Emergent N=2 superconformal symmetry at the multicritical point

Determine whether the multicritical intersection of the h_{c_2} and h_{c_3} critical branches supports an emergent N=2 superconformal symmetry, including the organization of its scaling operators into supermultiplets and realization of the full superconformal algebra, beyond the established coexistence of Ising and Luttinger-liquid sectors with effective central charge c_eff=3/2.

Background

The paper identifies the intersection of the h_{c_2} and h_{c_3} critical branches as a multicritical point with simultaneous gaplessness at k=0 and k=±π/3. Its low-energy theory consists of an Ising/Majorana sector with c_eff=1/2 and a Dirac/Luttinger-liquid sector with c_eff=1, giving a total effective central charge c_eff=3/2. Although this central charge matches that of the second N=2 superconformal minimal model, the paper emphasizes that central-charge matching and mode counting do not establish the full superconformal structure. Establishing such symmetry would require identifying the relevant scaling-operator organization and demonstrating the associated superalgebra.

References

Interestingly, this conformal decomposition coincides with the field content of the second $\mathcal{N}=2$ superconformal minimal model, whose central charge is also $c_{\rm eff}=3/2$. Nevertheless, the present analysis establishes only the decomposition of the low-energy conformal degrees of freedom and the corresponding effective central charge. Demonstrating an emergent $\mathcal{N}=2$ superconformal symmetry would require additional evidence beyond the present mode-counting analysis, such as the organization of scaling operators into supermultiplets or the realization of the full superconformal algebra.

Therefore, our continuum analysis provides a microscopic explanation for the observed $c_{\rm eff}=3/2$ criticality in terms of coexisting Ising and Luttinger-liquid critical sectors. The agreement between this low-energy mode counting and the independently extracted effective central charge strongly supports this conformal decomposition, while leaving open the interesting possibility that a richer superconformal structure may emerge in the low-energy limit.

— Fermi-Point Topology Determines Emergent Conformal Criticality in Extended Quantum Spin Chains  (2609.03708 - Abbasi et al., 3 Sep 2026) in Appendix, Section “Low-Energy Effective Field Theory at the Multicritical Intersection Point” (label: multicritical_cft)