Kalogerakis, Ioannis (2023). A study of Bosonic and Fermionic Theories at Large Charge. (Thesis). Universität Bern, Bern

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Abstract

The aim of this thesis is to systematically and consistently study strongly coupled bosonic and fermionic conformal field theories using the large quantum number expansion. The idea behind it is to study sectors of conformal field theories that are characterised by large quantum numbers under global symmetries. In this limit, the conformal field theories, even if they initially were strongly coupled and interacting, can now be written in terms of an effective field theory that is weakly coupled. Some common effective field theories that appear in the literature are the bosonic conformal superfluid and the Fermi sphere, condensed matter systems characterised by a high particle density, making the study of such systems a cross-disciplinary matter. In the first part of the thesis, we start by reviewing concepts of quantum field theories, conformal field theories and of the large charge expansion that are essential for the subsequent chapters. The second part of the thesis is devoted to the analysis of the O(2) vector model in the large charge expansion, where we start by reviewing the classical treatment of the model, and we continue by examining its quantum behaviour. Following that, we compute three and four-point correlation functions of large charge primaries with insertions of the conserved current Jμ and/or the energy momentum tensor Tμν and in the final part of the chapter, we compute three and four-point correlation functions of spinning charged primary operators OQℓm with the insertion of light charged spinning primary operators Oq with q ≪ Q in the middle. In the third part of the thesis, we use the resurgence methodology to study the asymptotics of the O(N) vector model. We start by introducing the O(N) model at large charge and large-N and we study its asymptotics on the torus T2 and the sphere S2 using the resurgence framework. Then, we derive a worldline interpretation of the heat-kernel trace that replicates the previously computed results, and we deduce that its geometric nature is robust enough to allow us to extrapolate the results to finite N. Finally, we compare the resurgent results with the small-charge regime which is accessible at the doubling-scaling limit, while we theorise that our conjunctions hold for finite values of N, and we find the value of optimal truncation. In the last part of the thesis, we study various fermionic models with a four-fermion interaction at large charge and large-N. We start by presenting the models that we will examine in the subsequent sections and afterwards, we discuss the symmetry breaking pattern of the models, and we investigate the appearance of a condensate. We continue by studying the spectrum of the fluctuations for the models, and we compute the scaling dimension of the Gross-Neveu model at large charge and of the Nambu–Jona–Lasinio model both at large and small-charge regime.

Item Type:	Thesis
Dissertation Type:	Single
Date of Defense:	29 March 2023
Subjects:	500 Science > 530 Physics
Institute / Center:	08 Faculty of Science > Institute of Theoretical Physics
Depositing User:	Hammer Igor
Date Deposited:	09 May 2023 17:00
Last Modified:	29 Mar 2024 23:25
URI:	https://boristheses.unibe.ch/id/eprint/4278

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