31,526 research outputs found
Thermodynamics of AdS Black Holes in Einstein-Scalar Gravity
We study the thermodynamics of -dimensional static asymptotically AdS
black holes in Einstein gravity coupled to a scalar field with a potential
admitting a stationary point with an AdS vacuum. Such black holes with
non-trivial scalar hair can exist provided that the mass-squared of the scalar
field is negative, and above the Breitenlohner-Freedman bound. We use the Wald
procedure to derive the first law of thermodynamics for these black holes,
showing how the scalar hair (or "charge") contributes non-trivially in the
expression. We show in general that a black hole mass can be deduced by
isolating an integrable contribution to the (non-integrable) variation of the
Hamiltonian arising in the Wald construction, and that this is consistent with
the mass calculated using the renormalised holographic stress tensor and also,
in those cases where it is defined, with the mass calculated using the
conformal method of Ashtekar, Magnon and Das. Similar arguments can also be
given for the smooth solitonic solutions in these theories. Neither the black
hole nor the soliton solutions can be constructed explicitly, and we carry out
a numerical analysis to demonstrate their existence and to provide approximate
checks on some of our thermodynamic results.Comment: 42 pages, 2 figures. Version published in JHEP, plus a "Note Added"
expanding on our definition of "mass" via the first la
Three-Loop Leading Singularities and BDS Ansatz for Five Particles
We use the leading singularity technique to determine the planar three-loop
five-particle amplitude in N=4 super Yang-Mills in terms of a simple basis of
integrals. We analytically compute the integral coefficients for both the
parity-even and the parity-odd parts of the amplitude. The parity-even part
involves only dual conformally invariant integrals. Using the method of
obstructions we numerically evaluate two previously unfixed coefficients which
appear in the three-loop BDS ansatz.Comment: 20 pages, 2 figures, v2: very minor change
The Finite Basis Problem for Kiselman Monoids
In an earlier paper, the second-named author has described the identities
holding in the so-called Catalan monoids. Here we extend this description to a
certain family of Hecke--Kiselman monoids including the Kiselman monoids
. As a consequence, we conclude that the identities of
are nonfinitely based for every and exhibit a finite
identity basis for the identities of each of the monoids and
.
In the third version a question left open in the initial submission has beed
answered.Comment: 16 pages, 1 table, 1 figur
Exact Solution of a Monomer-Dimer Problem: A Single Boundary Monomer on a Non-Bipartite Lattice
We solve the monomer-dimer problem on a non-bipartite lattice, the simple
quartic lattice with cylindrical boundary conditions, with a single monomer
residing on the boundary. Due to the non-bipartite nature of the lattice, the
well-known method of a Temperley bijection of solving single-monomer problems
cannot be used. In this paper we derive the solution by mapping the problem
onto one on close-packed dimers on a related lattice. Finite-size analysis of
the solution is carried out. We find from asymptotic expansions of the free
energy that the central charge in the logarithmic conformal field theory
assumes the value .Comment: 15 pages, 1 figure, submitted to Phy. Rev. E; v2: revised
Acknowledgment
QCD Glueball Masses from AdS-6 Black Hole Description
By using the generalized version of gauge/gravity correspondence, we study
the mass spectra of several typical QCD glueballs in the framework of
AdS black hole metric of Einstein gravity theory. The obtained glueball
mass spectra are numerically in agreement with those from the AdS
black hole metric of the 11-dimensional supergravity.Comment: 10 pages, references updated and minor change
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