Conserved current correlators of conformal field theories in 2+1 dimensions

TL;DR

This work investigates universal current correlators in 2+1D CP^{N-1} CFTs, relevant to deconfined quantum criticality in antiferromagnets. Using a large-$N$ expansion and a tensor-integral method ($\text{Tensoria}$), the authors compute the two-point functions of the SU($N$) flavor current and the topological current, as well as the gauge-field propagator, to next-to-leading order in $1/N$. They report explicit constants $C_J^{CP^{N-1}} = \frac{1}{16} - \frac{0.171}{N}$ and $C_A = \frac{16}{N}\left(1 + \frac{0.578}{N}\right)$, along with Goldstone-masslessness to $O(1/N)$ in the symmetry-broken phase and a correlation-length exponent $\nu = 1 - \frac{48}{N\pi^2}$. These results satisfy conformal constraints through cancellation of log divergences and provide quantitative benchmarks for numerical simulations and experimental probes of deconfined criticality in 2+1D spin systems.

Abstract

We compute current correlators of the CP^{N-1} field theory in 2+1 dimensions, both at the critical point and in the phase with spontaneously broken SU(N) symmetry. Universal constants are obtained to next-to-leading order in the 1/N expansion. Implications are noted for quantum critical points of antiferromagnets, and their vicinity.

Figures (10)

• Figure 1: Propagators and vertices of $CP^{N-1}$ model used in the $1/N$-expansion.
• Figure 2: Feynman rule for the $O(M)$ current vertex. Here the straight line is the propagator for real fields $\langle \phi_a (-p) \phi_b(p) \rangle = \delta_{ab}/p^2$.
• Figure 3: Diagrams for the current-current correlator in the $O(M)$ model. (0) is the only diagram at $M\rightarrow \infty$. (1) and (2) are of order $1/M$. Blue-dashed boxes are $O(M)$ current-vertices, where the current is defined in Eq. (\ref{['eq:def_on_current']}). Dashed line is the $\lambda$ propagator $\langle \lambda(-p)\lambda(p)\rangle^{O(M)}_{M\rightarrow \infty} = 16 p$ which, for real fields, comes with an additional factor of 2 compared to Eq. (\ref{['eq:1loop']}) podolsky1.
• Figure 4: Feynman rules for the $S\!U(N)$ flavor current vertices.
• Figure 5: Diagrams for the current-current correlator of the CP$^{N-1}$ model to order $1/N$.