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We show that the geometric notion of duality behind $T$-duality, between two string theories on different manifolds $E, \hat{E}$ in the sense of \cite{BHM1}\cite{BHM2}, is precisely that of Lie bialgebroids due to Mackenzie and Xu \cite{MX}.
Externí odkaz:
http://arxiv.org/abs/2207.13733
Autor:
Cardona, Alexander
In this paper we study the relationship between the extended symmetries of exact Courant algebroids over a manifold $M$, defined by Bursztyn, Cavalcanti and Gualtieri, and the Poisson algebras of admissible functions associated to twisted Dirac struc
Externí odkaz:
http://arxiv.org/abs/1207.7126
Autor:
Cardona, Alexander
We define algebras of admissible functions associated to twisted Dirac structures, and we show that they are Poisson algebras. We study the standard cases associated to Dirac structures defined by graphs of non-degenerate 2-forms.
Comment: 9 pag
Comment: 9 pag
Externí odkaz:
http://arxiv.org/abs/1207.7123
Publikováno v:
Commun.Math.Phys.242:31-65,2003
zeta-regularized traces, resp. super-traces, are defined on a classical pseudo-differential operator A by: tr^Q(A):= f.p.tr(A Q^{-z})_{|_{z=0}}, resp. str^Q(A):= f.p.str(A Q^{-z})_{|_{z=0}}, where f.p. refers to the finite part and Q is an (invertibl
Externí odkaz:
http://arxiv.org/abs/math-ph/0207029
Autor:
Cardona, Alexander
From a path integral point of view (e.g. \cite{Q98}) physicists have shown how {\it duality} in antisymmetric quantum field theories on a closed space-time manifold $M$ relies in a fundamental way on Fourier Transformations of formal infinite-dimensi
Externí odkaz:
http://arxiv.org/abs/hep-th/0009200
Publikováno v:
Journal of Physics: Conference Series; Nov2023, Vol. 2667 Issue 1, p1-10, 10p
Autor:
Cardona, Alexander1,2 cardona@math.univ-bpclermont.fr, Ducourtioux, Catherine1 catherine.ducourtioux@math.univ-bpclermont.fr, Paycha, Sylvie1 sylvie.paycha@math.univ-bpclermont.fr
Publikováno v:
Communications in Mathematical Physics. Nov2003, Vol. 242 Issue 1/2, p31-65. 35p.