Chiral Gauge Anomalies on Noncommutative R^4

We discuss the noncommutative counterparts of chiral gauge theories and compute the associated anomalies.Comment: 11 pages, plain tex. Further comments on the main result have been added. Version to appear in Phys. Lett.

Stable Solutions of the Double Compactified D=11 Supermembrane Dual

The hamiltonian formulation of the supersymmetric closed 2-brane dual to the double compactified D=11 closed supermembrane is presented. The formulation is in terms of two U(1) vector fields related by the area preserving constraint of the SUSY 2-brane. Stable solutions of the field equations, which are local minima of the hamiltonian, are found. In the semiclassical approximation around the stable solutions the action becomes the reduction of D=10 Super-Maxwell to the worldvolume. The solutions carry RR charges as a type of magnetic charges associated with the worldvolume vector field. The geometrical interpretation of the solution in terms of U(1) line bundles over the worldvolume is obtained.Comment: 14 pages, late

Discreteness of the spectrum of the compactified D=11 supermembrane with non-trivial winding

We analyze the Hamiltonian of the compactified D=11 supermembrane with non-trivial central charge in terms of the matrix model constructed recently by some of the authors. Our main result provides a rigorous proof that the quantum Hamiltonian of the supersymmetric model has compact resolvent and thus its spectrum consists of a discrete set of eigenvalues with finite multiplicity.Comment: 16 pages, final versio

On the E-polynomials of a family of character varieties

textWe compute the E-polynomials of a family of twisted character varieties M [superscript g] (Sl [subscript n]) by proving they have polynomial count, and applying a result of N. Katz on the counting functions. To compute the number of F [subscript q]-points of these varieties as a function of q, we used a formula of Frobenius. Our calculations made use of the character tables of Gl [subscript n](q) and Sl subscript n](q), previously computed by J. A. Green and G. Lehrer, and a result of Hanlon on the Möbius function of a subposet of set-partitions. The Euler Characteristics of the M [superscript g] (Sl [subscript n]) are calculated then with these polynomial.Mathematic

UV/IR mixing and the Goldstone theorem in noncommutative field theory

Noncommutative IR singularities and UV/IR mixing in relation with the Goldstone theorem for complex scalar field theory are investigated. The classical model has two coupling constants, $\lambda_1$ and $\lambda_2$, associated to the two noncommutative extensions $\phi^*\star\phi\star\phi^*\star\phi$ and $\phi^*\star\phi^*\star\phi\star\phi$ of the interaction term $|\phi|^4$ on commutative spacetime. It is shown that the symmetric phase is one-loop renormalizable for all $\lambda_1$ and $\lambda_2$ compatible with perturbation theory, whereas the broken phase is proved to exist at one loop only if $\lambda_2=0$, a condition required by the Ward identities for global U(1) invariance. Explicit expressions for the noncommutative IR singularities in the 1PI Green functions of both phases are given. They show that UV/IR duality does not hold for any of the phases and that the broken phase is free of quadratic noncommutative IR singularities. More remarkably, the pion selfenergy does not have noncommutative IR singularities at all, which proves essential to formulate the Goldstone theorem at one loop for all values of the spacetime noncommutativity parameter $\theta$.Comment: 30 pages, 7 eps figures. V2: references adde

The differential geometry behind Maxwell’s equations

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Joana Cirici[en] Modern physics relies heavily on differential geometry in order to establish the mathematical formulation of its conceptual framework. This tendency started with Maxwell’s equations in the XIX century and has since then only intensified. This work aims at establishing a more geometric approach to Maxwell’s equations using differential forms in order to generalize them to other manifolds than \mathbb {R}^3, an imperative for any physical theory ever since Einstein laid the foundations of Special and General Relativity. We will therefore show a modern approach to physics delving into differential geometry to define the objects that we will deal with in Maxwell’s equations which will give us deeper insight about the mathematical structure of these equations and their physical consequence

A measure of conductivity for lattice fermions at finite density

We study the linear response to an external electric field of a system of fermions in a lattice at zero temperature. This allows to measure numerically the Euclidean conductivity which turns out to be compatible with an analytical calculation for free fermions. The numerical method is generalizable to systems with dynamical interactions where no analytical approach is possible.Comment: version to be published in Physics Letters

On the Universality Class of Monopole Percolation in Scalar QED

We study the critical properties of the monopole-percolation transition in U(1) lattice gauge theory coupled to scalars at infinite ($\beta=0$) gauge coupling. We find strong scaling corrections in the critical exponents that must be considered by means of an infinite-volume extrapolation. After the extrapolation, our results are as precise as the obtained for the four dimensional site-percolation and, contrary to previously stated, fully compatible with them.Comment: 11 pages, 3 figure

SMA observations of the proto brown dwarf candidate SSTB213 J041757

Context. The previously identified source SSTB213 J041757 is a proto brown dwarf candidate in Taurus, which has two possible components A and B. It was found that component B is probably a class 0/I proto brown dwarf associated with an extended envelope. Aims. Studying molecular outflows from young brown dwarfs provides important insight into brown dwarf formation mechanisms, particularly brown dwarfs at the earliest stages such as class 0, I. We therefore conducted a search for molecular outflows from SSTB213 J041757. Methods. We observed SSTB213 J041757 with the Submillimeter Array to search for CO molecular outflow emission from the source. Results. Our CO maps do not show any outflow emission from the proto brown dwarf candidate. Conclusions. The non-detection implies that the molecular outflows from the source are weak; deeper observations are therefore needed to probe the outflows from the source.Comment: 7 pages, 4 figures, accepted for publication in A&