Calorons on the lattice - a new perspective

We discuss the manifestation of instanton and monopole solutions on a periodic lattice at finite temperature and their relation to the infinite volume analytic caloron solutions with asymptotic non-trivial Polyakov loops. As a tool we use improved cooling and twisted boundary conditions. Typically we find 2Q lumps for topological charge Q. These lumps are BPS monopoles.Comment: Latex. 16 pages, 9 figure

Volatility and dividend risk in perpetual American options

American options are financial instruments that can be exercised at any time before expiration. In this paper we study the problem of pricing this kind of derivatives within a framework in which some of the properties --volatility and dividend policy-- of the underlaying stock can change at a random instant of time, but in such a way that we can forecast their final values. Under this assumption we can model actual market conditions because some of the most relevant facts that may potentially affect a firm will entail sharp predictable effects. We will analyse the consequences of this potential risk on perpetual American derivatives, a topic connected with a wide class of recurrent problems in physics: holders of American options must look for the fair price and the optimal exercise strategy at once, a typical question of free absorbing boundaries. We present explicit solutions to the most common contract specifications and derive analytical expressions concerning the mean and higher moments of the exercise time.Comment: 21 pages, 5 figures, iopart, submitted for publication; deep revision, two new appendice

Natural PQ symmetry in the 3-3-1 model with a minimal scalar sector

In the framework of a 3-3-1 model with a minimal scalar sector we make a detailed study concerning the implementation of the PQ symmetry in order to solve the strong CP problem. For the original version of the model, with only two scalar triplets, we show that the entire Lagrangian is invariant under a PQ-like symmetry but no axion is produced since an U(1) subgroup remains unbroken. Although in this case the strong CP problem can still be solved, the solution is largely disfavored since three quark states are left massless to all orders in perturbation theory. The addition of a third scalar triplet removes the massless quark states but the resulting axion is visible. In order to become realistic the model must be extended to account for massive quarks and invisible axion. We show that the addition of a scalar singlet together with a Z_N discrete gauge symmetry can successfully accomplish these tasks and protect the axion field against quantum gravitational effects. To make sure that the protecting discrete gauge symmetry is anomaly free we use a discrete version of the Green-Schwarz mechanism.Comment: 18 pages, 1 figure, 3 table

Recent results on self-dual configurations on the torus

We review the recent progress on our understanding of self-dual SU(N) Yang-Mills configurations on the torus.Comment: Latex 3 pages, 1 figure. Contribution to the Lat99 Proceeding

Foreword

Granites and Related Rocks: a tribute to Guillermo Corretgé (Geologica Acta 15, 4, Special Issue). Foreword

How much dark matter is there inside early-type galaxies?

We study the luminous mass as a function of the dynamical mass inside the effective radius (r_e) of early-type galaxies (ETGs) to search for differences between these masses. We assume Newtonian dynamics and that any difference between these masses is due to the presence of dark matter. We use several samples of ETGs -ranging from 19 000 to 98 000 objects- from the ninth data release of the Sloan Digital Sky Survey. We perform Monte Carlo (MC) simulations of galaxy samples and compare them with real samples. The main results are: i) MC simulations show that the distribution of the dynamical vs. luminous mass depends on the mass range where the ETGs are distributed (geometric effect). This dependence is caused by selection effects and intrinsic properties of the ETGs. ii) The amount of dark matter inside r_e is approximately 7% +- 22%. iii) This amount of dark matter is lower than the minimum estimate (10%) found in the literature and four times lower than the average (30%) of literature estimates. However, if we consider the associated error, our estimate is of the order of the literature average.Comment: 24 pages, 12 figures. MNRAS accepte