Science (Faculty of)
http://hdl.handle.net/10012/9936
2019-08-19T18:36:02ZOn Cohomological Algebras in Supersymmetric Quantum Field Theories
http://hdl.handle.net/10012/14891
On Cohomological Algebras in Supersymmetric Quantum Field Theories
Ishtiaque, Nafiz
In this thesis we compute certain supersymmetric subsectors of the algebra of observables in some QFTs and demonstrate an application of such computation in checking an instance of Holographic duality. Computing the algebra of observables beyond perturbative approximation in weakly coupled field theories is far from a tractable problem. In some special, yet interesting large classes of supersymmetric theories, supersymmetry can be used to extract exact nonperturbative information about certain subsets of observables. This is an old idea which we advance in this thesis by introducing new techniques of computations, computing certain observalbes for the first time, and reproducing earlier results about some other observables. We also propose a new toy model of holographic duality involving topological/holomorphic theories, demonstrating the power of exact computations in supersymmetric subsectors. To be more specific, the subject of this thesis includes the following:
1. Computing the algebra of chiral and twisted chiral operators in 2d N=(2,2) theories -- while these algebras were previously known, we demonstrate how they can be computed using relatively modern techniques of supersymmetric localization.
2. Computing the chiral rings of 4d N=2 SCFTs -- we compute this algebra for the first time. We use the same method of supersymmetric localization that we use in the 2d case.
3. Computing the algebra of operators on a defect in the topological 2d BF theory, along with its holographic dual. This is a new toy model of holographic duality set in the world of 6d topological string theory. We also argue that this setup is in fact a certain supersymmetric subsector of the holographic duality involving 4d N=4 SYM theory and its 10d supergravity dual -- both involving some defects.
In order to be able to discuss these different theories in different dimensions with different symmetries without sounding disparate and ad hoc, we employ the language of cohomological algebra. Since this is perhaps not a language most commonly used in the standard physics literature, we would like to emphasize that this is not a novel idea, it is merely a convenient thematic and linguistic umbrella that covers all the topics of this thesis. In the BV formulation of a QFT, the algebra of observables is presented as the cohomology algebra of a certain complex consisting of fields and anti-fields. In this language restriction to supersymmetric subsectors correspond to modifying the BV differential by the addition of the relevant supersymmetry generator. We simply refer to this modification as reduction to cohomology (with respect to the choice of supersymmetry).
2019-08-16T00:00:00ZComputational and Spectroscopic Investigations of Intermolecular Interactions in Clusters
http://hdl.handle.net/10012/14890
Computational and Spectroscopic Investigations of Intermolecular Interactions in Clusters
Carr, Patrick
In this thesis, the study of intermolecular interactions within cluster systems is presented. Covalently and non-covalently bound clusters possess oftentimes unique and unexpected properties which can be tuned by adjustment of size, composition, and geometry to target desired properties for use in nanotechnologies. Additionally, clusters present a computationally tractable model of bulk systems such as reactive sites on bulk heterogeneous catalysts. Infrared spectra have been collected of various clusters and theoretical computations have been conducted to interpret spectra and provide predictions for other properties to guide future works. Investigations of the forces binding cluster species together are conducted to provide insight into the fundamental underpinning of molecular properties with applications in the field of nanomaterial design.
A variety of clusters have been studied here. Computational studies of size-dependency in nitrous oxide reactions with rhodium sulphide clusters have been conducted. Barriers to competing N2O desorption and decomposition have been ascertained and compared with and without thermal corrections. Inclusion of the sulphur atom is found to alter which reaction pathway is preferred, as seen by comparison with analogous studies on pure rhodium clusters. Infrared multiple photon dissociation (IRMPD) spectroscopy is utilized to probe the additional clusters; a series of palladium coordination complexes and a series of clusters containing icosahedral [B12X12]2─ (X = H, halogen) cages complexed with a cationic transition metal atom, a cationic amine, or a neutral polar cyclohexane-based compound. This IRMPD technique successfully produced infrared spectra for these species in the gas phase and unique properties were observed for each cluster upon IR induced dissociation. Density functional theory calculations determined geometries, dissociation thresholds, and interpreted IR spectra. Additional theoretical tools quantified molecular orbital interactions and topographical parameters of the electron density.
