Nahm Transformation on the Lattice
By studying zero modes of the Dirac equation on the lattice, we explicitly construct the Nahm transform of some topologically non-trivial gauge field configurations.
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arXiv subjects
A. Gonzalez-Arroyo
Publications and source records attributed to A. Gonzalez-Arroyo.
Self-dual vortex-like configurations in SU(2) Yang-Mills Theory
We show that there are solutions of the SU(2) Yang-Mills classical equations of motion in R^4, which are self-dual and vortex-like(fluxons). The action density is concentrated along a thick two-dimensional wall (the world sheet of a straight infinite vortex line). The configurations are constructed from self-dual R^2 x T^2 configurations.
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Yang-Mills Fields on the 4-dimensional torus. Part I: Classical Theory
We review some of the most important results obtained over the years on the study of Yang-Mills fields on the four dimensional torus at the classical level.
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Yang-Mills classical solutions and fermionic zero modes from lattice calculations
We study a series of problems in classical Yang-Mills theories using lattice methods. We first investigate SU(N) self-dual configurations on the torus with twisted boundary conditions. We also study the zero modes of the Dirac equation in topological non-trivial background Yang-Mills fields.
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Confining Classical Configurations
We construct a family of smooth, almost self-dual, non-thermalized SU(2) gauge field configurations, and measure the average of the fundamental, adjoint and spin $\frac{3}{2}$ representation Wilson loops on them. We get area law in all three cases. We also study thermalised configurations at $β= 2.325$ after cooling. The ratio of string tension in the spin j representation over that in the fundamental, stays constant with cooling.
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Do classical configurations produce Confinement?
We show that certain classical SU(2) pure gauge configurations give rise to a non-zero string tension. We then investigate cooled configurations generated by Monte Carlo simulations on the lattice and find similar properties. We infer evidence in favour of a classical model of Confinement.
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Gauge invariant investigation of the nature of Confinement
We observe a strong correlation between the decrease in the number of action density peaks in SU(2) Yang-Mills configurations with cooling and that of the string tension. The nature and distribution of these peaks is investigated. The relationship with monopole currents after the abelian projection is also considered.
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Investigating Yang-Mills theory and Confinement as a function of the spatial volume
We study the volume dependence of electric flux energies for SU(2) gauge theory with twisted boundary conditions. The curves interpolate smoothly between the perturbative semiclassicalresults and the Confinement regime. On the basis of our results, we propose that the Confinement property might be caused by a class of non-dilute multi-instanton configurations.
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FERMIONIC ZERO MODES FOR DYONS AND CHIRAL SYMMETRY BREAKING IN QCD
Dyonic classical solutions of Yang-Mills theory are considered and the complete set of fermionic zero modes of these solutions are studied. Representing the QCD vacuum as a gas of dyons, one obtains chiral symmetry breaking due to zero modes similarly to the case of instantonic vacuum.
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Peeping into the SU(2) Gauge Vacuum
We study thermalised configurations of SU(2) gauge fields by cooling. An analysis of the effect of cooling is presented and global and statistical information is extracted.
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Numerical study of Yang-Mills classical solutions on the twisted torus
We use the lattice cooling method to investigate the structure of some gauge fixed SU(2) Yang-Mills classical solutions of the euclidean equations of motion which are defined in the 3-torus with symmetric twisted boundary conditions.
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