Asymptotically conical Calabi-Yau manifolds, I

This is the first part in a two-part series on complete Calabi-Yau manifolds asymptotic to Riemannian cones at infinity. We begin by proving general existence and uniqueness results. The uniqueness part relaxes the decay condition $O(r^{-n-\epsilon})$ needed in earlier work to $O(r^{-\epsilon})$, relying on some new ideas about harmonic functions. We then look at a few examples: (1) Crepant resolutions of cones. This includes a new class of Ricci-flat small resolutions associated with flag manifolds. (2) Affine deformations of cones. One focus here is the question of the precise rate of decay of the metric to its tangent cone. We prove that the optimal rate for the Stenzel metric on $T^*S^n$ is $-2\frac{n}{n-1}$.Comment: 27 pages, various corrections, final versio

Moduli and multi-field inflation

Moduli with flat or run-away classical potentials are generic in theories based on supersymmetry and extra dimensions. They mix between themselves and with matter fields in kinetic terms and in the nonperturbative superpotentials. As the result, interesting structure appears in the scalar potential which helps to stabilise and trap moduli and leads to multi-field inflation. The new and attractive feature of multi-inflationary setup are isocurvature perturbations which can modify in an interesting way the final spectrum of primordial fluctuations resulting from inflation.Comment: 8 pages, 5 figures, based on talks given at CTP Symposium on Supersymmetry at LHC (Cairo, March 11-14 2007) and String Phenomenology 2007 (Frascati, June 4-8 2007

A 3.55 keV line from DM→a→γ\text{DM}\rightarrow a \rightarrow \gamma: predictions for cool-core and non-cool-core clusters

We further study a scenario in which a 3.55 keV X-ray line arises from decay of dark matter to an axion-like particle (ALP), that subsequently converts to a photon in astrophysical magnetic fields. We perform numerical simulations of Gaussian random magnetic fields with radial scaling of the magnetic field magnitude with the electron density, for both cool-core `Perseus' and non-cool-core `Coma' electron density profiles. Using these, we quantitatively study the resulting signal strength and morphology for cool-core and non-cool-core clusters. Our study includes the effects of fields of view that cover only the central part of the cluster, the effects of offset pointings on the radial decline of signal strength and the effects of dividing clusters into annuli. We find good agreement with current data and make predictions for future analyses and observations.Comment: 14 pages, 6 figure

"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

The moduli problem at the perturbative level

Moduli fields generically produce strong dark matter -- radiation and baryon -- radiation isocurvature perturbations through their decay if they remain light during inflation. We show that existing upper bounds on the magnitude of such fluctuations can thus be translated into stringent constraints on the moduli parameter space m_\sigma (modulus mass) -- \sigma_{inf} (modulus vacuum expectation value at the end of inflation). These constraints are complementary to previously existing bounds so that the moduli problem becomes worse at the perturbative level. In particular, if the inflationary scale H_{inf}~10^{13} GeV, particle physics scenarios which predict high moduli masses m_\sigma > 10-100 TeV are plagued by the perturbative moduli problem, even though they evade big-bang nucleosynthesis constraints.Comment: 4 pages, 3 figures (revtex) -- v2: an important correction on the amplitude/transfer of isocurvature modes at the end of inflation, typos corrected, references added, basic result unchange