16 research outputs found
Extended Supersymmetry on Curved Spaces
We study N=2 superconformal theories on Euclidean and Lorentzian
four-manifolds with a view toward applications to holography and localization.
The conditions for supersymmetry are equivalent to a set of differential
constraints including a "generalised" conformal Killing spinor equation
depending on various background fields. We solve these equations in the general
case and give very explicit expressions for the auxiliary fields that we need
to turn on to preserve some supersymmetry. As opposed to what has been observed
for the N=1 case, the conditions for unbroken supersymmetry turn out to be
almost independent of the signature of spacetime, with the exception of few
degenerate cases including the topological twist. Generically, the only
geometrical constraint coming from supersymmetry is the existence of a
conformal Killing vector on the manifold, all other constraints determine the
background auxiliary fields.Comment: 31 pages, v2: minor changes and important references adde
A journey to 3d: exact relations for adjoint SQCD from dimensional reduction
In this note we elaborate on the reduction of four dimensional Seiberg
duality with adjoint matter to three dimensions. We use the exact formulation
of the superconformal index and of the partition function as instruments to
test this reduction. We translate the identity between indices of the dual 4d
theories to 3d. This produces various new identities between partition
functions of 3d dual phases.Comment: 18 pages, appendix added on the large mass scaling of the partition
function, version published in JHE
The M-theory origin of global properties of gauge theories
We show that global properties of gauge groups can be understood as geometric
properties in M-theory. Different wrappings of a system of N M5-branes on a
torus reduce to four-dimensional theories with gauge algebra and
different unitary groups. The classical properties of the wrappings determine
the global properties of the gauge theories without the need to impose any
quantum conditions. We count the inequivalent wrappings as they fall into
orbits of the modular group of the torus, which correspond to the S-duality
orbits of the gauge theories.Comment: 19 pages, 5 figure
4D/3D reduction of dualities: mirrors on the circle
We engineer a brane picture for the reduction of Seiberg dualities from 4D to
3D, valid also in the presence of orientifold planes. We obtain effective 3D
dualities on the circle by T-duality, geometrizing the non-perturbative
superpotential which is an affine Toda potential. When reducing to pure 3D, we
define a double-scaling limit which creates a confining sector, giving a
unified mechanism for the brane reduction of dualities.Comment: 27 pages, 16 figures, discussion improve
The braneology of 3D dualities
In this paper we study the reduction of four-dimensional Seiberg duality to
three dimensions from a brane perspective. We reproduce the non-perturbative
dynamics of the three-dimensional field theory via a T-duality at finite radius
and the action of Euclidean D-strings. In this way we also overcome certain
issues regarding the brane description of Aharony duality. Moreover we apply
our strategy to more general dualities, such as toric duality for M2-branes and
dualities with adjoint matter fields.Comment: 20 pages, 8 figures, published versio
The Large N Limit of Toric Chern-Simons Matter Theories and Their Duals
We compute the large N limit of the localized three dimensional free energy
of various field theories with known proposed AdS duals. We show that
vector-like theories agree with the expected supergravity results, and with the
conjectured F-theorem. We also check that the large N free energy is preserved
by the three dimensional Seiberg duality for general classes of vector like
theories. Then we analyze the behavior of the free energy of chiral-like
theories by applying a new proposal. The proposal is based on the restoration
of a discrete symmetry on the free energy before the extremization. We apply
this procedure at strong coupling in some examples and we discuss the results.
We conclude the paper by proposing an alternative geometrical expression for
the free energy.Comment: 40 pages, 7 figures, using jheppub.sty, references adde