Investigating the large N limit of SU(N) Yang-Mills gauge theories on the lattice
Authors
Department
Mathematisch-Naturwissenschaftliche Fakultät
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Abstract
In dieser Arbeit praesentieren wir Resultate der topologischen Suszeptibilitaet “chi” und untersuchen die Faktorisierung der reinen SU(N) Yang-Mills Eichtheorie im 't Hooft'schen Grenzwert grosser N. Ein entscheidender Teil der Berechnung von chi in der Gittereichtheorie ist die Abschaetzung des topologischen Ladungsdichtekorrelators, die durch ein schlechtes Signal-Rausch- Verhaeltnis beeintraechtigt ist. Um dieses Problem abzuschwaechen, fuehren wir einen neuen, auf einem mehrstufigen Vorgehen beruhenden Algorithmus ein, um die Korrelationsfunktion von Observablen zu berechnen, die mit dem Yang-Mills Gradientenfluss geglaettet wurden. Angewandt auf unsere Observablen, erhalten wir Ergebnisse, deren Fehlerskalierung besser ist, als die von herkoemmlichen Monte-Carlo Simulationen.
Wir bestimmen die topologische Suszeptibilitaet in der reinen Yang-Mills Eichtheorie fuer Eichgruppen mit N = 4,5,6 und drei verschiedenen Gitterabstaenden. Um das Einfrieren der Topologie zu umgehen, wenden wir offene Randbedingungen an. Zusaetzlich wenden wir die korrekte Definition der topologischen Ladungsdichte durch den Gradientenfluss an. Unser Endresultat im des Grenzfalls von grossen N repraesentiert eine neue Qualitaet in der Verifikation der Witten-Veneziano Formel.
Schliesslich benutzen wir die Gitterformulierung, um die Erwartungswertfaktorisierung des Produkts eichinvarianter Operatoren im Grenzwert grosser N zu verifizieren. Wir arbeiten mit durch den Yang-Mills Grandientenfluss geglaetteten Wilsonschleifen und Simulationen bis zur Eichgruppe SU(8). Die Extrapolationen zu grossen N sind in Ueberstimmung mit der Faktorisierung sowohl fuer endlichen Gitterabstand als auch in Kontinnumslimes. Unsere Daten erlauben uns nicht nur die Verifizierung der Faktorisierung, sondern auch einen hochpraezisen Test des 1/N Skalierungsverhaltens. Hier konnten wir das quadratische Skalierungsverhalten in 1/N finden, welches von 't Hooft vorhergesagt wurde.
In this thesis we present results for the topological susceptibility “chi”, and investigate the property of factorization in the 't Hooft large N limit of SU(N) pure Yang-Mills gauge theory. A key component in the lattice gauge theory computation of chi 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 our observables, the results show an scaling of the error which is better than the one of standard Monte-Carlo simulations. 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. In addition, we employ the theoretically sound definition of the topological charge density through the gradient flow. Our final result in the limit N to infinity, 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). The large N extrapolations at finite lattice spacing and in the continuum are compatible with factorization. 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 quadratic series in 1/N as predicted originally by 't Hooft for the case of the pure Yang-Mills gauge theory.
In this thesis we present results for the topological susceptibility “chi”, and investigate the property of factorization in the 't Hooft large N limit of SU(N) pure Yang-Mills gauge theory. A key component in the lattice gauge theory computation of chi 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 our observables, the results show an scaling of the error which is better than the one of standard Monte-Carlo simulations. 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. In addition, we employ the theoretically sound definition of the topological charge density through the gradient flow. Our final result in the limit N to infinity, 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). The large N extrapolations at finite lattice spacing and in the continuum are compatible with factorization. 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 quadratic series in 1/N as predicted originally by 't Hooft for the case of the pure Yang-Mills gauge theory.
Description
Keywords
Gitter-QCD, Grenzwert grosser N, topologische Suszeptibilitaet, mehrstufiger Algorithmus, Faktorisierung, Lattice QCD, large N limit, topological susceptibility, multilevel algorithm, Wilson loops, factorization
Dewey Decimal Classification
530 Physik
Citation
García Vera, Miguel Francisco.(2017). Investigating the large N limit of SU(N) Yang-Mills gauge theories on the lattice. 10.18452/18123