NC FUZZY GAUGE FIELD · Simulating Chiral Gauge theory with Matrix Models : Non-commutative Geometry and Fuzzy Approximations
FP6 — Marie Curie Actions (Human Resources and Mobility)
- Duration
- 2006-08-01 → 2008-07-31
- EU contribution
- €148,558
- Participants
- 1
- Scheme
- IIF
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Results in brief
Final Activity Report Summary - NC FUZZY GAUGE FIELD (Simulating Chiral Gauge Theory with Matrix Models : Noncommutative Geometry and Fuzzy Approximations)
Field theory in a space-time with non-commuting coordinates is a promising approach to understand the physics at smallest, yet still not accessible, scales. The investigation of the properties of such theories and models is becoming a more and more exciting topic for field theoreticians working on models beyond the standard ones of elementary particles. Since non-perturbative methods are also required, Monte Carlo techniques, well-known in statistical physics, lattice gauge theories and matrix models, can be successfully applied. The aim of this project was to perform theoretical and numerical investigations of the phase structure of the two-dimensional non-commutative fuzzy Yang-Mills theory and of the non-commutative fuzzy Schwinger model. During the two-year period this plan became naturally extended to obtain emergent geometry from matrix models and simulate supersymmetry. The last point was the most exciting one, since it could lead to the full simulation of M-theory. The discussion of the non-cummutative Schwinger model might also be relevant for supersymmetry, since it involved the simulation of fermions on non-commutative spaces. It turned out to be additionally interesting from a quantum chromodynamics point of view.
Data: CORDIS, © European Union
Project objective
Non-commutative geometry was proposed earlier than renormalization as a possible way to eliminate ultraviolet divergences in quantum field theories. On the other hand quantum field theories on non-commutative spaces are generally unknown beyond the one-lo op approximation. A gauge-covariant, chiral-invariant regularization of gauge theories can be achieved by quantizing the underlying space-time manifold thereby replacing it by a non-commutative matrix model or a fuzzy manifold''. Indeed if the underlying space-time manifold can be treated as a phase space one can quantize it in the usual way with a parameter theta assuming the role of hbar. Naturally the emergent quantum space is fuzzy with non-commuting coordinates and a finite number of degrees of freedom and as a consequence it is ultraviolet finite. The continuum limit is the semi-classical theta goes to zero limit. These are essentially matrix models. The advantage of this regulator compared to ordinary lattice prescription is that discretization by quantization is remarkably successful in preserving symmetries and topological features and altogether avoiding the fermion-doubling problem. As it turns out fuzzy spaces can also be used to regularize infinite dimensional non-commutative spaces such as Moya l-Weyl spaces. The main focus of this proposal is the construction of a new non-perturbative method for chiral gauge theories based on the fuzzy tw-spheres and their Cartesian products.More precisely we will use Monte Carlo numerical simulations to:a) determine the phase structure of 2-dimensional non-commutative fuzzy Yang-Mills theory , andb) to solve the non-commutative fuzzy Schwinger model.This will provide a crucial step towards understanding chiral gauge theories on infinite dimensional non-commutative Moyal-Weyl spaces. But it will also lay the foundation for the study of ordinary QCD in two and four dimensions using fuzzy approximations."
Original text from CORDIS.
Participants
- Humboldt-Universität zu Berlin · BerlinCoordinatorGermany
Links
Data: CORDIS, © European Union