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Title: Probing large-order perturbative expansions in lattice gauge theories with fermions
Author: Filaci, Gianluca
ISNI:       0000 0004 7969 4358
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2019
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Many perturbative expansions in quantum field theories are believed to be plagued by factorial divergences. This can be seen as a reflection of the fact that an all-order perturbative computation cannot give a complete description of the theory, as it misses all the nonperturbative features. In some cases the divergence is related to the existence of condensates, and being able to keep the asymptotic behaviour of the series under control is necessary to provide a sound definition of the condensates themselves. The goal of this work is to investigate the large-order behaviour of perturbative expansions in gauge theories. In order to achieve that, we employ Numerical Stochastic Perturbation Theory (NSPT), a numerical technique that allows for perturbative computations in quantum field theory. We present an implementation of NSPT that is able to yield results for high orders in the perturbative expansion of lattice gauge theories coupled to fermions. Performing calculations with fermions requires to overcome some challenges, due for example to the lack of chiral symmetry, or to the presence of doublers. Moreover, twisted boundary conditions (TBC), used to remove the gauge zero-momentum mode that spoils the convergence of the stochastic process, cannot accommodate easily fermions in all representations. In particular, we are forced to introduce a smell degree of freedom in order to include fermions in the fundamental representation with TBC. As a first application, we compute with NSPT the critical mass of two flavours of Wilson fermions up to order O(β-7) in a SU(3) gauge theory. We also implement, for the first time, staggered fermions in NSPT. The residual chiral symmetry of staggered fermions protects the theory from an additive mass renormalisation. We compute the perturbative expansion of the plaquette with two flavours of massless staggered fermions up to order O(β-35) in a SU(3) gauge theory, and investigate the renormalon behaviour of such series. We are able to subtract the power divergence in the Operator Product Expansion (OPE) for the plaquette and estimate the gluon condensate in massless QCD. Our results confirm that NSPT provides a viable way to probe systematically the asymptotic behaviour of perturbative series in QCD and, eventually, gauge theories with fermions in higher representations.
Supervisor: Del Debbio, Luigi ; Kennedy, Anthony Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: lattice ; nspt ; plaquette ; renormalon ; condensate ; critical mass ; quantum field theory