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

"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

Seeing the Invisible Axion in the Sparticle Spectrum

I describe how under favourable circumstances the invisible axion may manifest its existence at the LHC through the sparticle spectrum; in particular through a gluino \sim \ln (M_P/m_{3/2}) times heavier than other gauginos.Comment: 4 pages, REVTe

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

Astrophysical and Cosmological Implications of Large Volume String Compactifications

We study the spectrum, couplings and cosmological and astrophysical implications of the moduli fields for the class of Calabi-Yau IIB string compactifications for which moduli stabilisation leads to an exponentially large volume V ~ 10^{15} l_s^6 and an intermediate string scale m_s ~ 10^{11}GeV, with TeV-scale observable supersymmetry breaking. All K\"ahler moduli except for the overall volume are heavier than the susy breaking scale, with m ~ ln(M_P/m_{3/2}) m_{3/2} ~ (\ln(M_P/m_{3/2}))^2 m_{susy} ~ 500 TeV and, contrary to standard expectations, have matter couplings suppressed only by the string scale rather than the Planck scale. These decay to matter early in the history of the universe, with a reheat temperature T ~ 10^7 GeV, and are free from the cosmological moduli problem (CMP). The heavy moduli have a branching ratio to gravitino pairs of 10^{-30} and do not suffer from the gravitino overproduction problem. The overall volume modulus is a distinctive feature of these models and is an M_{planck}-coupled scalar of mass m ~ 1 MeV and subject to the CMP. A period of thermal inflation can help relax this problem. This field has a lifetime ~ 10^{24}s and can contribute to dark matter. It may be detected through its decays to 2\gamma or e^+e^-. If accessible the e^+e^- decay mode dominates, with Br(\chi \to 2 \gamma) suppressed by a factor (ln(M_P/m_{3/2}))^2. We consider the potential for detection of this field through different astrophysical sources and find that the observed gamma-ray background constrains \Omega_{\chi} <~ 10^{-4}. The decays of this field may generate the 511 keV emission line from the galactic centre observed by INTEGRAL/SPI.Comment: 31 pages, 2 figures; v2. refs adde

Spin Dynamics in Pyrochlore Heisenberg Antiferromagnets

We study the low temperature dynamics of the classical Heisenberg antiferromagnet with nearest neighbour interactions on the pyrochlore lattice. We present extensive results for the wavevector and frequency dependence of the dynamical structure factor, obtained from simulations of the precessional dynamics. We also construct a solvable stochastic model for dynamics with conserved magnetisation, which accurately reproduces most features of the precessional results. Spin correlations relax at a rate independent of wavevector and proportional to temperature.Comment: 4 pages, 4 figures, submitted to PR

On two problems in graph Ramsey theory

We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bounded-degree graphs and that of estimating the induced Ramsey number for a graph with a given number of vertices. The Ramsey number r(H) of a graph H is the least positive integer N such that every two-coloring of the edges of the complete graph $K_N$ contains a monochromatic copy of H. A famous result of Chv\'atal, R\"{o}dl, Szemer\'edi and Trotter states that there exists a constant c(\Delta) such that r(H) \leq c(\Delta) n for every graph H with n vertices and maximum degree \Delta. The important open question is to determine the constant c(\Delta). The best results, both due to Graham, R\"{o}dl and Ruci\'nski, state that there are constants c and c' such that 2^{c' \Delta} \leq c(\Delta) \leq 2^{c \Delta \log^2 \Delta}. We improve this upper bound, showing that there is a constant c for which c(\Delta) \leq 2^{c \Delta \log \Delta}. The induced Ramsey number r_{ind}(H) of a graph H is the least positive integer N for which there exists a graph G on N vertices such that every two-coloring of the edges of G contains an induced monochromatic copy of H. Erd\H{o}s conjectured the existence of a constant c such that, for any graph H on n vertices, r_{ind}(H) \leq 2^{c n}. We move a step closer to proving this conjecture, showing that r_{ind} (H) \leq 2^{c n \log n}. This improves upon an earlier result of Kohayakawa, Pr\"{o}mel and R\"{o}dl by a factor of \log n in the exponent.Comment: 18 page

F-theory, GUTs, and the Weak Scale

In this paper we study a deformation of gauge mediated supersymmetry breaking in a class of local F-theory GUT models where the scale of supersymmetry breaking determines the value of the mu term. Geometrically correlating these two scales constrains the soft SUSY breaking parameters of the MSSM. In this scenario, the hidden SUSY breaking sector involves an anomalous U(1) Peccei-Quinn symmetry which forbids bare mu and B mu terms. This sector typically breaks supersymmetry at the desired range of energy scales through a simple stringy hybrid of a Fayet and Polonyi model. A variant of the Giudice-Masiero mechanism generates the value mu ~ 10^2 - 10^3 GeV when the hidden sector scale of supersymmetry breaking is F^(1/2) ~ 10^(8.5) GeV. Further, the B mu problem is solved due to the mild hierarchy between the GUT scale and Planck scale. These models relate SUSY breaking with the QCD axion, and solve the strong CP problem through an axion with decay constant f_a ~ M_(GUT) * mu / L, where L ~ 10^5 GeV is the characteristic scale of gaugino mass unification in gauge mediated models, and the ratio \mu / L ~ M_(GUT)/M_(pl) ~ 10^(-3). We find f_a ~ 10^12 GeV, which is near the high end of the phenomenologically viable window. Here, the axino is the goldstino mode which is eaten by the gravitino. The gravitino is the LSP with a mass of about 10^1 - 10^2 MeV, and a bino-like neutralino is (typically) the NLSP with mass of about 10^2 - 10^3 GeV. Compatibility with electroweak symmetry breaking also determines the value of tan(beta) ~ 30 +/- 7.Comment: v3: 94 pages, 9 figures, clarification of Fayet-Polonyi model and instanton corrections to axion potentia