Titlebook: Strings, Branes and Dualities; Laurent Baulieu,Philippe Francesco,Paul Windey Book 1999 Springer Science+Business Media Dordrecht 1999 Gra

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adhesive

Seiberg-Witten Theory and S-Duality classical gauge groups .(.), .(.), .(.) [3, 4, 5, 7, 8, 9, 10] and provides a wealth of information on the strong coupling dynamics of gauge theories. There are excellent pedagogical reviews on Seiberg-Witten theory [11, 12, 13].

atopic-rhinitis

Ferritin

Notes on Matrix and Micro Stringstwo types of extended objects present in M-theory, respectively the membrane and the fivebrane. Upon compactification, these extended objects give rise to a rich spectrum of particles, with many quantized charges corresponding to the various possible wrapping numbers and internal Kaluza-Klein momenta.

conception

indubitable

Seiberg-Witten Theory and S-Dualitylls theories. Seiberg-Witten solution [1, 2] is the first exact solution in strongly-coupled quantum gauge theories in 4-dimensions. The solution was first constructed for .(2) Yang-Mills theory with 0 ≤ .. ≤ 4 hypermultiplets in vector representations. It was subsequently generalized to the case of

colloquial

Dualities in the Classical Supergravity Limits case of 4. + 2 dimensions seems to be related to classical Lie-Poisson actions leading to Quantum groups, indeed the latter were discovered in 2 dimensional theories. The duality group gets its name from some of its elements that are actually Hodge dualities like in Dirac’s famous analysis of the e

bromide

M-Theory from Its Superalgebrary [1]. Its existence, and uniqueness subject to standard assumptions, was established with the construction of D=11 supergravity [2]. The linearized theory can be deduced from an analysis of the standard D=11 super-Poincaré algebra and it will prove worthwhile to first present a variant of this ana

GRACE

Lectures on Heterotic-Type I Dualitye discovery of various duality symmetries; these, in particular, invert the coupling constant and exchange perturbative states with non-perturbative solitonic excitations. Since inversion of the coupling involves the Planck constant ., duality symmetries can be realized only at the quantum level. On

伸展

Connections between M-Theory and Superstringsils of any microscopic model, such as the matrix model. Certain of these properties must be inevitable consequences of eleven-dimensional supersymmetry. Others may depend on assuming the validity of the intricate web of duality inter-relationships between the perturbative string theories.