Large-charge effective field theory for nonzero Chern–Simons level

Determine which large-charge effective field theory describes three-dimensional QED₃ and scalar QED₃ with nonzero Chern–Simons level in the large-N,k limit with fixed k/N, and determine whether the associated large-charge q⁰ coefficient is universal.

Background

The paper extracts the q⁰ term in the large-charge expansion of monopole scaling dimensions. For fermionic QED₃ at nonzero Chern–Simons level, the fitted q⁰ term agrees numerically with the nonzero universal value associated with the superfluid effective field theory of parity-preserving U(1)-symmetric conformal field theories. For scalar QED₃ at nonzero level, the fitted q⁰ term instead vanishes, as in the large-charge effective theory of a free fermion.

Because a nonzero Chern–Simons term breaks parity, the appropriate effective description is not determined a priori. Establishing that description and its universality properties is also important for testing whether the large-N,k results can be extrapolated consistently to finite N and k, particularly in light of the duality between N=1, k=-3/2 QED₃ and N=1, k=2 scalar QED₃.

References

Since parity is broken for $k\neq0$, it is not a priori clear what large charge EFT should describe these theories, nor how universal the value should be.

— Monopoles, duality, and large charge in Chern-Simons QED$_3$  (2609.37795 - Chester et al., 29 Sep 2026) in Section 1, Introduction, paragraph beginning “For all the QED₃ and sQED₃ results with nonzero k”