A hitchhiker's guide to quantum field theoretic aspects of N=4 SYM theory and its deformations

2017/01/03 by Jan Fokken, Fokken, Jan
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies

paper · pdf · doi:10.48550/arxiv.1701.00785

openalex publication_date 2017/01/03 · openalex created_date 2017/02/03 · openalex updated_date 2026/07/28

Abstract

In this thesis, we investigate properties of the one-parameter β- and the three-parameter γ_i-deformed descendents of N=4 SYM theory. We find additional multi-trace interactions that must be included in the deformed theories to prevent persistent divergences in observables. For the γ_i-deformation, we show in an explicit Feynman-diagrammatic calculation that these interactions have running coupling constants which spoil the conformal invariance of the quantised theory, even in the 't Hooft limit. We show that the running coupling constant in principle also affect the anomalous dimensions of composite operators by calculating the K=L loop leading order wrapping corrections to the operators tr(ϕ_i^L). For the β-deformation, we analyse the impact of multi-trace couplings on the one-loop spectrum and determine the complete one-loop dilatation operator of the conformal β-deformation in the 't Hooft limit. Based on the field-theoretic data from the β- and γ_i-deformation, we propose a test to determine whether supersymmetry and/or exact conformal invariance are necessary prerequisites of the quantum integrability found for N=4 SYM theory. We also generalise the Pólya-theoretic approach to the thermal one-loop partition function to be also applicable in the setting of the β- and γ_i-deformation. We find that the deconfinement phase-transition temperature in the deformed theories is the same as in the undeformed theory at one-loop level and we conjecture that it remains the same even non-perturbatively. Finally, we also provide many technical details concerning Feynman-diagram techniques and present the tool FokkenFeynPackage which implements these rules into Mathematica.

Citations

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• On the generalized ward identity
• The dilatation operator of conformal super-Yang–Mills theory
• Gauge-string duality for (non)supersymmetric deformations of N=4 super-Yang–Mills theory
• Observation of Gravitational Waves from a Binary Black Hole Merger

Related

• The Emergence of Supersymmetry in γ_i-deformed \cal N=4 super-Yang-Mills theory
• Exploring the ground state spectrum of gamma-deformed N=4 SYM
• Conformal invariance and finiteness theorems for non-planar beta-deformed N=4 SYM theory
• Form factors and the dilatation operator in N=4 super Yang-Mills theory and its deformations
• A note on perturbative aspects of Leigh-Strassler deformed N=4 SYM theory