2019-08-15T00:00:00ZComplexity in the AdS/CFT correspondence
http://hdl.handle.net/10012/14880
Complexity in the AdS/CFT correspondence
Marrochio, Hugo
The main goal of this thesis is to carefully analyze aspects of the gravitational quantities conjectured to be dual to quantum complexity in the AdS/CFT correspondence. The two most promising candidates for such holographic proposals are known as the complexity=volume (CV) and complexity=action (CA) proposals, which will be the main objects of study in this thesis. The latter involves the evaluation of the gravitational action in a region of spacetime known as the Wheeler-DeWitt patch, whose boundary includes null hypersurfaces and null codimension-two joints. There are several subtleties when evaluating the action in a region bounded by null surfaces, and a major part of the work presented here is based on a careful treatment of the boundary contributions to the gravitational action.
We start by evaluating the complexity of formation in holography, which is the additional complexity required to build the thermofield double state (TFD) in comparison to the complexity of building two copies of the vacuum. From the gravitational perspective, such quantity is interesting as it involves geometries with black holes. We find that for AdS-Schwarzschild black holes, both the CA and CV proposals yield a UV finite complexity of formation, and at large temperatures it becomes proportional to the thermodynamic entropy for boundary spacetime dimensions d>2.
In addition, we investigate dynamical properties of the holographic duals of complexity. We study the time evolution of the thermofield double state for AdS-Schwarzschild and AdS-Reissner-Nordstrom black holes. In the AdS/CFT correspondence, this time evolution corresponds to time slices that cover the interior region of the black hole. We find the striking result that the late time rate of change of complexity in the CA proposal is approached from above, which implies that the originally proposed connection to the conjectured Lloyd's bound on computation rate is violated. In contrast, the CV proposal growth rate is approached from below at late times for these geometries.
Next, we investigate the time evolution of holographic complexities when the bulk spacetime has non-trivial dynamics. We investigate both one-sided and two-sided Vaidya geometries, which are sourced by the collapse of an infinitesimally thin layer of null dust. In order to evaluate the complexity in the CA proposal, we construct a null fluid action that sources the Vaidya geometry. Our main result is that the inclusion of a surface counterterm that ensures reparametrization invariance to the null normals at the null boundaries of the Wheeler-DeWitt patch is necessary in order to reproduce desired properties of complexity, such as the switchback effect. In addition, we find that for one-sided black holes, the late time rate of change is approached from below in the CA approach, in contrast to what was found in two-sided geometries.
2019-08-14T00:00:00ZStable Isotope Ecology of Tropical Bats
http://hdl.handle.net/10012/14867
Stable Isotope Ecology of Tropical Bats
Oelbaum, Phillip
Stable isotopes have been used to characterize differences in animal diet and behaviour since experimental studies by DeNiro and Epstein (1979; 1981). Examining isotopic ratios enables researchers to track how animals interact with their environment as these ratios are derived from intake of nutrients and are fractionated into tissue at a calculable factor; in short, ‘you are what you eat’ (Tykot 2004). Studying bats, I use carbon (δ13C) and nitrogen (δ15N) stable isotopes to: (1) characterize community structure of a diverse fauna in Belize, (2) examine dietary differences between populations in a fragmented forest in Brazil, and (3) tested multiple tissues from the same individual to discern seasonal difference in diet in species from both the Neotropics and Paleotropics. In Belize, I found significant amounts of niche overlap between species which I predicted would belong to different guilds, and several cases of overlap which would suggest that species may compete for resources. In Brazil, I found that habitat composition (i.e., vegetation density) was more important than landscape metrics (sic fragment area, fragment nearest neighbour distance, etc.) in predicting the diets of frugivorous bats. I also found that multi-tissue stable isotope analysis is valuable in determining both individual variation in diet throughout the year and tracking seasonal changes as a result of resource availability or local-scale migration. Stable isotope analysis is a valuable tool in understanding the dietary ecology of animals.
2019-08-12T00:00:00Z