Dissertation/Thesis Abstract

Investigating the Large N Limit of SU(N) Yang-Mills Gauge Theories on the Lattice
by García Vera, Miguel Francisco, Ph.D., Humboldt Universitaet zu Berlin (Germany), 2017, 121; 27732932
Abstract (Summary)

In this thesis we present results for the topological susceptibility χYM, and investigate the property of factorization in the ’t Hooft large N limit of SU(N) pure Yang-Mills gauge theory. The study of χYM is motivated by the Witten-Veneziano relation, which explains the large mass of the η' meson when compared to the rest of light pseudoscalar mesons. A key component in the lattice gauge theory computation of χYM is the estimation of the topological charge density correlator, which is affected by a severe signal to noise problem. To alleviate this problem, we introduce a novel algorithm that uses a multilevel type approach to compute the correlation function of observables smoothed with the Yang-Mills gradient flow. When applied to the topological charge density and the Yang-Mills energy density, our results agree with a scaling of the error proportional to 1/n, instead of the 1/√n scaling from traditional Monte-Carlo simulations, where n is the number of independent measurements.

We compute the topological susceptibility in the pure Yang-Mills gauge theory for the gauge groups with N = 4, 5, 6 and three different lattice spacings. In order to deal with the freezing of topology, we use open boundary conditions, which allows us to go to finer lattice spacings when compared to previous works in the literature. In addition, we employ the theoretically sound definition of the topological charge density through the gradient flow. Our final result for the dimensionless quantity t20χYM = 7.03(13) × 10-4 in the limit N → 1, represents a new quality in the verification of the Witten-Veneziano formula.

Lastly, we use the lattice formulation to verify the factorization of the expectation value of the product of gauge invariant operators in the large N limit. We work with Wilson loops smoothed with the Yang-Mills gradient flow and simulations up to the gauge group SU(8). Loops at different N are matched using the scale t0, and thanks to the favourable renormalization properties of the flow, we study factorization in the continuum. Our extrapolations to 1/N → 0 are compatible with factorization, and, for our particular observables, we observe the coefficients of the 1/N expansion to be of O(1). Our data allow us not only to verify factorization, but also to test the 1/N scaling up to very high precision, where we find it to agree very well with a series in 1/N2 as predicted originally by ’t Hooft for the case of the pure Yang-Mills gauge theory.

Indexing (document details)
Advisor: Sommer , Rainer , Wolff , Ulrich , Lucini , Biagio
School: Humboldt Universitaet zu Berlin (Germany)
School Location: Germany
Source: DAI-C 81/7(E), Dissertation Abstracts International
Subjects: Theoretical physics
Publication Number: 27732932
ISBN: 9781392577288
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