- Title Information
- Title
- Singularities of Scattering Amplitudes: Symbol Letters, Cluster Adjacency, and Plabic Graphs
- Type of Resource (primo)
- dissertations
- Name:
Personal
- Name Part
- Mago Trejo, Jorge Leonardo
- Role
- Role Term:
Text
- creator
- Name:
Personal
- Name Part
- Volovich, Anastasia
- Role
- Role Term:
Text
- Advisor
- Name:
Personal
- Name Part
- Jevicki, Antal
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Gates, Sylvester James
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Department of Physics
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2022
- Physical Description
- Extent
- , None p.
- digitalOrigin
- born digital
- Note:
thesis
- Thesis (Ph. D.)--Brown University, 2022
- Genre (aat)
- theses
- Abstract
- In this thesis, we present a study of the singularity
structure of scattering amplitudes in maximally supersymmetric
Yang-Mills (N=4 SYM). We first consider the cluster adjacency
properties of the singularities, and later we discuss a method to
generate symbol letters from plabic graphs.
We start our discussion by making use of the Sklyanin Poisson bracket
on Gr(4,n) to investigate pair-wise cluster adjacency of singularities
of rational Yangian invariants in N=4 SYM, and to establish that the
n-point one-loop NMHV ratio function satisfies Steinmann cluster
adjacency. We also present a series of conjectures about cluster
adjacency.
We continue our study of Yangian invariants in N=4 SYM by classifying
all positive n-particle N^kMHV Yangian invariants in the theory with
n=5k. We show that this problem is equivalent to that of enumerating
plane cactus graphs with k pentagons and use this to enumerate the
cyclic classes of these invariants. We provide an alternative (but
equivalent) classification by showing that a product of k
five-brackets with disjoint sets of indices is a positive Yangian
invariant if and only if the sets are all weakly separated.
Finally, we suggest an algorithm for computing symbol alphabets from
plabic graphs by solving matrix equations of the form C Z = 0 to
associate functions on Gr(m,n) to parameterizations of certain cells
of Gr(k,n) indexed by plabic graphs. For m=4 and n=8 we show that this
association precisely reproduces the 18 algebraic symbol letters of
the two-loop NMHV eight-particle amplitude from four plabic graphs. We
also show that it is possible to obtain all rational symbol letters by
solving matrix equations of the form C Z = 0 if one allows C to be an
arbitrary cluster parameterization of the top cell of Gr_+(n-4,n). We
finish our discussion by identifying sets of parameterizations of the
top cell of Gr_+(5,9) for which the solutions produce all of (and
only) the cluster variable letters of the two-loop nine-particle NMHV
amplitude, and identify plabic graphs from which all of its algebraic
letters originate.
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01063025")
- Topic
- Physics
- Subject
- Topic
- scattering amplitudes
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01012104")
- Topic
- Mathematical physics
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01763173")
- Topic
- Cluster algebras
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01139038")
- Topic
- Supersymmetry
- Subject
- Topic
- Yang-Mills Theory
- Language
- Language Term (ISO639-2B)
- English
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20220706