23,066 research outputs found
Holographic perfect fluidity, Cotton energy-momentum duality and transport properties
We investigate background metrics for 2+1-dimensional holographic theories
where the equilibrium solution behaves as a perfect fluid, and admits thus a
thermodynamic description. We introduce stationary perfect-Cotton geometries,
where the Cotton--York tensor takes the form of the energy--momentum tensor of
a perfect fluid, i.e. they are of Petrov type D_t. Fluids in equilibrium in
such boundary geometries have non-trivial vorticity. The corresponding bulk can
be exactly reconstructed to obtain 3+1-dimensional stationary black-hole
solutions with no naked singularities for appropriate values of the black-hole
mass. It follows that an infinite number of transport coefficients vanish for
holographic fluids. Our results imply an intimate relationship between
black-hole uniqueness and holographic perfect equilibrium. They also point
towards a Cotton/energy--momentum tensor duality constraining the fluid
vorticity, as an intriguing boundary manifestation of the bulk mass/nut
duality.Comment: V3: 1+39 pages, JHEP versio
The Arithmetic of Elliptic Fibrations in Gauge Theories on a Circle
The geometry of elliptic fibrations translates to the physics of gauge
theories in F-theory. We systematically develop the dictionary between
arithmetic structures on elliptic curves as well as desingularized elliptic
fibrations and symmetries of gauge theories on a circle. We show that the
Mordell-Weil group law matches integral large gauge transformations around the
circle in Abelian gauge theories and explain the significance of Mordell-Weil
torsion in this context. We also use Higgs transitions and circle large gauge
transformations to introduce a group law for genus-one fibrations with
multi-sections. Finally, we introduce a novel arithmetic structure on elliptic
fibrations with non-Abelian gauge groups in F-theory. It is defined on the set
of exceptional divisors resolving the singularities and divisor classes of
sections of the fibration. This group structure can be matched with certain
integral non-Abelian large gauge transformations around the circle when
studying the theory on the lower-dimensional Coulomb branch. Its existence is
required by consistency with Higgs transitions from the non-Abelian theory to
its Abelian phases in which it becomes the Mordell-Weil group. This hints
towards the existence of a new underlying geometric symmetry.Comment: 43 pages, 3 figure
Homogeneous compact geometries
We classify compact homogeneous geometries of irreducible spherical type and
rank at least 2 which admit a transitive action of a compact connected group,
up to equivariant 2-coverings. We apply our classification to polar actions on
compact symmetric spaces.Comment: To appear in: Transformation Group
Asymptotically Hyperbolic Non Constant Mean Curvature Solutions of the Einstein Constraint Equations
We describe how the iterative technique used by Isenberg and Moncrief to
verify the existence of large sets of non constant mean curvature solutions of
the Einstein constraints on closed manifolds can be adapted to verify the
existence of large sets of asymptotically hyperbolic non constant mean
curvature solutions of the Einstein constraints.Comment: 19 pages, TeX, no figure
KdV-like solitary waves in two-dimensional FPU-lattices
We prove the existence of solitary waves in the KdV limit of two-dimensional
FPU-type lattices using asymptotic analysis of nonlinear and singularly
perturbed integral equations. In particular, we generalize the existing results
by Friesecke and Matthies since we allow for arbitrary propagation directions
and non-unidirectional wave profiles.Comment: revised version with several changes in the presentation of the
technical details; 25 pages, 15 figure
A 3-Manifold with no Real Projective Structure
We show that the connected sum of two copies of real projective 3-space does
not admit a real projective structure. This is the first known example of a
connected 3-manifold without a real projective structure.Comment: Minor corrections suggested by refere
Coulomb branches with complex singularities
We construct 4d superconformal field theories (SCFTs) whose Coulomb branches
have singular complex structures. This implies, in particular, that their
Coulomb branch coordinate rings are not freely generated. Our construction also
gives examples of distinct SCFTs which have identical moduli space (Coulomb,
Higgs, and mixed branch) geometries. These SCFTs thus provide an interesting
arena in which to test the relationship between moduli space geometries and
conformal field theory data.
We construct these SCFTs by gauging certain discrete global symmetries of
superYang-Mills (sYM) theories. In the simplest cases, these
discrete symmetries are outer automorphisms of the sYM gauge group, and so
these theories have lagrangian descriptions as sYM theories with
disconnected gauge groups.Comment: 43 page
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