8,380 research outputs found
Path-dependent SDEs in Hilbert spaces
We study path-dependent SDEs in Hilbert spaces. By using methods based on
contractions in Banach spaces, we prove existence and uniqueness of mild
solutions, continuity of mild solutions with respect to perturbations of all
the data of the system, G\^ateaux differentiability of generic order n of mild
solutions with respect to the starting point, continuity of the G\^ateaux
derivatives with respect to all the data. The analysis is performed for generic
spaces of paths that do not necessarily coincide with the space of continuous
functions
Supergravity with Self-dual B fields and Instantons in Noncommutative Gauge Theory
We study Type IIB supergravity in the presence of (euclidean) D3 branes and
nonzero self-dual B-fields. We point out that the Einstein frame metric is
identical to the full geometry for D3 branes without B fields turned on.
Furthermore, in a decoupling limit in which the theory is conjectured to be
dual to noncommutative Yang-Mills theory, the entire Einstein metric remains
intact, and in particular, is asymptotically flat. We construct D-instanton
solutions in this geometry. We show that in the decoupling limit the
D-instanton action agrees with the action of the corresponding instanton in the
noncommutative Yang-Mills theory and is expressed in terms of the open string
coupling. Some other aspects of this correspondence, which have unusual
features because the underlying metric is asymptotically flat, are explored.Comment: 25 pages, harvma
Entropy of Anisotropic Universe and Fractional Branes
We obtain the entropy of a homogeneous anisotropic universe applicable, by
assumption, to the fractional branes in the universe in the model of Chowdhury
and Mathur. The entropy for the 3 or 4 charge fractional branes thus obtained
is not of the expected form E^{{3/2}} or E^2. One way the expected form is
realised is if p \to \rho for the transverse directions and if the compact
directions remain constant in size. These conditions are likely to be enforced
by brane decay and annihilation, and by the S, T, U dualities. T duality is
also likely to exclude high entropic cases, found in the examples, which arise
due to the compact space contracting to zero size. Then the 4 charge fractional
branes may indeed provide a detailed realisation of the maximum entropic
principle we proposed recently to determine the number (3 + 1) of large
spacetime dimensions.Comment: Version 2: 21 pages. More discussion and references added. To appear
in General Relativity and Gravitatio
- …