Abstract
We calculate the scaling dimensions of operators with large global charge and spin in 2+1 dimensional conformal field theories. By the state-operator correspondence, these operators correspond to superfluids with vortices and can be systematically studied using effective field theory. As the spin increases from zero to the unitarity bound, the superfluid state corresponding to the lowest dimension operator passes through three distinct regimes: (1) a single phonon, (2) two vortices, and (3) multiple vortices. We also calculate correlation functions with two such operators and the Noether current.
Highlights
By the state-operator correspondence, these operators correspond to superfluids with vortices and can be systematically studied using effective field theory
As the spin increases from zero to the unitarity bound, the superfluid state corresponding to the lowest dimension operator passes through three distinct regimes: (i) a single phonon, (ii) two vortices, and (iii) multiple vortices
Perhaps a way to phrase the main difference between high energy physics and condensed matter physics is that high energy physics mostly occurs in the vacuum while condensed matter physics occurs at finite density
Summary
Perhaps a way to phrase the main difference between high energy physics and condensed matter physics is that high energy physics mostly occurs in the vacuum while condensed matter physics occurs at finite density. In a conformal field theory (CFT), this particular difference disappears: The state-operator correspondence maps finite density states to local operators and maps finite density correlators to vacuum correlators. This idea was applied using superfluids [1–9]. Superfluids are described by an effective field theory (EFT), allowing the computation of correlators in a systematic perturbative expansion [10] This EFT was used to study the CFT operator spectrum at large global charge [1–9]. A superfluid EFT that incorporates vortices was recently constructed [26] We will use this EFT to study operators that have large spin as well as large charge
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