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Hugo Garcia-Compean

Publications and source records attributed to Hugo Garcia-Compean.

43 records · Page 3Linked to original sources
arXiv1998

On the Deformation Quantization Description of Matrix Compactifications

Matrix theory compactifications on tori have associated Yang-Mills theories on the dual tori with sixteen supercharges. A noncommutative description of these Yang-Mills theories based in deformation quantization theory is provided. We show that this framework allows a natural generalization of the `Moyal B-deformation' of the Yang-Mills theories to non-constant background B-fields on curved spaces. This generalization is described through Fedosov's geometry of deformation quantization.

hep-th↗
arXiv1997

The Geometry of Deformation Quantization and Self-Dual Gravity

A geometric formulation of the Moyal deformation for the Self-dual Yang-Mills theory and the Chiral Model approach to Self-dual gravity is given. We find in Fedosov's geometrical construction of deformation quantization the natural geometrical framework associated to the Moyal deformation of Self-dual gravity.

hep-th↗
arXiv1997

On the Weyl-Wigner-Moyal Description of SU$(\infty)$ Nahm Equations

We show how the reduced Self-dual Yang-Mills theory described by the Nahm equations can be carried over to the Weyl-Wigner-Moyal formalism employed recently in Self-dual gravity. Evidence of the existence of correspondence between BPS magnetic monopoles and space-time hyper-Kähler metrics is given.

hep-th↗
arXiv1997

Geometry Associated with Self-dual Yang-Mills and the Chiral Model Approaches to Self-dual Gravity

A geometric formulation of the Moyal deformation for the Self-dual Yang-Mills theory and the Chiral Model approach to Self-dual gravity is given. We find in Fedosov's geometrical construction of deformation quantization the natural geometrical framework associated to the Moyal deformation of the six-dimensional version of the second heavenly equation and the Park-Husain heavenly equation. The Wess-Zumino-Witten-like Lagrangian of Self-dual gravity is re-examined within this context.

hep-th↗
arXiv1996

A Hopf Algebra Structure in Self-dual Gravity

The two-dimensional non-linear sigma model approach to Self-dual Yang-Mills theory and to Self-dual gravity given by Q-Han Park is an example of the deep interplay between two and four dimensional physics. In particular, Husain's two-dimensional chiral model approach to Self-dual gravity is studied. We show that the infinite hierarchy of conservation laws associated to the Husain model carries implicitly a hidden infinite Hopf algebra structure.

hep-th↗