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Flavoured large N gauge theory on a compact space with an external magnetic field
Get PDFThe phase structure of flavoured N = 2 SYM on a three sphere in an external magnetic field is studied. The pairing effect of the magnetic field competes with the dissociating effect of the Casimir energy, leading to an interesting phase structure of confined and deconfined phases separated by a critical curve of a first order quantum phase transition. At vanishing magnetic field the phase transition is of a third order. For sufficiently strong magnetic field, the only stable phase is the confined phase and magnetic catalysis of chiral symmetry breaking is realized. The meson spectra of the theory exhibit Zeeman splitting and level crossing and feature a finite jump at the phase transition between the confined and deconfined phases. At strong magnetic field the ground state has a massless mode corresponding to the Goldstone boson associated with the spontaneously broken U(1) R-symmetry analogous to the η' meson in QCD
Scalar and Spinor Field Actions on Fuzzy S^4: fuzzy CP^3 as a S^2_F bundle over S^4_F
Get PDFWe present a manifestly Spin(5) invariant construction of squashed fuzzy CP^3 as a fuzzy S^2 bundle over fuzzy S^4. We develop the necessary projectors and exhibit the squashing in terms of the radii of the S^2 and S^4. Our analysis allows us give both scalar and spinor fuzzy action functionals whose low lying modes are truncated versions of those of a commutative S^4
Fr Séamas Ó Muraidheagh OP (c. 1703-1767): an Irish scribe and poet at Louvain
Get PDFLiterary associations and remains of an Irish Dominican associated with counties Clare and Derry, resident at Louvain and Paris in the first half of the eighteenth centur
Near commuting multi-matrix models
Get PDFWe investigate the radial extent of the eigenvalue distribution for Yang-Mills type matrix models. We show that, a three matrix Gaussian model with complex Myers coupling, to leading order in strong coupling is described by commuting matrices whose joint eigenvalue distribution is uniform and confined to a ball of radius R = (3π/2g)^1/3 then study, perturbatively, a 3-component model with a pure commutator action and find a radial extent broadly consistent with numerical simulations
Generation by Sections and k-Ampleness
Get PDFIn the article “Submanifold of abelian varieties”, A.J. Sommese proved that direct sum and tensor product of two vector bundles E and F over a smooth projective variety are k-ample if E and F are k-ample and are generated by global sections. Here we show that the latter condition is not needed
Feynman path integral approach to electron diffraction for one and two slits: analytical results
Get PDFIn this article we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulas, we exhibit various approximations of the electron distribution which facilitate the interpretation of the results. Our derivation is based on the Feynman path integral formula and this work could therefore also serve as an interesting pedagogical introduction to Feynman’s formulation of quantum mechanics for university students dealing with the foundations of quantum mechanics