Abstract
We study Schrödinger invariant field theories (nonrelativistic conformal field theories) in the large charge (particle number) sector. We do so by constructing the effective field theory (EFT) for a Goldstone boson of the associated U(1) symmetry in a harmonic potential. This EFT can be studied semi-classically in a large charge expansion. We calculate the dimensions of the lowest lying operators, as well as correlation functions of charged operators. We find universal behavior of three point function in large charge sector. We comment on potential applications to fermions at unitarity and critical anyon systems.
Highlights
We are still lacking many concrete calculational tools for these theories
We study Schrodinger invariant field theories in the large charge sector
We will be dealing with systems with non relativistic scale and conformal invariance i.e. systems invariant under Schrodinger symmetry
Summary
The Schrodinger algebra has been extensively explored in [8,9,10,11,12,13]. Here we take the readers through a quick tour of the essential features of Schrodinger algebra, that we are going to use through out this paper. It is natural to define a transformation from Galilean coordinates x = (t, x) to the “oscillator frame” y = (τ, y) where the time translation τ → τ + a is generated by Hω. This is given by ωτ = arctan ωt , x y= √. Where c is a numerical constant, ∆i is the dimension of the operator Oi, Qi is the charge of Oi. The symmetry algebra constrains the general form of a three-point function upto a arbitrary function of a cross-ratio vijk defined below: O1(x1)O2(x2)O3(x3) ≡ G(x1; x2; x3).
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