On the Moyal deformation of Nahm Equations in seven dimensions (2009)
Garcia-Compean, Hugo, Martinez-Merino, Aldo A.
We show how the reduced (anti-)self-dual Yang-Mills equations in seven dimensions described by the Nahm equations can be carried over to the Weyl-Wigner-Moyal formalism. In the process some new...
Link Invariants for Flows in Higher Dimensions (2009)
Garcia-Compean, Hugo, Santos-Silva, Roberto
Linking numbers in higher dimensions and their generalization including gauge fields are studied in the context of BF theories. The linking numbers associated to $n$-manifolds with smooth flows...
Deformation Quantization of Relativistic Particles in Electromagnetic Fields (2007)
Sanchez, Laura, Galaviz, Imelda, Garcia-Compean, Hugo
The Weyl-Wigner-Moyal formalism for Dirac second class constrained systems has been proposed recently as the deformation quantization of Dirac bracket. In this paper, after a brief review of this...
Noncommutative Effects in the Black Hole Evaporation in Two Dimensions (2006)
Garcia-Compean, Hugo, Soto-Campos, Carlos
We discuss some possible implications of a two-dimensional toy model for black hole evaporation in noncommutative field theory. While the noncommutativity we consider does not affect gravity, it can...
Matos, Tonatiuh, Luevano, Jose-Ruben, Garcia-Compean, Hugo
We start with a particular cosmological model derived from type IIB supergravity theory with fluxes, where usually the dilaton is interpreted as a Quintessence field. Instead of that, in this letter...
N=2 String Geometry and the Heavenly Equations (2004)
In this paper we survey some of the relations between Plebanski description of self-dual gravity through the heavenly equations and the physics (and mathematics) of N=2 Strings. In particular we...
Gravitational Anomalies in Noncommutative Field Theory (2004)
Estrada-Jimenez, Sendic, Garcia-Compean, Hugo, Soto-Campos, Carlos
Gravitational axial and chiral anomalies in a noncommutative space are examined through the explicit perturbative computation of one-loop diagrams in various dimensions. The analysis depend on how...
A Noncommutative Deformation of Topological Field Theory (2004)
Garcia-Compean, Hugo, Paniagua, Pablo
Cohomological Yang-Mills theory is formulated on a noncommutative differentiable four manifold through the $\theta$-deformation of its corresponding BRST algebra. The resulting noncommutative field...
Amador, Xavier, Caceres, Elena, Garcia-Compean, Hugo, Guijosa, Alberto
We examine the extension of the Klebanov-Witten gauge/gravity correspondence away from the low-energy conformal limit, to a duality involving the full, asymptotically Ricci-flat background describing...
Branes and Fluxes in Orientifolds and K-theory (2002)
Garcia-Compean, Hugo, Loaiza-Brito, Oscar
RR fields in string backgrounds including orientifold planes and branes on top of them are classified by K-theory. Following the idea introduced in hep-th/0103183, we also classify such fluxes by...
On the Berezin Description of Kahler Quotients (2002)
Carrillo-Ibarra, Iliana, Garcia-Compean, Hugo
We survey geometric quantization of finite dimensional affine Kahler manifolds. Its corresponding prequantization and the Berezin's deformation quantization formulation, as proposed by Cahen et al.,...
Remarks on Noncommutative Solitons (2001)
Garcia-Compean, Hugo, Moreno, Jorge
In the first part of this work we consider an unstable non-BPS Dp-\bar{Dp}-brane pair in Type II superstring theory. Turning on a background NS-NS B-field (constant and nonzero along two spatial...
Topics on Strings, Branes and Calabi-Yau Compactifications (2000)
Garcia-Compean, Hugo, Loaiza-Brito, Oscar
Basics of some topics on perturbative and non-perturbative string theory are reviewed. After a mathematical survey of the Standard Model of particle physics and GUTs, the bosonic string kinematics...
Lectures on Strings, D-branes and Gauge Theories (2000)
Garcia-Compean, Hugo, Loaiza-Brito, Oscar
In these lectures we review the basic ideas of perturbative and non-perturbative string theory. On the non-perturbative side we give an introduction to D-branes and string duality. The elementary...
D-branes on Group Manifolds and Deformation Quantization (1999)
Garcia-Compean, Hugo, Plebanski, Jerzy F.
Recently M. Kontsevich found a combinatorial formula defining a star-product of deformation quantization for any Poisson manifold. Kontsevich's formula has been reinterpreted physically as quantum...
D-branes in Orbifold Singularities and Equivariant K-Theory (1998)
The study of brane-antibrane configurations in string theory leads to the understanding of supersymmetric D$p$-branes as the bound states of higher dimensional branes. Configurations of pairs...
A Note on the Hitchin System in a Background B-field (1998)
The space of solutions to the Hitchin equations on the dual torus with punctures determines the Higgs branch of certain impurity theories. An alternative description of this Higgs branch is provided,...
On the Deformation Quantization Description of Matrix Compactifications (1998)
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...
The Geometry of Deformation Quantization and Self-Dual Gravity (1997)
Garcia-Compean, Hugo, Plebanski, Jerzy F., Przanowski, Maciej
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...
Garcia-Compean, Hugo, Plebanski, Jerzy F., Przanowski, Maciej
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...
On the Weyl-Wigner-Moyal Description of SU$(\infty)$ Nahm Equations (1996)
Garcia-Compean, Hugo, Plebanski, Jerzy F.
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...
On the Reduced SU(N) Gauge Theory in the Weyl-Wigner-Moyal Formalism (1996)
Garcia-Compean, Hugo, Plebanski, Jerzy F., Quiroz-Perez, Norma
Weyl-Wigner-Moyal formalism is used to describe the large-$N$ limit of reduced SU$(N)$ quenching gauge theory. Moyal deformation of Schild-Eguchi action is obtained.
Further Remarks on the Chiral Model Approach to Self-Dual Gravity (1995)
Garcia-Compean, Hugo, Plebanski, Jerzy F., Przanowski, Maciej
It is shown how some results on harmonic maps within the chiral model can be carried over to self-dual gravity. The WZW-like action for self-dual gravity is found.
A Hopf Algebra Structure in Self-dual Gravity (1994)
Garcia-Compean, Hugo, Morales, Laura E., Plebanski, Jerzy F.
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...