87,920 research outputs found
A family of extremal hypergraphs for Ryser's conjecture
Ryser's Conjecture states that for any -partite -uniform hypergraph,
the vertex cover number is at most times the matching number. This
conjecture is only known to be true for in general and for
if the hypergraph is intersecting. There has also been considerable effort made
for finding hypergraphs that are extremal for Ryser's Conjecture, i.e.
-partite hypergraphs whose cover number is times its matching number.
Aside from a few sporadic examples, the set of uniformities for which
Ryser's Conjecture is known to be tight is limited to those integers for which
a projective plane of order exists.
We produce a new infinite family of -uniform hypergraphs extremal to
Ryser's Conjecture, which exists whenever a projective plane of order
exists. Our construction is flexible enough to produce a large number of
non-isomorphic extremal hypergraphs. In particular, we define what we call the
{\em Ryser poset} of extremal intersecting -partite -uniform hypergraphs
and show that the number of maximal and minimal elements is exponential in
.
This provides further evidence for the difficulty of Ryser's Conjecture
Non-extremal D-instantons
We construct the most general non-extremal deformation of the D-instanton
solution with maximal rotational symmetry. The general non-supersymmetric
solution carries electric charges of the SL(2,R) symmetry, which correspond to
each of the three conjugacy classes of SL(2,R). Our calculations naturally
generalise to arbitrary dimensions and arbitrary dilaton couplings.
We show that for specific values of the dilaton coupling parameter, the
non-extremal instanton solutions can be viewed as wormholes of non-extremal
Reissner-Nordstr\"om black holes in one higher dimension. We extend this result
by showing that for other values of the dilaton coupling parameter, the
non-extremal instanton solutions can be uplifted to non-extremal non-dilatonic
p-branes in p+1 dimensions higher.
Finally, we attempt to consider the solutions as instantons of (compactified)
type IIB superstring theory. In particular, we derive an elegant formula for
the instanton action. We conjecture that the non-extremal D-instantons can
contribute to the R^8-terms in the type IIB string effective action.Comment: 31 pages, 4 figures. v3: minor correction and reference adde
Large Charge Four-Dimensional Non-Extremal N=2 Black Holes with R^2-Terms
We consider N=2 supergravity in four dimensions with small R^2 curvature
corrections. We construct large charge non-extremal black hole solutions in all
space, with either a supersymmetric or a non-supersymmetric extremal limit, and
analyze their thermodynamic properties. This generalizes some of the extremal
solutions presented in [arXiv:0902.0831]. The indexed entropy of the
non-extremal extension of the supersymmetric black hole, has the form of the
extremal entropy, with the charges replaced by a function of the charges, the
moduli at infinity and the non-extremality parameter. This is the same behavior
as in the case without R^2-terms.Comment: 13 pages. v2: stripped down to letter format, based on the background
given in [arXiv:0902.0831]. v3: up to date with CQG versio
Holographic Dual of Linear Dilaton Black Hole in Einstein-Maxwell-Dilaton-Axion Gravity
Motivated by the recently proposed Kerr/CFT correspondence, we investigate
the holographic dual of the extremal and non-extremal rotating linear dilaton
black hole in Einstein-Maxwell-Dilaton-Axion Gravity. For the case of extremal
black hole, by imposing the appropriate boundary condition at spatial infinity
of the near horizon extremal geometry, the Virasoro algebra of conserved
charges associated with the asymptotic symmetry group is obtained. It is shown
that the microscopic entropy of the dual conformal field given by Cardy formula
exactly agrees with Bekenstein-Hawking entropy of extremal black hole. Then, by
rewriting the wave equation of massless scalar field with sufficient low energy
as the SL(2, R)SL(2, R) Casimir operator, we find the hidden
conformal symmetry of the non-extremal linear dilaton black hole, which implies
that the non-extremal rotating linear dilaton black hole is holographically
dual to a two dimensional conformal field theory with the non-zero left and
right temperatures. Furthermore, it is shown that the entropy of non-extremal
black hole can be reproduced by using Cardy formula.Comment: 15 pages, no figure, published versio
Holographic description of three dimensional Godel black hole
Three dimensional G\"{o}del black hole is a solution to
Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant. We
have studied the hidden conformal symmetry for massive scalar field without any
additional condition in the background of three dimensional non-extremal and
extremal G\"{o}del black holes. This conformal symmetry is uncovered by the
observation that the radial wave equations in both cases can all be rewritten
in the form of Casimir operators through introducing two sets of
conformal coordinates to write the generators. At last, we give the
holographic dual descriptions of Bekenstein-Hawking entropies of non-extremal
and extremal black holes from Cardy formula of conformal field theory.Comment: 7 pages, no figur
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