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Central extensions and stochastic processes associated with the Lie algebra of the renormalized higher powers of white noise

Luigi Accardi, Andreas Boukas (2010)

Banach Center Publications

In the first part of the paper we discuss possible definitions of Fock representation of the *-Lie algebra of the Renormalized Higher Powers of White Noise (RHPWN). We propose one definition that avoids the no-go theorems and we show that the vacuum distribution of the analogue of the field operator for the n-th renormalized power of WN defines a continuous binomial process. In the second part of the paper we present without proof our recent results on the central extensions of RHPWN, its subalgebras...

Cocalibrated G 2 -manifolds with Ricci flat characteristic connection

Thomas Friedrich (2013)

Communications in Mathematics

Any 7-dimensional cocalibrated G 2 -manifold admits a unique connection with skew symmetric torsion (see [8]). We study these manifolds under the additional condition that the -Ricci tensor vanish. In particular we describe their geometry in case of a maximal number of -parallel vector fields.

Fourier Mukai transforms and applications to string theory.

Björn Andreas, Daniel Hernández Ruipérez (2005)


El artículo es una introducción a la transformación de Fourier-Mukai y sus aplicaciones a varios problemas de móduli, teoría de cuerdas y simetría "mirror". Se desarrollan los fundamentos necesarios para las transformaciones de Fourier-Mukai, entre ellos las categorías derivadas y los functores integrales. Se explican además sus versiones relativas, que se necesitan para precisar la noción de T-dualidad fibrada en variedades de Calabi-Yau elípticas de dimensión tres. Se consideran también varias...

Gravity, strings, modular and quasimodular forms

P. Marios Petropoulos, Pierre Vanhove (2012)

Annales mathématiques Blaise Pascal

Modular and quasimodular forms have played an important role in gravity and string theory. Eisenstein series have appeared systematically in the determination of spectrums and partition functions, in the description of non-perturbative effects, in higher-order corrections of scalar-field spaces, ...The latter often appear as gravitational instantons i.e. as special solutions of Einstein’s equations. In the present lecture notes we present a class of such solutions in four dimensions, obtained by...

Ground states of supersymmetric matrix models

Gian Michele Graf (1998/1999)

Séminaire Équations aux dérivées partielles

We consider supersymmetric matrix Hamiltonians. The existence of a zero-energy bound state, in particular for the d = 9 model, is of interest in M-theory. While we do not quite prove its existence, we show that the decay at infinity such a state would have is compatible with normalizability (and hence existence) in d = 9 . Moreover, it would be unique. Other values of d , where the situation is somewhat different, shall also be addressed. The analysis is based on a Born-Oppenheimer approximation. This seminar...

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