Title Information
Title
Landau Singularities and Positive Geometries
Name: Personal
Name Part
Stanojevic, Stefan
Role
Role Term: Text
creator
Name: Personal
Name Part
Spradlin, Marcus
Role
Role Term: Text
Advisor
Name: Personal
Name Part
Jevicki, Antal
Role
Role Term: Text
Reader
Name: Personal
Name Part
Alexander, Stephon
Role
Role Term: Text
Reader
Name: Corporate
Name Part
Brown University. Department of Physics
Role
Role Term: Text
sponsor
Origin Information
Copyright Date
2020
Physical Description
Extent
9, 109 p.
digitalOrigin
born digital
Note: thesis
Thesis (Ph. D.)--Brown University, 2020
Genre (aat)
theses
Abstract
This work studies the analytical structure of scattering amplitudes in a class of toy models, from the perspective of novel geometrical structures underlying scattering amplitudes, and utilizing discrete mathematics. We find the set of all-loop n - point Landau singularities of the first type arising in any massless planar theory using graph operations inspired by the theory of electrical circuits. We also describe how to find the set of possible branch points of amplitudes at any fixed loop order and all particle multiplicities in planar N = 4 SYM theory, using the information contained in the boundaries of the amplituhedra. Along the way, we devise a method for classifying the boundaries of amplituhedra for any loop order L and helicity k. We determine the branch points of all two-loop NMHV amplitudes by solving the Landau equations for the relevant configurations and are led thereby to a conjecture for the symbol alphabets of all such amplitudes. The study of amplituhedra is then pushed beyond the realm of N = 4 SYM theory. We provide an efficient recursive formula to compute the canonical forms of arbitrary d-dimensional simple polytopes, and illustrate our method via an application to Stokes polytopes, related to scalar theory with quartic coupling.
Subject (fast) (authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01085105")
Topic
Quantum field theory
Subject (fast) (authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/00946584")
Topic
Graph theory
Subject (fast) (authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01070819")
Topic
Polytopes
Language
Language Term (ISO639-2B)
English
Record Information
Record Content Source (marcorg)
RPB
Record Creation Date (encoding="iso8601")
20200720
Access Condition: rights statement (href="http://rightsstatements.org/vocab/InC/1.0/")
In Copyright
Access Condition: restriction on access
Collection is open for research.
Type of Resource (primo)
dissertations