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Thesis Format

Integrated Article


Doctor of Philosophy




Buchel, Alex


We present new results on different aspects of quantum field theory, which are divided into three main parts. In part I, we find and prove a new behavior of massless tree-level scattering amplitudes, including the biadjoint scalar theory, the U(N) non-linear sigma model, and the special Galileon, within specific subspaces of the kinematic space. We also derive new formulas for the double-ordered biadjoint scalar and $\phi^p$ amplitudes, which can be obtained as integrals over the positive tropical Grassmannian and under limiting procedures on the kinematic invariants. This reveals surprising connections with cubic amplitudes. We also present alternative versions of the formulas for $\phi^p$ amplitudes from combinatorial considerations in terms of non-crossing chord diagrams. In part II, we investigate the generalization of quantum field theory introduced by Cachazo, Early, Guevara and Mizera (CEGM) in 2019. We use soft limits to determine the number of singular solutions of the generalized scattering equations in certain cases and propose a general classification of all configurations that can support singular solutions. We also describe the generalized Feynman diagrams that compute CEGM amplitudes. These are planar arrays of Feynman diagrams satisfying certain compatibility conditions, and we propose combinatorial bootstrap methods to obtain them. Finally, in part III, we analyze different types of quark gluon plasmas in the presence of a background magnetic field using top-down holographic models. We explore conformal and nonconformal theories as consistent truncations of ${\cal N}=8$ gauged supergravity and identify a universal behavior in the ${\cal N}=2^*$ gauge theory.

Summary for Lay Audience

Quantum field theory provides an excellent mathematical framework for explaining natural phenomena. In recent years, new approaches have emerged, allowing for the discovery of novel properties and alternative perspectives on the framework. This thesis investigates various aspects of quantum field theory. Firstly, we focus on scattering amplitudes, the primary physical observables of the theory that determine the likelihood of a scattering process, and which are tested in particle accelerators. Our research identifies new properties of scattering amplitudes for massless particles, and introduces new formulas for their computation using the positive tropical Grassmannian space. Our study is motivated by the fact that obtaining new information on the behavior and structure of scattering amplitudes is important in order to understand what makes such functions special and relevant to the physical world.

In addition, we explore the recent CEGM generalization of quantum field theory. Its physical relevance is still mysterious, but we study it with the aim of developing new tools for learning more about nature. Specifically, we analyze solutions to the equations that govern the CEGM formula and characterize the objects that compute the corresponding generalized amplitudes from a more familiar quantum field theoretic perspective.

Finally, we use the AdS/CFT correspondence, a duality between a quantum field theory and a gravitational theory, to study aspects of the quark gluon plasma, a state of matter similar to that which prevailed in the early universe and that can be reproduced in experiments. We identify a universal behavior in a theory with intrinsic scale which partially resembles the theory of quantum chromodynamics. This enables us to gain a better understanding of the properties of more realistic quark gluon plasmas.

Overall, this thesis presents new insights into quantum field theory observables, as well as exploring aspects of the CEGM generalization and the potential of the AdS/CFT duality for enhancing our knowledge of the physical world.

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.