IPM

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.