Antonio Amariti joined the Institute in the autumn 2012. He had obtained his PhD

in 2009 in Milan and had done a first postdoc at UCSD. He has worked on a vari-

ety of subjects since he joined the Institute, mostly within the framework of three dimensional dualities [1] - [8]. The main results obtained are related to the dimen-

sional reduction to three dimensions of four dimensional dualities for supersymmetric

field theories with the minimal amount of supersymmetry in four dimensions. These

models are three dimensional theories with four supercharges, the minimal amount

of supersymmetry in three dimensions that preserves holomorphy (allowing for three

dimensional non-renormalization theorems).

He has applied the dimensional reduction to the 4d superconformal index, an

invariant quantity counting a well defined and protected set of operators in 4d [1]. By

following the reduction to three dimensions a well-defined exact quantity is obtained

[2], the supersymmetric partition function computed on a (possibly squashed) three

sphere [4]. This object is relevant in the study of three dimensional supersymmetric

field theories because it is believed to count the degrees of freedom in renormalization

group flows to the infrared and monotonically reduces during a flow. Further work is

concerned with dualities involving Chern-Simons matter [5, 6].

More recently, in [7], in collaboration with Claudius Klare (CEA-Saclay), he ob-

tained (new) three dimensional integral identities for the reduced dualities, by starting

from the four dimensional exact relations. This procedure requires to compute some

limits of integrals involving elliptic gamma functions. In such a procedure new exact

mathematical identities involving integrals of hyperbolic gamma function have been

obtained [11]. This can be of particular interest also in other fields, like the analysis

of integrable systems and in pure mathematics.

The other main aspect of his recent research has been the study of this reduction

in the context of brane engineering of supersymmetric gauge theories. Indeed, the

dynamics of the theories under consideration can be analyzed in the framework of

string theory, by an embedding in type IIA supergravity, where Dirichlet and Neveu-

Schwarz branes play a prominent role. By applying a string theory duality, called

T-duality, on the compact direction, a general framework to study the three dimen-

sional reduced dualities is obtained. In this way in [8], in collaboration with Davide

Forcella ULB, Bruxelles), Claudius Klare (CEA Saclay), Domenico Orlando (ENS,

Paris) and Susanne Reffert (CERN), he understood many involved properties of the

field theory reduction in a simple and elegant manner. Moreover, this analysis unifies

apparently different reductions involving complex and real gauge groups or a compli-

cated matter content, and it offers a new and general perspective of the structure of

three dimensional dual pairs.

Antonio Amariti left the ENS after 3 years (2 years at the Philiipe Meyer Institute

and a third year paid from a different grant) and took a position at City College, New

York.