N}=2$ or $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a…
We consider supersymmetry algebras in arbitrary spacetime dimension and signature. Minimal and maximal superalgebras are given for single and extended supersymmetry. It is seen that the supersymmetric extensions are uniquely determined by…
In this review article we describe the localization of three dimensional N=2 supersymmetric theories on compact manifolds, including the squashed sphere, S^3_b, the lens space, S^3_b/Z_p, and S^2 x S^1. We describe how to write…
We establish a direct connection between the representation theories of Lie algebras and Lie superalgebras (of type A) via Fock space reformulations of their Kazhdan-Lusztig theories. As a consequence, the characters of finite-dimensional…