Moser, Rafael (2023). Emergent descriptions at large charge: A foray into the structure of conformal field theories and beyond. (Thesis). Universität Bern, Bern

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Abstract
Conformal Field Theories (CFT)s play a central role in the study of Quantum Field Theory (QFT). They represent the fixed point of the Wilsonian Renormalization Group (RG) flow and any QFT is in principle describable as a relevant deformation of the associated nearby Conformal Field Theory (CFT). This thesis aims to explore the structure of CFTs with global internal symmetries and beyond via the LargeCharge Expansion (LCE), a semiclassical expansion applicable for states with large global quantum numbers. In the first part of this thesis we study CFT and Spontaneous Symmetry Breaking (SSB). We discuss the symmetryconstraints imposed by conformal invariance on the quantum theory, introduce the concept of CFT data and the Operator–Product Expansion (OPE). Concerning SSB, we discuss the existence of Nambu–Goldstone (NG) modes, the general counting rule for the number of NG modes under the spontaneous breaking of global internal symmetries and a generalization of the Goldstone theorem at finite density. In the second part of this thesis we discuss the current stateoftheart understanding of the LCE and systematically study CFTs with a global O(2) symmetry in the context of the LCE. We present the LCE in the broader context of the different methods available for accessing CFT data. Particularly, we discuss its relation to largespin expansions in CFTs and the description of operators with both large spin and large charge. We discuss the emergence of effective condensedmatter descriptions, in particular superfluids, in correlators involving states with large global quantum numbers. Finally, we use the superfluid Effective Field Theory (EFT) description to systematically study two, three and fourpoint functions for CFTs with a global O(2) symmetry. Using the EFT approach we derive universal results for the spectrum of scaling dimensions and threepoint coefficients at large charge. In the last part of this thesis we study CFTs in the doublescaling limit of large charge and large N. We discuss the D = 3Wilson–Fisher (WF) fixed point at large N and derive the leading order asymptotics at large charge Q in the double scaling limit Q/N fixed, where scaling dimensions can be studied analytically in the limit Q/2N ≫1, where we recover the superfluid EFT structure, and Q/2N ≪1, where we recover the free meanfield limit. These limits can be connected by resurgent analysis. We also study the spectrum of fluctuations to confirm EFT predictions. Next, we use a fixedcharge approach to gain access to the leading order effective potential for the ϕ4 theory, which we then study for spacetime dimensions 2 <D < 6. In D = 3, we reproduce and extend old results originally found by resumming Feynman diagrams. In D = 5, under the assumption of unitarity the ϕ4model does not appear to be Ultra–Violet (UV) complete. Finally, we discuss the interacting fixed points of threedimensional fermionic CFTs in the doublescaling limit of large charge and large N. While the Gross–Neveu (GN)model exhibits a Fermisphere description at large charge, whose fate at finite N is yet to be determined, for the Nambu–Jona–Lasinio (NJL)type models we find a Bose–Einstein Condensate (BEC). The largecharge sector of these models is therefore captured by the superfluid EFT approach.
Item Type:  Thesis 

Dissertation Type:  Single 
Date of Defense:  17 October 2023 
Subjects:  500 Science > 530 Physics 
Institute / Center:  08 Faculty of Science > Institute of Theoretical Physics 
Depositing User:  Hammer Igor 
Date Deposited:  21 Nov 2023 09:32 
Last Modified:  27 Nov 2023 03:16 
URI:  https://boristheses.unibe.ch/id/eprint/4729 
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