Supersymmetric 4d gauge theories and Integrability
Bonini, Alfredo <1986>
Subject
FIS/02 Fisica teorica, modelli e metodi matematici
Description
Taking advantage of the integrable structures emergent in the theory, non-local observables
such as null polygonal Wilson loops are studied in 4d planar N = 4 Super Yang-Mills. Their
duality with the 4d gluon scattering amplitudes makes the analysis even more interesting.
The so-called Pentagon approach, an application of the Operator Product Expansion (OPE)
method to the null polygonal Wilsol loops, makes possible a non-perturbative evaluation of
these objects. They are recast as an OPE series over the 2d GKP flux-tube excitations, a
description reminescent of the QCD flux-tube stretching between quarks. The integrability
of the flux-tube allows us to evaluate the series, in principle, for any value of the coupling
constant. From this analysis, several results have been obtained. In the strong coupling
regime we reproduced the TBA-like equations expected from the minimal area problem
in string theory, finding agreement with the AdS/CFT prediction. In this respect, of
fundamental importance is the emergence of effective bound states between elementary
fermionic excitations. Along the way, we encountered some intriguing analogies between
these null polygonal Wilson loops and the Nekrasov instanton partition function Z for
N = 2 theories. Furthermore, a new non-perturbative enhancement of the classical string
argument has been confirmed, stemming from the dynamics of the string in the five sphere
S5 and described by the non-linear σ-model O(6). Some properties of a fundamental
building block of the OPE series, the SU(4) structure of the form factors of a specific twist
operator P, have been analysed. This SU(4) matrix part is given a representation in terms
of rational functions, organized in a Young tableaux pattern.
Bonini, Alfredo (2018) Supersymmetric 4d gauge theories and Integrability, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Fisica , 29 Ciclo. DOI 10.6092/unibo/amsdottorato/8707.