Holographic Bilayer/Monolayer Phase Transitions

In the present work, we discuss the phase structure of bilayer and monolayer phases in the (2+1)-dimensional defect field theory whose gravity dual is obtained by embedding D5/anti-D5 probe flavour branes in the singular conifold. We study in detail the embedding equations and compare the free energies of the resulting configurations at non-zero temperature and external magnetic field perpendicular to the defects. Moreover, we analyse the meson spectrum and confirm the stability of the single bilayer solution.Comment: 24 pages, 8 figure

A Novel (2+1)-Dimensional Model of Chiral Symmetry Breaking

We propose a new model of flavour chiral symmetry breaking in a (2+1)-dimensional defect gauge theory of strongly coupled fermions by introducing probe D5/anti-D5-flavour branes on the conifold. After working out the flavour brane embeddings at zero temperature, we thoroughly investigate the spectra of small fluctuations on the world volume of the flavour branes (meson spectrum) and conclude that they are free of tachyons. Thus the proposed probe brane embedding is stable. Moreover, we introduce finite temperature and an external magnetic field and study the thermodynamics of the resulting configurations. Namely, we compute the free energies, entropies, heat capacities and magnetisations. The results are used to establish a detailed phase diagram of the model. We find that the effect of magnetic catalysis of chiral symmetry breaking is realised in our model and show that the meson-melting phase transition coincides with the chiral symmetry breaking phase transition. Furthermore, we show that the model is in a diamagnetic phase.Comment: 1+28 pages, 23 figures, PDFTeX, v2: comments and refs. added, version accepted for publication by JHE

Analysis of the pion-kaon sigma-term and related topics

We calculate the one-loop contributions to the difference \Delta_{\pi K} between the isoscalar on-shell pion-kaon scattering amplitude at the Cheng-Dashen point and the scalar form factor \Gamma_K (2M_\pi^2) in the framework of three flavor chiral perturbation theory. These corrections turn out to be small. This is further sharpened by treating the kaons as heavy fields (two flavor chiral perturbation theory). We also analyze the two-loop corrections to the kaon scalar form factor based on a dispersive technique. We find that these corrections are smaller than in the comparable case of the scalar form factor of the pion. This is related to the weaker final state interactions in the pion-kaon channel.Comment: 25 pp, 3 fig

Dual Systems of Sequents and Tableaux for Many-Valued Logics

The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value and the exclusion of the opposite truth value describe the same situation.