68 research outputs found
't Hooft Conditions in Supersymmetric Dual Theories
The matching of global anomalies of a supersymmetric gauge theory and its
dual is seen to follow from similarities in their classical chiral rings. These
similarities provide a formula for the dimension of the dual gauge group. As
examples we derive 't Hooft consistency conditions for the duals of
supersymmetric QCD and SU(N) theories with matter in the adjoint, and obtain
the dimension of the dual groups.Comment: 9 pages, Revte
Black hole nonmodal linear stability: the Schwarzschild (A)dS cases
The nonmodal linear stability of the Schwarzschild black hole established in
Phys. Rev. Lett. 112 (2014) 191101 is generalized to the case of a nonnegative
cosmological constant . Two gauge invariant combinations of
perturbed scalars made out of the Weyl tensor and its first covariant
derivative are found such that the map
with domain the set of equivalent classes under gauge
transformations of solutions of the linearized Einstein's equation, is
invertible. The way to reconstruct a representative of in
terms of is given. It is proved that, for an arbitrary perturbation
consistent with the background asymptote, and are bounded in the
the outer static region. At large times, the perturbation decays leaving a
linearized Kerr black hole around the Schwarzschild or Schwarschild de Sitter
background solution. For negative cosmological constant it is shown that there
is a choice of boundary conditions at the time-like boundary under which the
Schwarzschild anti de Sitter black hole is unstable. The root of
Chandrasekhar's duality relating odd and even modes is exhibited, and some
technicalities related to this duality and omitted in the original proof of the
case are explained in detail.Comment: Typos corrected, changes in the Introduction (including example of
nonmodal instability
The wave equation on the extreme Reissner-Nordstr\"om black hole
We study the scalar wave equation on the open exterior region of an extreme
Reissner-Nordstr\"om black hole and prove that, given compactly supported data
on a Cauchy surface orthogonal to the timelike Killing vector field, the
solution, together with its derivatives of arbitrary order,
a tortoise radial coordinate, is bounded by a constant that depends only on
the initial data. Our technique does not allow to study transverse derivatives
at the horizon, which is outside the coordinate patch that we use. However,
using previous results that show that second and higher transverse derivatives
at the horizon of a generic solution grow unbounded along horizon generators,
we show that any such a divergence, if present, would be milder for solutions
with compact initial data.Comment: Minor correction
Petrov type of linearly perturbed type D spacetimes
We show that a spacetime satisfying the linearized vacuum Einstein equations
around a type D background is generically of type I, and that the splittings of
the Principal Null Directions (PNDs) and of the degenerate eigenvalue of the
Weyl tensor are non analytic functions of the perturbation parameter of the
metric. This provides a gauge invariant characterization of the effect of the
perturbation on the underlying geometry, without appealing to differential
curvature invariants. This is of particular interest for the Schwarzschild
solution, for which there are no signatures of the even perturbations on the
algebraic curvature invariants. We also show that, unlike the general case, the
unstable even modes of the Schwarzschild naked singularity deforms the Weyl
tensor into a type II one.Comment: 9 page
Gravitational instability of the inner static region of a Reissner-Nordstrom black hole
Reissner--Nordstr\"om black holes have two static regions:
r > \ro and 0 < r < \ri, where \ri and \ro are the inner and outer
horizon radii. The stability of the exterior static region has been established
long time ago. In this work we prove that the interior static region is
unstable under linear gravitational perturbations, by showing that field
perturbations compactly supported within this region will generically excite a
mode that grows exponentially in time. This result gives an alternative reason
to mass inflation to consider the space time extension beyond the Cauchy
horizon as physically irrelevant, and thus provides support to the strong
cosmic censorship conjecture, which is also backed by recent evidence of a
linear gravitational instability in the interior region of Kerr black holes
found by the authors. The use of intertwiners to solve for the evolution of
initial data plays a key role, and adapts without change to the case of
super-extremal \rn black holes, allowing to complete the proof of the linear
instability of this naked singularity. A particular intertwiner is found such
that the intertwined Zerilli field has a geometrical meaning -it is the first
order variation of a particular Riemann tensor invariant-. Using this,
calculations can be carried out explicitely for every harmonic number.Comment: 24 pages, 4 figures. Changes and corrections in proof using
intertwiners, also in figure
Discrete anomalies and the null cone of SYM theories
A stronger version of an anomaly matching theorem (AMT) is proven that allows
to anticipate the matching of continuous as well as discrete global anomalies.
The AMT shows a connection between anomaly matching and the geometry of the
null cone of SYM theories. Discrete symmetries are shown to be broken at the
origin of the moduli space in Seiberg-Witten theories.Comment: 8 pages, 3 figures, entirely re-written, one section remove
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