Gauge dependence and Dyson Schwinger equations II
Mathematics
Final Report Abstract
The structure of gauge theory and the intricacies of their dependence on renormalization schemes and covariant gauges were the topic of this work. This included abelian and non-abelian gauge theories as well as quantum gravity viewed as a covariant gauge theory. The wider context were renormalizable quantum field theories in two, four, and higher (even) dimensions of spacetime. Our work led to insights into the structure of such theories in particular with regards to: • The self-consistency of off-shell Slavnon–Taylor identities. Using Hopf-algebraic structures as well as diagrammatic techniques for determining the Slavnov-Taylor identities for QCD we constructed the relations for the off-shell triple and quartic gluon vertices. Analytic checks confirmed the result in loop computations. • Algebraic Interplay between Renormalization and Monodromy. The Hopf algebra structure of renormalization theory and the analytic structure of the scattering S-matrix cover two very different aspects of quantum field theory. It was shown for the first time that they are intimately related though the structure of cointeracting bialgebras. • Gracey’s work as Mercator Fellow on various aspects of the structure of quantum field theories. One of the major activities was the work in relation to ultraviolet completeness and emergent symmetries through the compilation of new explicit high order perturbative and large N results. For instance, the five loop renormalization of the Wess-Zumino model in the MS and momentum subtraction (MOM) schemes advanced the forty year old 4 loop work to a new order. This level of precision meant Bellon and Schaposnik’s Hopf algebra (itself based on Kreimer’s work) could be analysed. • Off-shell Diagrammatics for Quantum Gravity. It was shown how diagrammatic identities of Yang–Mills theory translate to diagrammatics for pure gravity. By analogy to Yang–Mills theory, cancelation identities were confirmed up to six external gravitions.
Publications
- Self-consistency of off-shell Slavnov-Taylor identities in QCD, Phys. Rev. D 100 (2019) no.8, 085001
J. A. Gracey, H. Kißler and D. Kreimer
(See online at https://doi.org/10.1103/PhysRevD.100.085001) - “Asymptotic freedom from the two-loop term of the β function in a cubic theory,” Phys. Rev. D 101 (2020) 125022
J.A. Gracey
(See online at https://doi.org/10.1103/PhysRevD.101.125022) - “Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics,” Phys. Rev. D 101 (2020) 094505
N. Zerf, R. Boyack, P. Marquard, J.A. Gracey and J. Maciejko
(See online at https://doi.org/10.1103/PhysRevD.101.094505) - Critical exponent η at O(1/N^3) in the chiral XY model using the large N conformal bootstrap,” Phys. Rev. D 103 (2021) 065018
J.A. Gracey
(See online at https://doi.org/10.1103/PhysRevD.103.065018) - Off-shell diagrammatics for quantum gravity, Phys. Lett. B 816 (2021), 136219
H. Kißler
(See online at https://doi.org/10.1016/j.physletb.2021.136219) - “Five-loop renormalization of φ3 theory with applications to the Lee-Yang edge singularity and percolation theory,”1ditor’s Suggestion. Phys. Rev. D 103 (2021) 116024
M. Borinsky, J.A. Gracey, M.V. Kompaniets and O. Schnetz
(See online at https://doi.org/10.1103/PhysRevD.103.116024) - “Two-loop corrections to the QCD propagators within the Curci-Ferrari model,” Phys. Rev. D 104 (2021) 094019
N. Barrios, J.A. Gracey, M. Peláez and and U. Reinosa
(See online at https://doi.org/10.1103/PhysRevD.104.094019) - “Five loop renormalization of the Wess-Zumino model,” Phys. Rev. D 105 (2022) 025004
J.A. Gracey
(See online at https://doi.org/10.1103/PhysRevD.105.025004)
