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جنبههای نظریههای میدان همنوع فوق متقارن در ابعاد مختلف
Aspects of Supersymmetric Conformal Field Theories in Various Dimensions
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 A,D,E singularities, particularly the novelties that arise when the fields are matrices. We focus on four-dimensional N = 1 variants of supersymmetric QCD, with U( Nc) or SU(Nc) gauge group, Nf fundamental flavors, and adjoint matter fields X and Y appearing in WA,D,E(X,Y) superpotentials. We explore these issues by considering various deformations of the WA,D,E superpotentials, and the resulting RG flows and IR theories. In Chapter 4, we examine the infrared fixed points of four-dimensional N = 1 supersymmetric SU(2) gauge theory coupled to an adjoint and two fundamental chiral multiplets. We focus on a particular RG flow that leads to the N = 2 Argyres-Douglas theory H0, and a further deformation to an N = 1 SCFT with low a 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 N = 1 quantum field theories by compactifying the 6d (2,0) theories on a Riemann surface with genus g and n punctures, where the normal bundle decomposes into a sum of two line bundles with possibly negative degrees p and q. 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 N = 2 supersymmetry, and derive terms that account for the local data at the punctures.
مبانی استنتاج و کاربرد آن در فیزیک بنیادی
The Foundations of Inference and Its Application to Fundamental Physics
This thesis concerns the foundations of inference—probability theory, entropic inference, information geometry, etc. — and its application to the Entropic Dynamics (ED) approach to Quantum Mechanics (QM).
The first half of this thesis, chapters 2–6, concern the development of the inference framework. We begin in chapter 2 by discussing deductive inference, which involves formal logic and it’s role in accessing the truth of propositions. We eventually discover that deductive inference is incomplete, in that it can’t address situations in which we have incomplete information. This necessitates a theory of inductive inference (probability theory), which is developed in chapter 3. Probability theory is derived as a framework for manipulating degrees of belief of propositions, in a way which is consistent with its deductive counterpart. In chapter 4 we review the construction of entropic inference as a means for updating our beliefs in the presence o new information. The entropy functional is designed through the process of eliminative induction by imposing a principle of minimal updating (PMU) and various constraints. Chapter 5 considers the design of another entropic functional, the total correlation and all its variants, for the purposes of ranking join distributions with respect to their correlations. Finally, in chapter 6, we discuss the application of a special case of the correlation functionals from chapter 5, the mutual information, to problems in experimental physics and machine learning.
The second half of this thesis, chapters 7–9, concerns the ED approach to QM. In particular, chapters 8 and 9 involve the inclusion of particles with spin 1/2 into the framework. These developments are the main contribution of this thesis to the body of work in the ED approach. The problem is defined as an application of inference to the dynamics of quantum particles which have definite yet unknown positions and follow continuous trajectories. Through the method of maximum entropy developed in chapter 4, we can determine the transition probability that these particles will move from one location to another. Geometric algebra (GA) is chosen as the preferred representation for the algebra of spin, which is then introduced through constraints in the maximum entropy method. Aquantum mechanics is subsequently developed by constructing an epistemic phase space of probabilities and constraints and imposing that the physically relevant flows in this space are those which preserve a particular metric and symplectic form. These flows lead to a linear Pauli equation for one and two particles with spin.