We study 4d SCFTs obtained by orientifold projections on necklace quivers with fractional branes. The models obtained by this procedure are $mathcal{N}=1$ linear quivers with unitary, symplectic and orthogonal gauge groups, bifundamental and tensoria
l matter. Remarkably, models that are not dual in the unoriented case can have the same central charges and superconformal index after the projection. The reason for this behavior rests upon the ubiquitous presence of adjoint fields with R-charge one. We claim that the presence of such fields is at the origin of the notion of inherited S-duality on the models conformal manifold.
We compute $tau_{RR}$ minimization in gauged supergravity for M-theory and String Theory truncations with both massless and massive vector multiplets. We explicitly compute, as anticipated in cite{Amariti:2015ybz}, that massive vector fields at the v
acuum require the introduction of a constraint through a Lagrange multiplier. We illustrate this explicitly in two examples, namely the $U(1)^2$-invariant truncation dual to the mABJM model and the ISO(7) truncation in massive IIA, the latter being a theory with both electric and magnetic gauging. We revisit the vacuum constraints at $AdS_4$ and show how the supergravity analysis matches the results of the field theory dual computation.
We study the Cardy-like limit of the superconformal index of generic $mathcal{N}=1$ SCFTs with ABCD gauge algebra, providing strong evidence for a universal formula that captures the behavior of the index at finite order in the rank and in the fugaci
ties associated to angular momenta. The formula extends previous results valid at lowest order, and generalizes them to generic SCFTs. We corroborate the validity of our proposal by studying several examples, beyond the well-understood toric class. We compute the index also for models without a weakly-coupled gravity dual, whose gravitational anomaly is not of order one.
We study the superconformal index of 4d $mathcal{N}=4$ $USp(2N_c)$ and $SO(N_c)$ SYM from a matrix model perspective. We focus on the Cardy-like limit of the index. Both in the symplectic and orthogonal case the index is dominated by a saddle point s
olution which we identify, reducing the calculation to a matrix integral of a pure Chern-Simons theory on the three-sphere. We further compute the subleading logarithmic corrections, which are of the order of the center of the gauge group. In the $USp(2N_c)$ case we also study other subleading saddles of the matrix integral. Finally we discuss the case of the Leigh-Strassler fixed point with $SU(N_c)$ gauge group, and we compute the entropy of the dual black hole from the Legendre transform of the entropy function.
We study dualities for 3d $mathcal{N} = 2$ $SU(N_c)$ SQCD at Chern-Simons level $k$ in presence of an adjoint with polynomial superpotential. The dualities are dubbed chiral because there is a different amount of fundamentals $N_f$ and antifundamenta
ls $N_a$. We build a complete classification of such dualities in terms of $ |N_f - N_a| $ and $k$. The classification is obtained by studying the flow from the non-chiral case, and we corroborate our proposals by matching the three-sphere partition functions. Finally, we revisit the case of $SU(N_c)$ SQCD without the adjoint, comparing our results with previous literature.
It has recently been claimed that a Cardy-like limit of the superconformal index of 4d $mathcal{N}=4$ SYM accounts for the entropy function, whose Legendre transform corresponds to the entropy of the holographic dual AdS$_5$ rotating black hole. Here
we study this Cardy-like limit for $mathcal{N}=1$ toric quiver gauge theories, observing that the corresponding entropy function can be interpreted in terms of the toric data. Furthermore, for some families of models, we compute the Legendre transform of the entropy function, comparing with similar results recently discussed in the literature.
We construct several novel examples of 3d $mathcal{N}=2$ models whose free energy scales as $N^{3/2}$ at large $N$. This is the first step towards the identification of field theories with an M-theory dual. Furthermore, we match the volumes extracted
from the free energy with the ones computed from the Hilbert series. We perform a similar analysis for the 4d parents of the 3d models, matching the volume extracted from the $a$ conformal anomaly to that obtained from the Hilbert series. For some of the 4d models, we show the existence of a Sasaki-Einstein metric on the internal space of the candidate type IIB gravity dual.
We obtain the brane setup describing 3d $mathcal{N}=2$ dualities for $USp(2N_c)$ and $U(N_c)$ SQCD with monopole superpotentials. This classification follows from a complete analysis of affine and twisted affine compactifications from 4d. The analysi
s leads to a new duality for the unitary case that has been previously overlooked in the literature. We check this by matching of the three sphere partition function of the two sides of this new duality and find a perfect agreement. Furthermore we use the partition function to predict new 3d $mathcal{N}=2$ dualities for SQCD with monopole superpotentials and tensorial matter.
Aspects of three dimensional $mathcal{N}=2$ gauge theories with monopole superpotentials and their dualities are investigated. The moduli spaces of a number of such theories are studied using Hilbert series. Moreover, we propose new dualities involvi
ng quadratic powers for the monopole superpotentials, for unitary, symplectic and orthogonal gauge groups. These dualities are then tested using the three sphere partition function and matching of the Hilbert series. We also provide an argument for the obstruction to the duality for theories with quartic monopole superpotentials.
In this paper we provide a first attempt towards a toric geometric interpretation of scattering amplitudes. In recent investigations it has indeed been proposed that the all-loop integrand of planar N=4 SYM can be represented in terms of well defined
finite objects called on-shell diagrams drawn on disks. Furthermore it has been shown that the physical information of on-shell diagrams is encoded in the geometry of auxiliary algebraic varieties called the totally non negative Grassmannians. In this new formulation the infinite dimensional symmetry of the theory is manifest and many results, that are quite tricky to obtain in terms of the standard Lagrangian formulation of the theory, are instead manifest. In this paper, elaborating on previous results, we provide another picture of the scattering amplitudes in terms of toric geometry. In particular we describe in detail the toric varieties associated to an on-shell diagram, how the singularities of the amplitudes are encoded in some subspaces of the toric variety, and how this picture maps onto the Grassmannian description. Eventually we discuss the action of cluster transformations on the toric varieties. The hope is to provide an alternative description of the scattering amplitudes that could contribute in the developing of this very interesting field of research.
