A construction of integrated vertex operator in the pure spinor sigma-model in AdS(5) x S-5

Vertex operators in string theory me in two varieties: integrated and unintegrated. Understanding both types is important for the calculation of the string theory amplitudes. The relation between them is a descent procedure typically involving the b-ghost. In the pure spinor formalism vertex operators can be identified as cohomology classes of an infinite-dimensional Lie superalgebra formed by covariant derivatives. We show that in this language the construction of the integrated vertex from an unintegrated vertex is very straightforward, and amounts to the evaluation of the cocycle on the generalized Lax currents.

A simpler prescription for MHV graviton tree amplitudes in superstring theory

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Perturbative coherence in field theory

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Coupled Boltzmann calculation of mixed axion/neutralino cold dark matter production in the early universe

We calculate the relic abundance of mixed axion/neutralino cold dark matter which arises in R-parity conserving supersymmetric (SUSY) models wherein the strong CP problem is solved by the Peccei-Quinn (PQ) mechanism with a concommitant axion/saxion/axino supermultiplet. By numerically solving the coupled Boltzmann equations, we include the combined effects of 1. thermal axino production with cascade decays to a neutralino LSP, 2. thermal saxion production and production via coherent oscillations along with cascade decays and entropy injection, 3. thermal neutralino production and re-annihilation after both axino and saxion decays, 4. gravitino production and decay and 5. axion production both thermally and via oscillations. For SUSY models with too high a standard neutralino thermal abundance, we find the combined effect of SUSY PQ particles is not enough to lower the neutralino abundance down to its measured value, while at the same time respecting bounds on late-decaying neutral particles from BBN. However, models with a standard neutralino underabundance can now be allowed with either neutralino or axion domination of dark matter, and furthermore, these models can allow the PQ breaking scale f(a) to be pushed up into the 10(14) - 10(15) GeV range, which is where it is typically expected to be in string theory models.

Strong semiclassical gravity in the universe and the laboratory

Three published papers are resumed in this thesis. Different aspects of the semiclassical theory of gravity are discussed. In chapter 1 we find a new perturbative (yet analytical) solution to the unsolved problem of the metric junction between two Friedmann-Robertson-Walker using Israel's formalism. The case of an expanding radiation core inside an expanding or collapsing dust exterior is treated. This model can be useful in the "landscape" cosmology in string theory or for treating new gravastar configurations. In chapter 2 we investigate the possible use of the Kodama vector field as a substitute for the Killing vector field. In particular we find the response function of an Unruh detector following an (accelerated) Kodama trajectory. The detector has finite extension and backreaction is considered. In chapter 3 we study the possible creation of microscopic black holes at LHC in the brane world model. It is found that the black hole tidal charge has a fundamental role in preventing the formation of the horizon.

Quantum Correlations in Field Theory and Integrable Systems

In this thesis we will investigate some properties of one-dimensional quantum systems. From a theoretical point of view quantum models in one dimension are particularly interesting because they are strongly interacting, since particles cannot avoid each other in their motion, and you we can never ignore collisions. Yet, integrable models often generate new and non-trivial solutions, which could not be found perturbatively. In this dissertation we shall focus on two important aspects of integrable one- dimensional models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum quench. The first part of the thesis will be therefore devoted to the study of the entanglement entropy in one- dimensional integrable systems, with a special focus on the XYZ spin-1/2 chain, which, in addition to being integrable, is also an interacting model. We will derive its Renyi entropies in the thermodynamic limit and its behaviour in different phases and for different values of the mass-gap will be analysed. In the second part of the thesis we will instead study the dynamics of correlators after a quantum quench , which represent a powerful tool to measure how perturbations and signals propagate through a quantum chain. The emphasis will be on the Transverse Field Ising Chain and the O(3) non-linear sigma model, which will be both studied by means of a semi-classical approach. Moreover in the last chapter we will demonstrate a general result about the dynamics of correlation functions of local observables after a quantum quench in integrable systems. In particular we will show that if there are not long-range interactions in the final Hamiltonian, then the dynamics of the model (non equal- time correlations) is described by the same statistical ensemble that describes its statical properties (equal-time correlations).

Moduli stabilisation and soft supersymmetry breaking in string compactifications

In this thesis, we shall work in the framework of type IIB Calabi-Yau flux compactifications and present a detailed review of moduli stabilisation studying in particular the phenomenological implications of the LARGE-volume scenario (LVS). All the physical relevant quantities such as moduli masses and soft-terms, are computed and compared to the phenomenological constraints that today guide the research. The structure of this thesis is the following. The first chapter introduces the reader to the fundamental concepts that are essentially supersymmetry-breaking, supergravity and string moduli, which represent the basic framework of our discussion. In the second chapter we focus our attention on the subject of moduli stabilisation. Starting from the structure of the supergravity scalar potential, we point out the main features of moduli dynamics, we analyse the KKLT and LARGE-volume scenario and we compute moduli masses and couplings to photons which play an important role in the early-universe evolution since they are strictly related to the decay rate of moduli particles. The third chapter is then dedicated to the calculation of soft-terms, which arise dynamically from gravitational interactions when moduli acquire a non-zero vacuum expectation value (VeV). In the last chapter, finally, we summarize and discuss our results, underling their phenomenological aspects. Moreover, in the last section we analyse the implications of the outcomes for standard cosmology, with particular interest in the cosmological moduli problem.

Dynamics of settling charged particles in turbulence : theory and experiments

It has been proposed that inertial clustering may lead to an increased collision rate of water droplets in clouds. Atmospheric clouds and electrosprays contain electrically charged particles embedded in turbulent flows, often under the influence of an externally imposed, approximately uniform gravitational or electric force. In this thesis, we present the investigation of charged inertial particles embedded in turbulence. We have developed a theoretical description for the dynamics of such systems of charged, sedimenting particles in turbulence, allowing radial distribution functions to be predicted for both monodisperse and bidisperse particle size distributions. The governing parameters are the particle Stokes number (particle inertial time scale relative to turbulence dissipation time scale), the Coulomb-turbulence parameter (ratio of Coulomb ’terminalar speed to turbulence dissipation velocity scale), and the settling parameter (the ratio of the gravitational terminal speed to turbulence dissipation velocity scale). For the monodispersion particles, The peak in the radial distribution function is well predicted by the balance between the particle terminal velocity under Coulomb repulsion and a time-averaged ’drift’ velocity obtained from the nonuniform sampling of fluid strain and rotation due to finite particle inertia. The theory is compared to measured radial distribution functions for water particles in homogeneous, isotropic air turbulence. The radial distribution functions are obtained from particle positions measured in three dimensions using digital holography. The measurements support the general theoretical expression, consisting of a power law increase in particle clustering due to particle response to dissipative turbulent eddies, modulated by an exponential electrostatic interaction term. Both terms are modified as a result of the gravitational diffusion-like term, and the role of ’gravity’ is explored by imposing a macroscopic uniform electric field to create an enhanced, effective gravity. The relation between the radial distribution functions and inward mean radial relative velocity is established for charged particles.

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