Fieldwork interviews: From phonebooks to fascists

Fieldwork interviews in Eastern Europe can make big demands of young researchers. Careful preparation, creativity and persistence are the key to success, argue Erin Marie Saltman and Philipp Köker

Applications of patching to quadratic forms and central simple algebras

This paper provides applications of patching to quadratic forms and central simple algebras over function fields of curves over henselian valued fields. In particular, we use a patching approach to reprove and generalize a recent result of Parimala and Suresh on the u-invariant of p-adic function fields, for p odd. The strategy relies on a local-global principle for homogeneous spaces for rational algebraic groups, combined with local computations.Comment: 48 pages; connectivity now required in the definition of rational group; beginning of Section 4 reorganized; other minor change

Quaternion algebras with the same subfields

G. Prasad and A. Rapinchuk asked if two quaternion division F -algebras that have the same subfields are necessarily isomorphic. The answer is known to be "no" for some very large fields. We prove that the answer is "yes" if F is an extension of a global field K so that F /K is unirational and has zero unramified Brauer group. We also prove a similar result for Pfister forms and give an application to tractable fields

Open Problems on Central Simple Algebras

We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.Comment: v2 has some small revisions to the text. Some items are re-numbered, compared to v

"Big" Divisor D3/D7 Swiss Cheese Phenomenology

We review progress made over the past couple of years in the field of Swiss Cheese Phenomenology involving a mobile space-time filling D3-brane and stack(s) of fluxed D7-branes wrapping the "big" (as opposed to the "small") divisor in (the orientifold of a) Swiss-Cheese Calabi-Yau. The topics reviewed include reconciliation of large volume cosmology and phenomenology, evaluation of soft supersymmetry breaking parameters, one-loop RG-flow equations' solutions for scalar masses, obtaining fermionic (possibly first two generations' quarks/leptons) mass scales in the O(MeV-GeV)-regime as well as (first two generations') neutrino masses (and their one-loop RG flow) of around an eV. The heavy sparticles and the light fermions indicate the possibility of "split SUSY" large volume scenario.Comment: Invited review for MPLA, 14 pages, LaTe

Systematics of String Loop Corrections in Type IIB Calabi-Yau Flux Compactifications

We study the behaviour of the string loop corrections to the N=1 4D supergravity Kaehler potential that occur in flux compactifications of IIB string theory on general Calabi-Yau three-folds. We give a low energy interpretation for the conjecture of Berg, Haack and Pajer for the form of the loop corrections to the Kaehler potential. We check the consistency of this interpretation in several examples. We show that for arbitrary Calabi-Yaus, the leading contribution of these corrections to the scalar potential is always vanishing, giving an "extended no-scale structure". This result holds as long as the corrections are homogeneous functions of degree -2 in the 2-cycle volumes. We use the Coleman-Weinberg potential to motivate this cancellation from the viewpoint of low-energy field theory. Finally we give a simple formula for the 1-loop correction to the scalar potential in terms of the tree-level Kaehler metric and the correction to the Kaehler potential. We illustrate our ideas with several examples. A companion paper will use these results in the study of Kaehler moduli stabilisation.Comment: 34 pages and 3 figures; typos corrected and references adde

Rationality of quotients by linear actions of affine groups

Let G be the (special) affine group, semidirect product of SL_n and C^n. In this paper we study the representation theory of G and in particular the question of rationality for V/G where V is a generically free G-representation. We show that the answer to this question is positive if the dimension of V is sufficiently large and V is indecomposable. We have a more precise theorem if V is a two-step extension 0 -> S -> V -> Q -> 0 with S, Q completely reducible.Comment: 18 pages; dedicated to Fabrizio Catanese on the occasion of his 60th birthda

Stable de Sitter vacua in N=2, D=5 supergravity

We find 5D gauged supergravity theories exhibiting stable de Sitter vacua. These are the first examples of stable de Sitter vacua in higher-dimensional (D>4) supergravity. Non-compact gaugings with tensor multiplets and R-symmetry gauging seem to be the essential ingredients in these models. They are however not sufficient to guarantee stable de Sitter vacua, as we show by investigating several other models. The qualitative behaviour of the potential also seems to depend crucially on the geometry of the scalar manifold.Comment: 26 pages, v2:typos corrected, published versio

Nonrenormalization of Flux Superpotentials in String Theory

Recent progress in understanding modulus stabilization in string theory relies on the existence of a non-renormalization theorem for the 4D compactifications of Type IIB supergravity which preserve N=1 supersymmetry. We provide a simple proof of this non-renormalization theorem for a broad class of Type IIB vacua using the known symmetries of these compactifications, thereby putting them on a similar footing as the better-known non-renormalization theorems of heterotic vacua without fluxes. The explicit dependence of the tree-level flux superpotential on the dilaton field makes the proof more subtle than in the absence of fluxes.Comment: 16 pages, no figures. Final version, to appear in JHEP. Arguments for validity of R-symmetry made more explicit. Minor extra comments and references adde