<p> In this thesis, we develop manifestly covariant methods for 4 dimensional, <i> N</i> = 1 superconformal field theories. First, we generalize the embedding formalism in conformal field theories (CFTs) to <i>N</i> = 1 superconformal field theories (SCFTs). As applications we construct manifestly superconformally covariant expressions for land 3-point correlation functions involving the supercurrent multiplet or the global symmetry current superfield. Next, we combine this superembedding formalism with the shadow formalism in CFTs into a new method for computing superconformal blocks appearing in 4-point functions of SCFTs. This new method, called the supershadow formalism, expresses a superconformal block as manifestly covariant integrations over a product of 3-point functions. The supershadow formalism is much more efficient computationally than the brute force methods used previously in the literature. We obtain the superconformal blocks appearing in the 4-point functions of general scalar operator and then specialize to the 4-point functions involving chiral and global symmetry current multiplets. The results in the chiral case can be further generalized to <i> N</i> = 2 SCFTs. Finally, we present a systematic algorithm to extract the correlation functions of conformal primary component operators from the superfield correlation functions. We implemented this algorithm in <i> Mathematica</i> and applied it to the superfield 2-point function between general operators, from which we obtain all the component 2-point functions and all possible shortening conditions for a <i>N</i> = 1 superconformal multiplet. We also discuss a few potential directions for future researches. </p>

<p> Large vacuum fluctuations of a quantum stress tensor can be described by the asymptotic behavior of its probability distribution. Here we focus on stress tensor operators which have been averaged with a sampling function in time. The Minkowski vacuum state is not an eigenstate of the time-averaged operator, but can be expanded in terms of its eigenstates. We calculate the probability distribution and the cumulative probability distribution for obtaining a given value in a measurement of the time-averaged operator taken in the vacuum state. In these calculations, we use the normal ordered square of the time derivative of a massless scalar field in Minkowski spacetime as an example of a stress tensor operator. We analyze the rate of decrease of the tail of the probability distribution for different temporal sampling functions, such as compactly supported functions and the Lorentzian function. We find that the tails decrease relatively slowly, as exponentials of fractional powers, in agreement with previous work using the moments of the distribution. Our results lead additional support to the conclusion that large vacuum stress tensor fluctuations are more probable than large thermal fluctuations, and may have observable effects.</p><p>

<p> Elastic lepton scattering off of a nucleon has proven to be an efficient tool to study the structure of the hadron. In particular, the spatial distributions of the nucleon's charge and magnetization can be accessed through measurements of its electric (<i>G_E</i>) and magnetic (<i>G_M</i>) form factors. These form factors can be extracted from unpolarized cross sections measurements by using the Rosenbluth separation technique. At the current level of accuracy, a determination of <i>G_E</i> and <i>G_M</i> from an analysis of elastic lepton-nucleon scattering data requires effects beyond the leading-order (Born) approximation to be taken into account. </p><p> In this work, I study higher-order QED corrections to elastic lepton-nucleon scattering. First of all, I perform a model-independent calculation of conventional charge-dependent contributions in unpolarized lepton-proton scattering without making use of ultra-relativistic approximations. Second, in a connection to the future MUSE experiment in Switzerland, I estimate helicity-flip meson exchanges that make a difference in a comparison of ultra-relativistic vs non-ultra-relativistic lepton-proton scattering. Finally, I present a model calculation of the target-normal single-spin asymmetry in elastic electron-nucleon scattering. Such an asymmetry gives us a direct tool to studies of the imaginary part of the two-photon exchange amplitude.</p><p>

<p> We are at the dawn of a data-driven era in astrophysics and cosmology. A large number of ongoing and forthcoming experiments combined with an increasingly open approach to data availability offer great potential in unlocking some of the deepest mysteries of the Universe. Among these is understanding the nature of dark matter (DM)&mdash;one of the major unsolved problems in particle physics. Characterizing DM through its astrophysical signatures will require a robust understanding of its distribution in the sky and the use of novel statistical methods. </p><p> The first part of this thesis describes the implementation of a novel statistical technique which leverages the &ldquo;clumpiness&rdquo; of photons originating from point sources (PSs) to derive the properties of PS populations hidden in astrophysical datasets. This is applied to data from the <i> Fermi</i> satellite at high latitudes (|<i>b</i>| &ge; 30&deg;) to characterize the contribution of PSs of extragalactic origin. We find that the majority of extragalactic gamma-ray emission can be ascribed to unresolved PSs having properties consistent with known sources such as active galactic nuclei. This leaves considerably less room for significant dark matter contribution. </p><p> The second part of this thesis poses the question: &ldquo;what is the best way to look for annihilating dark matter in extragalactic sources?&rdquo; and attempts to answer it by constructing a pipeline to robustly map out the distribution of dark matter outside the Milky Way using galaxy group catalogs. This framework is then applied to <i>Fermi</i> data and existing group catalogs to search for annihilating dark matter in extragalactic galaxies and clusters.</p><p>

<p> In this dissertation we study properties of superconformal field theories (SCFTs) that arise from a variety of constructions. We begin with an extended review of various techniques in supersymmetry that are relevant throughout the work. In Chapter 3, we discuss aspects of theories with superpotentials given by Arnold's <i>A,D,E</i> singularities, particularly the novelties that arise when the fields are matrices. We focus on four-dimensional <i> N</i> = 1 variants of supersymmetric QCD, with <i>U</i>(<i> N_c</i>) or <i>SU</i>(<i>N_c</i>) gauge group, <i>N_f</i> fundamental flavors, and adjoint matter fields <i>X</i> and <i>Y</i> appearing in <i> W_A,D,E</i>(<i>X,Y</i>) superpotentials. We explore these issues by considering various deformations of the <i>W_A,D,E</i> superpotentials, and the resulting RG flows and IR theories. In Chapter 4, we examine the infrared fixed points of four-dimensional <i> N</i> = 1 supersymmetric <i>SU</i>(2) gauge theory coupled to an adjoint and two fundamental chiral multiplets. We focus on a particular RG flow that leads to the <i>N</i> = 2 Argyres-Douglas theory <i> H</i>₀, and a further deformation to an <i>N</i> = 1 SCFT with low <i>a</i> central charge. Then for the latter half of the dissertation we turn our attention to 4d SCFTs that arise from compactifications of M5-branes. In Chapter 6, we field-theoretically construct 4d <i>N </i> = 1 quantum field theories by compactifying the 6d (2,0) theories on a Riemann surface with genus <i>g</i> and <i>n</i> punctures, where the normal bundle decomposes into a sum of two line bundles with possibly negative degrees <i>p</i> and <i>q</i>. In Chapter 7, we study the 't Hooft anomalies of the SCFTs that arise from these compactifications. In general there are two independent contributions to the anomalies: there is a bulk term obtained by integrating the anomaly polynomial of the world-volume theory on the M5-branes over the Riemann surface, and there is a set of contributions due to local data at the punctures. Using anomaly inflow in M-theory, we describe how this general structure arises for cases when the four-dimensional theories preserve <i>N</i> = 2 supersymmetry, and derive terms that account for the local data at the punctures.</p><p>