Unitary vertex algebras and Wightman conformal field theories

We prove an equivalence between the following notions: (i) unitary Mobius vertex algebras, and (ii) Wightman conformal field theories on the circle (with finite-dimensional conformal weight spaces) satisfying an additional condition that we call uniformly bounded order. Reading this equivalence in one direction, we obtain new analytic and operator-theoretic information about vertex operators. In the other direction we characterize OPEs of Wightman fields and show they satisfy the axioms of a vertex algebra. As an application we establish new results linking unitary vertex operator algebras with conformal nets

Conformal Yangian and Tree Amplitudes in Scalar and Gauge Field Theories

Scattering amplitudes are intimately related to both experimental and theoretical ongoing efforts of testing the Standard Model of particle physics and our understanding of quantum field theory at large, through their computation to higher orders of precision and the study of their often unexpected and fascinating mathematical properties. It is within this latter field of study that our research lies. We investigate the infinite-dimensional Yangian extension of the conformal group $\text{SO}(2,n)$, where $n$ is the number of space-time dimensions, and its action on the tree-level scattering amplitudes of scalar $\lambda \, \phi^3$ theory and pure Yang-Mills theory. These two non-supersymmetric field theories are connected through the Cachazo-He-Yuan (CHY) scattering equations formalism. We first establish the consistency of the conformal Yangian algebra, $Y[\text{SO}(2,n)]$, for a differential operator representation of its generators in momentum-space. We prove that this representation satisfies the Serre relation, off-shell and in any number of space-time dimensions $n$ for scalar fields, but only on-shell and in $n=4$ space-time dimensions for spin-one gauge fields. We then show that the conformal Yangian generators annihilate individual off-shell scalar $\lambda \, \phi^3$ Feynman tree graphs in $n=6$ dimensions when the differential operator representation of $Y[\text{SO}(2,n)]$ is extended by graph-specific so-called evaluation parameter terms. We further show that the action of the conformal Yangian generators on the on-shell three-point and four-point pure Yang-Mills theory gluon tree amplitudes has a compact, albeit non-vanishing, form in $n=4$ dimensions. We conclude our investigation by exploring the action of the $Y[\text{SO}(2,n)]$ generators on the off-shell scattering polynomials of the CHY formalism relating the two theories.Doctor of Philosoph

Dualitites in quantum field theory from string theory

Quantum field theory (QFT), is a powerful framework to study diverse phenomena in physics. The range of topics includes the interactions of elementary particles, the continuum limit of condensed matter systems defined on a lattice, models of the expanding universe, as well as quantum gravity. Despite its enormous breadth of applications, it is still quite poorly understood. From a pragmatic point of view, a generic QFT is well understood in the per-turbative regime, where one has a small expansion parameter or coupling constant. That we have a satisfactory understanding of QFTs in the weakly coupled regime, is highlighted by the fact that we have a single formalism, namely feynman diagrams, that can be applied to any weakly coupled theory. Conversely, there is no universal framework to understand non-perturbative and strong coupling phenomena. Instead, we have a distinct set of tools, which apply to distinct sets of very special theories, such as those with supersymmetry or topolog-ical theories. From this perspective, to understand the strong coupling dynamics of a QFT, is to develop a unique formalism that can be applied to solve a generic strongly coupled QFT. The reader should be warned that this thesis will not achieve such an ambitious goal. How-ever, it is good to keep this general philosophy in mind, as a broader motivation for some of the work presented. We will provide, instead, a collection of data points for particular sec-tors of strongly coupled QFTs that are under analytic control. One can hope that some day, these data points can provide the foundations for a more systematic and universal approach. From a more formal viewpoint, quantum field theory, as of yet, has no rigorous mathemati-cal basis. This is particularly bothersome, given the deep interconnections between ideas in modern mathematics and those of QFT [1]. The goal of this thesis is to introduce its reader to a few notable examples, where the former issue can be overcome. The unifying theme of all these examples is their relation to brane dynamics in string theory [2]. We will make extensive use of the string theory embedding of the QFTs under consideration, in order to illuminate their strong coupling dynamics

Two aspects of gauge theories : higher-dimensional instantons on cones over Sasaki-Einstein spaces and Coulomb branches for 3-dimensional N = 4 gauge theories

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Generalized Symmetries in Supergravities and Superconformal Field Theories via String Theory

In this dissertation, we study the generalized symmetries in supergravities and superconformal field theories from the string theory perspective. Part one is devoted to the study of string universality in high spacetime dimensions. Answering this question requires us to combine the following two approaches. In the "top-down" approach, We focus on supergravity theories in 7, 8, and 9 dimensional spacetime with 16 supercharges. We emphasize two discrete aspects of these theories: generalized global symmetries and frozen singularities. We give an exhaustive classification of IIB supergravity theory in 8D, particularly emphasizing these two discrete aspects. In the "bottom-up" approach, we present a consistency condition of general 8D supergravity theories involving their higher-form symmetries use it to rule out many global structures of the gauge groups in 8D supergravity theories that do not admit string theory constructions. Part two studies the generalized global symmetries of geometrically-engineered quantum field theories via string theory. We examined branes wrapping on relative topological cycles that give heavy defects that are charged under generalized global symmetries, which can then be used to construct new lower-dimensional theories. By investigating the string theory origin of the topological operators, we provide a general construction of these topological operators in the context of geometric engineering as branes wrapped on the homological cycles in the asymptotic boundary of the internal geometry. We illustrate this proposal by determining non-invertible 2-form symmetries in 6D superconformal field theories. Furthermore, by wrapping type IIB 7-brane on the entire asymptotic boundary of the internal manifold, we explicitly give a unified string-theoretic construction of two different types of field-theoretic non-invertible duality defects.Comment: Ph.D. Dissertatio

Surface variability of climate-relevant trace gases (N2O, CO2, CO) in the tropical eastern South Pacific Ocean

Given the climatic relevance of marine-derived trace gases, the investigation of their distribution and emissions from key oceanic regions is a crucial need in our efforts to better understand potential responses of the ocean and the overlying atmosphere to environmental changes such as warming and deoxygenation. Low-oxygen waters connected to coastal upwelling systems and the associated oxygen minimum zones(OMZ) are well-recognized strong sources of several trace gases. Our main goal during the M135-M138 cruises was to assess the distribution of different gases which are relevant for the biogeochemical cycling of carbon and nitrogen in the OMZ off Peru, as well as the spatial and temporal variability of their sea-air fluxes