In this review article we describe the localization of three dimensional= 2 N supersymmetric
theories on compact manifolds, including the squashed sphere, Sb 3, the lens space, Sb p …

We study the N= 2 four-dimensional superconformal index in various interesting limits, such
that only states annihilated by more than one supercharge contribute. Extrapolating from the …

The conjectured F-theorem for three-dimensional field theories states that the finite part of
the free energy on S 3 decreases along RG trajectories and is stationary at the fixed points …

A bstract The analytic properties of the\(\mathcal {N}= 2\) superconformal index are given a
physical interpretation in terms of certain BPS surface defects, which arise as the IR limit of …

A bstract Motivated by physical constructions of homological knot invariants, we study their
analogs for closed 3-manifolds. We show that fivebrane compactifications provide a …

The Higgs branch of 4D N= 2 superconformal field theories can be analyzed via the Hilbert
series of the Higgs branch or, in special cases, by computing the Hall-Littlewood index. For …

A bstract Partition functions of\(\mathcal {N}= 2\) theories on the squashed 3-sphere have
been recently shown to localise to matrix integrals. By explicitly evaluating the matrix integral …

A bstract Argyres-Douglas (AD) theories constitute an infinite class of superconformal field
theories in four dimensions with a number of interesting properties. We study several new …

The four dimensional N= 4 super-Yang-Mills (SYM) theory exhibits rich dynamics in the
presence of codimension-one conformal defects. The new structure constants of the …

We find the warped AdS 4⋉ K type-IIB supergravity solutions holographically dual to a large
family of three dimensional\(\mathcal {N}= 4\) superconformal field theories labeled by a …