New Aspects of Scattering Amplitudes, Higher-k Amplitudes, and Holographic Quark Gluon Plasmas

Abstract

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