Following the flow for large N and large charge

Abstract

We discuss the O(2N) vector model in three dimensions. While this model flows to the Wilson-Fisher fixed point when fine tuned, working in a double-scaling limit of large N and large charge allows us to study the model away from the critical point and even to follow the RG flow from the UV to the IR. The crucial observation is that the effective potential -- at leading order in N but exact to all orders in perturbation theory -- is the Legendre transform of the grand potential at fixed charge. This allows us to write an effective action and the free energy for generic values of the coupling in a very simple fashion and without evaluating any Feynman diagrams.

arXiv comment20 pages, 4 figures

References in corpus (7)

• Quantum Field Theory in the Large N Limit: a review
• Compensating strong coupling with large charge
• Large charge at large N
• Feynman diagrams and the large charge expansion in $3-\epsilon$ dimensions
• An AdS/EFT correspondence at large charge
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Cited by in corpus (5)

• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Nonrelativistic CFTs at Large Charge: Casimir Energy and Logarithmic Enhancements
• Long Range, Large Charge, Large $N$
• Spinning correlators in large-charge CFTs
• The analytic structure of the fixed charge expansion