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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 $\nabla$ with skew symmetric torsion (see [8]). We study these manifolds under the additional condition that the $\nabla$ -Ricci tensor vanish. In particular we describe their geometry in case of a maximal number of $\nabla$ -parallel vector fields.

Dualités de champs et de cordes

Daniel Bennequin (2001/2002)

Séminaire Bourbaki

Dynamical symmetries in supersymmetric matrix models.

Bach, V., Hoppe, J., Lundholm, D. (2008)

Documenta Mathematica

Fixed Points and D-branes

Elaine Beltaos (2013)

Publications de l'Institut Mathématique

Fourier Mukai transforms and applications to string theory.

Björn Andreas, Daniel Hernández Ruipérez (2005)

RACSAM

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...

Free field construction of D-branes in rational models of CFT and Gepner models.

Parkhomenko, Sergei E. (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Fuchsian groups and uniformization of Hurwitz spaces.

S. M. Natanzon (1999)

Disertaciones Matemáticas del Seminario de Matemáticas Fundamentales

Geometric physics.

Vafa, Cumrun (1998)

Documenta Mathematica

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...

Instantons, topological strings, and enumerative geometry.

Szabo, Richard J. (2010)

Advances in Mathematical Physics

Integrable string models in terms of chiral invariants of $S U (n), S O (n), S P (n)$ groups.

Gershun, Victor D. (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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