Description
- Abstract:
- In this thesis, we present novel perspectives on the explicit evaluation and analytic structure of correlation functions and scattering amplitudes in flat and expanding spacetimes. Specifically, we analyze wavefunction coefficients in a toy model theory of conformally coupled scalars within power-law FRW cosmologies, examine unitarity constraints on dual resonant string amplitudes, and further our understanding of the flat-space S-matrix using the framework of celestial amplitudes. First, we explore intriguing connections between positive geometries, on-shell methods, and bootstrap principles studied within the modern scattering amplitudes program to the Bunch-Davies wavefunction in toy models of FRW cosmologies. Leveraging recent advances in twisted cohomology and generalized unitarity from the Feynman integral literature, we develop an algorithm to construct a physical basis that simplifies the computation of differential equations for all tree and loop-level wavefunction contributions. Furthermore, we unravel the existence of hidden zeros in the cosmological wavefunction and demonstrate a universal factorization behavior associated with the kinematics of near-zero configurations for all tree and loop graphs. Second, we investigate the constraints of partial wave unitarity on dual resonant amplitudes from the viewpoint of the modern S-matrix bootstrap. Focusing on the Coon amplitude - a one-parameter deformation of the Veneziano amplitude with logarithmic Regge trajectories - we establish manifest positivity on certain Regge trajectories while identifying regions of unitarity violation in parameter space using tools from q-calculus and numerical methods. Finally, we make substantial advances in the study of celestial amplitudes by investigating the dual celestial conformal field theory (CCFT) and the role of light-ray operators, which are increasingly recognized as fundamental components of the CCFT spectrum. We present new computations of tree-level correlation functions for these operators, demonstrating their appearance in the operator product expansion of gluon primaries. Additionally, we examine the treatment of distributional low-point correlators by introducing a background that breaks bulk translation invariance, yielding correlators that more closely resemble those found in traditional two-dimensional CFTs.
- Notes:
- Thesis (Ph. D.)--Brown University, 2025
Citation
De, Shounak,
"Aspects of Cosmological, Celestial and String Amplitudes"
(2025).
Physics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://repository.library.brown.edu/studio/item/bdr:z29s5mjh/
