QCD Heat Kernel in Covariant Gauge

We report the calculation of the fourth coefficient in an expansion of the heat kernel of a non-minimal, non-abelian kinetic operator in an arbitrary background gauge in arbitrary space-time dimension. The fourth coefficient is shown to bring a nontrivial gauge dependence due to the contribution of the lowest order off-shell gauge invariant structure.Comment: 6 pages + title page, standart LaTe

Wide Localized Solitons in Systems with Time and Space-Modulated Nonlinearities

In this work we apply point canonical transformations to solve some classes of nonautonomous nonlinear Schr\"{o}dinger equation namely, those which possess specific cubic and quintic - time and space dependent - nonlinearities. In this way we generalize some procedures recently published which resort to an ansatz to the wavefunction and recover a time and space independent nonlinear equation which can be solved explicitly. The method applied here allow us to find wide localized (in space) soliton solutions to the nonautonomous nonlinear Schr\"{o}dinger equation, which were not presented before. We also generalize the external potential which traps the system and the nonlinearities terms.Comment: 19 pages, 5 figure

Pair Distribution Function of One-dimensional "Hard Sphere" Fermi and Bose Systems

The pair distributions of one-dimensional "hard sphere" fermion and boson systems are exactly evaluated by introducing gap variables.Comment: 4 page

Nonlinear magnetic response of the magnetized vacuum to applied electric field

We find first nonlinear correction to the field, produced by a static charge at rest in a background constant magnetic field. It is quadratic in the charge and purely magnetic. The third-rank polarization tensor - the nonlinear response function - is written within the local approximation of the effective action in an otherwise model- and approximation-independent way within any P-invariant nonlinear electrodynamics, QED included.Comment: 11 pages without figures or tables. Numerical coefficients and some signs in Version I corrected, three new references and two equations adde

The Fluxed MSSM

Recent developemnts in string compactifications in the presence of antisymmetric field backgrounds suggest a new simple and predictive structure for soft terms in the MSSM depending only on two parameters. They give rise to a positive definite scalar potential, a solution to the $\mu$-problem, flavor universality and absence of a SUSY-CP problem.Comment: 23 pages, no figures. Addendum on intersecting D7-branes included. Referencese added and minor change

Gravitational duality near de Sitter space

Gravitational instantons ''Lambda-instantons'' are defined here for any given value Lambda of the cosmological constant. A multiple of the Euler characteristic appears as an upper bound for the de Sitter action and as a lower bound for a family of quadratic actions. The de Sitter action itself is found to be equivalent to a simple and natural quadratic action. In this paper we also describe explicitly the reparameterization and duality invariances of gravity (in 4 dimensions) linearized about de Sitter space. A noncovariant doubling of the fields using the Hamiltonian formalism leads to first order time evolution with manifest duality symmetry. As a special case we recover the linear flat space result of Henneaux and Teitelboim by a smooth limiting process.Comment: 13 pages, no figure - v2 contains only small redactional changes (one reference added) and is essentially the published versio

Braided Cyclic Cocycles and Non-Associative Geometry

We use monoidal category methods to study the noncommutative geometry of nonassociative algebras obtained by a Drinfeld-type cochain twist. These are the so-called quasialgebras and include the octonions as braided-commutative but nonassociative coordinate rings, as well as quasialgebra versions \CC_{q}(G) of the standard q-deformation quantum groups. We introduce the notion of ribbon algebras in the category, which are algebras equipped with a suitable generalised automorphism $\sigma$, and obtain the required generalisation of cyclic cohomology. We show that this \emph{braided cyclic cocohomology} is invariant under a cochain twist. We also extend to our generalisation the relation between cyclic cohomology and differential calculus on the ribbon quasialgebra. The paper includes differential calculus and cyclic cocycles on the octonions as a finite nonassociative geometry, as well as the algebraic noncommutative torus as an associative example.Comment: 36 pages latex, 9 figure

Emergent non-commutative matter fields from Group Field Theory models of quantum spacetime

We offer a perspective on some recent results obtained in the context of the group field theory approach to quantum gravity, on top of reviewing them briefly. These concern a natural mechanism for the emergence of non-commutative field theories for matter directly from the GFT action, in both 3 and 4 dimensions and in both Riemannian and Lorentzian signatures. As such they represent an important step, we argue, in bridging the gap between a quantum, discrete picture of a pre-geometric spacetime and the effective continuum geometric physics of gravity and matter, using ideas and tools from field theory and condensed matter analog gravity models, applied directly at the GFT level.Comment: 13 pages, no figures; uses JPConf style; contribution to the proceedings of the D.I.C.E. 2008 worksho