On First Order Formalism in String Theory

We consider the first order formalism in string theory, providing a new off-shell description of the nontrivial backgrounds around an "infinite metric". The OPE of the vertex operators, corresponding to the background fields in some "twistor representation", and conditions of conformal invariance results in the quadratic equation for the background fields, which appears to be equivalent to the Einstein equations with a Kalb-Ramond B-field and a dilaton. Using a new representation for the Einstein equations with B-field and dilaton we find a new class of solutions including the plane waves for metric (graviton) and the B-field. We discuss the properties of these background equations and main features of the BRST operator in this approach.Comment: LaTeX2e, 18 pages, Phys. Lett. B, in press, corrected typo

Strongly Polarized Optical Afterglows of Gamma-Ray Bursts

The optical afterglows of the gamma ray bursts can be strongly polarized, in principle up to tens of percents, if: (i) the afterglow is synchrotron radiation from an ultra-relativistic blast, (ii) the blast is beamed during the afterglow phase, i.e. the shock propagates within a narrow jet, (iii) we observe at the right time from the right viewing angle, (iv) magnetic fields parallel and perpendicular to the jet have different proper strengths.Comment: 5 pages, submitted to Ap

Fools for Christ\u27S Sake

1 Corinthians 3:16-4:13

Local-global principles for embedding of fields with involution into simple algebras with involution

In this paper we prove local-global principles for embedding of fields with involution into central simple algebras with involution over a global field. These should be of interest in study of classical groups over global fields. We deduce from our results that in a group of type D_n, n>4 even, two weakly commensurable Zariski-dense S-arithmetic subgroups are actually commensurable. A consequence of this result is that given an absolutely simple algebraic K-group G of type D_n, n>4 even, K a number field, any K-form G' of G having the same set of isomorphism classes of maximal K-tori as G, is necessarily K-isomorphic to G. These results lead to results about isolength and isospectral compact hyperbolic spaces of dimension 2n-1 with n even