Supersymmetric V-systems

We construct ${\mathcal N}=4 \,$ $\, D(2,1;\alpha)$ superconformal quantum mechanical system for any configuration of vectors forming a V-system. In the case of a Coxeter root system the bosonic potential of the supersymmetric Hamiltonian is the corresponding generalised Calogero-Moser potential. We also construct supersymmetric generalised trigonometric Calogero-Moser-Sutherland Hamiltonians for some root systems including $BC_N$.Comment: 31 pages; minor change

Frobenius structures, Coxeter discriminants, and supersymmetric mechanics

This thesis contains two directions both related to Frobenius manifolds. In the first part we deal with the orbit space $M_W = V/W$ of a finite Coxeter group $W$ acting in its reflection representation $V$. The orbit space $M_W$ carries the structure of a Frobenius manifold and admits a pencil of flat metrics of which the Saito flat metric $η$, defined as the Lie derivative of the $W$-invariant form $g$ on $V$ is the key object. In the main result of the first part we find the determinant of Saito metric restricted on the Coxeter discriminant strata in $M_W$ . It is shown that this determinant in the flat coordinates of the form $g$ is proportional to a product of linear factors. We also find multiplicities of these factors in terms of Coxeter geometry of the stratum. In the second part we study $N = 4$ supersymmetric extensions of quantum mechanical systems of Calogero–Moser type. We show that for any $∨$-system, in particular, for any Coxeter root system, the corresponding Hamiltonian can be extended to the supersymmetric Hamiltonian with $D(2,1;α)$ symmetry. We also obtain $N = 4$ supersymmetric extensions of Calogero–Moser–Sutherland systems. Thus, we construct supersymmetric Hamiltonians for the root systems $BC_N$, $F_4$ and $G_2$

Law of refraction for generalised confocal lenslet arrays

We derive the law of generalised refraction for generalised confocal lenslet arrays, which are arrays of misaligned telescopes. We have implemented this law of refraction in TIM, a custom open-source ray tracer.Comment: 4 pages, 3 figure

Constraining modified gravity theories with scalar fields using black-hole images

We study a number of well-motivated theories of modified gravity with the common overarching theme that they predict the existence of compact objects such as black holes and wormholes endowed with scalar hair. We compute the shadow radius of the resulting compact objects and demonstrate that black hole images such as that of M87$^*$ or the more recent SgrA$^*$ by the Einstein Horizon Telescope (EHT) collaboration may provide a powerful way to constrain deviations of the metric functions from what is expected from general relativity (GR) solutions. We focus our attention on Einstein-scalar-Gauss-Bonnet (EsGB) theory with three well motivated couplings, including the dilatonic and $Z_2$ symmetric cases. We then analyze the shadow radius of black holes in the contest of the spontaneous scalarization scenario within EsGB theory with an additional coupling to the Ricci scalar (EsRGB). Finally, we turn our attention to spontaneous scalarization in the Einstein-Maxwell-Scalar (EMS) theory and demonstrate the impact of the parameters on the black hole shadow. Our results show that black hole imaging is an important tool for constraining black holes with scalar hair and for some part of the parameter space, black holes solutions with scalar hair may be marginally favoured compared to solutions of GR.Comment: 17 pages, 9 figures, 2 table

Five-dimensional Gravity and the Weak Gravity Conjecture

University of Minnesota M.S. thesis. May 2019. Major: Physics. Advisor: Tony Gherghetta. 1 computer file (PDF); vi, 41 pages.The beginning of this thesis provides a brief guide to the notation we are going to use. After that, we present the Randall-Sundrum model and we outline the way it solves the hierarchy problem. To analyze the solutions the Lagrangian is perturbed up to second order. We then examine the possibility for a massive graviton, in the context of the Randall-Sundrum models. In particular, we examine the existence of the scalar modes of the metric decomposition. We present the de-Sitter, brane-world solutions corresponding to a dS five-dimensional space. Moreover, we discuss the swampland and focus on the Weak Gravity conjecture as well as on the AdS instability conjecture which follows from the former. We give the motivation and arguments supporting the Weak Gravity conjecture, derived from black hole physics. Then, we review the application of the AdS instability conjecture on Standard Model compactifications, and we retrieve recent results that support Dirac neutrinos and the normal hierarchy of the neutrino masses. We proceed by applying the same conjecture to the five-dimensional brane-world models. For the purposes of the present thesis, we limit the analysis to relatively simple cases, involving only a small number of particles in the five-dimensional bulk. We examine the constraints set on the masses of the fermionic/bosonic degrees of freedom, as well as on the five-dimensional cosmological constant, in order to avoid AdS minima. Finally, we discuss the Scalar Weak Gravity Conjecture and a recent modification of it

New perspectives on scalar fields in strong gravity

Recent developments in the field of gravitational physics, including the emergence of gravitational wave astronomy, black hole images, and more accurate telescopes, have allowed us to probe the strong-field character of gravity in a novel and revolutionary manner. This accessibility related to strong gravity brings into the foreground discussions about potential modifications to General Relativity (GR) that are particularly relevant in high curvature regimes. The most straightforward way to generalize GR is to consider an additional degree of freedom, in the form of a scalar field. In this thesis, we study generalized scalar tensor theories that predict interesting strong-gravity phenomenology. First, we review scalar no-hair theorems and the conditions under which they can be evaded. Next, we study solutions of black holes with scalar hair and the way in which higher derivative terms alter their properties. We then move our discussion to the spontaneously scalarized solutions, which only deviate from GR in the strong-field regime. We propose a model consistent with compact object scalarization, that allows for a GR attractor at late times, without fine-tuning (EsRGB model). Then, we proceed to study properties of black holes and neutron stars in this theory, revealing the interesting phenomenology of the solutions. We also study the radial stability of black holes in EsRGB and perform a preliminary analysis of the hyperbolicity of the problem. Finally, we take a look at the shadows of black holes and wormholes in theories with scalar fields, in light of recent observations of black hole shadows