Tensor product theorem for Hitchin pairs -An algebraic approach

We give an algebraic approach to the study of Hitchin pairs and prove the tensor product theorem for Higgs semistable Hitchin pairs over smooth projective curves defined over algebraically closed fields $k$ of characteristic $0$ and characteristic $p$, with $p$ satisfying some natural bounds. We also prove the corresponding theorem for polystable bundles.Comment: To appear in Annales de l'Institut Fourier, Volume 61 (2011

An analogue of the Narasimhan-Seshadri theorem and some applications

We prove an analogue in higher dimensions of the classical Narasimhan-Seshadri theorem for strongly stable vector bundles of degree 0 on a smooth projective variety $X$ with a fixed ample line bundle $\Theta$. As applications, over fields of characteristic zero, we give a new proof of the main theorem in a recent paper of Balaji and Koll\'ar and derive an effective version of this theorem; over uncountable fields of positive characteristics, if $G$ is a simple and simply connected algebraic group and the characteristic of the field is bigger than the Coxeter index of $G$, we prove the existence of strongly stable principal $G$ bundles on smooth projective surfaces whose holonomy group is the whole of $G$.Comment: 42 pages. Theorem 3 of this version is new. Typos have been corrected. To appear in Journal of Topolog

Single Field Baryogenesis

We propose a new variant of the Affleck-Dine baryogenesis mechanism in which a rolling scalar field couples directly to left- and right-handed neutrinos, generating a Dirac mass term through neutrino Yukawa interactions. In this setup, there are no explicitly CP violating couplings in the Lagrangian. The rolling scalar field is also taken to be uncharged under the $B - L$ quantum numbers. During the phase of rolling, scalar field decays generate a non-vanishing number density of left-handed neutrinos, which then induce a net baryon number density via electroweak sphaleron transitions.Comment: 4 pages, LaTe

Semistable principal bundles-II (positive characteristics)

Let H be a semisimple algebraic group and let X be a smooth projective curve defined over an algebraically closed field k. The principal aim of this paper is to prove the existence and projectivity of the moduli spaces of principal H-bundles on X for fields of characteristic p, p > Ψ, where Ψ is a certain representation-theoretic index associated to H. The projectivity is a consequence of the semistable reduction theorem for principal H-bundles