1,700 research outputs found
On real projective connections, V.I. Smirnov's approach, and black hole type solutions of the Liouville equation
We consider real projective connections on Riemann surfaces and corresponding
solutions of the Liouville equation. It is shown that these solutions have
singularities of special type (of a black hole type) on a finite number of
simple analytical contours. The case of the Riemann sphere with four real
punctures, considered in V.I. Smirnov's thesis (Petrograd, 1918), is analyzed
in detail.Comment: 13 pages, final versio
On parametric Gevrey asymptotics for initial value problems with infinite order irregular singularity and linear fractional transforms
This paper is a continuation a previous work of the authors where parametric
Gevrey asymptotics for singularly perturbed nonlinear PDEs has been studied.
Here, the partial differential operators are combined with particular Moebius
transforms in the time variable. As a result, the leading term of the main
problem needs to be regularized by means of a singularly perturbed infinite
order formal irregular operator that allows us to construct a set of genuine
solutions in the form of a Laplace transform in time and inverse Fourier
transform in space. Furthermore, we obtain Gevrey asymptotic expansions for
these solutions of some order in the perturbation parameter
Comments on supergravity dual of pure N=1 Super Yang Mills theory with unbroken chiral symmetry
Maldacena and Nunez [hep-th/0008001] identified a gravity solution describing
pure N=1 Yang-Mills (YM) in the IR. Their (smooth) supergravity solution
exhibits confinement and the U(1)_R chiral symmetry breaking of the dual YM
theory, while the singular solution corresponds to the gauge theory phase with
unbroken U(1)_R chiral symmetry. In this paper we discuss supersymmetric type
IIB compactifications on resolved conifolds with torsion. We rederive singular
background of [hep-th/0008001] directly from the supersymmetry conditions. This
solution is the relevant starting point to study non-BPS backgrounds dual to
the high temperature phase of pure YM. We construct the simplest black hole
solution in this background. We argue that it has a regular Schwarzschild
horizon and provides a resolution of the IR singularity of the chirally
symmetric extremal solution as suggested in [hep-th/0011146].Comment: 34 pages, LaTeX, v2: references added, v3: section 2 reduced, minor
clarifications, to be published in PR
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