Comments on Non-invertible Symmetries in Argyres-Douglas Theories
Federico Carta, Simone Giacomelli, Noppadol Mekareeya, Alessandro Mininno
TL;DR
The paper investigates non-invertible symmetries in a broad class of 4d N=2 Argyres-Douglas theories built from diagonal gauging of D_p(SU(N)) flavors and 6d N=(1,0) theories on T^2. By combining 6d/F-theory constructions, mirror Calabi–Yau LG descriptions, and class S trinions, it identifies a concrete (A_2, D_4) example that exhibits non-invertible duality and triality defects reminiscent of N=4 SYM, and then extends these insights to infinite families organized by whether a=c or a≠c. The authors analyze higher-form symmetries, 1-form and 2-form defect data, SL(2,Z) dualities, and mixed anomalies to explain when non-invertible gauging and defects arise, including one-dimensional conformal manifolds parametrized by τ. Their findings reveal a robust parallel between certain AD theories and N=4 SYM in their non-invertible symmetry structures and open avenues to explore similar phenomena in other AD and N=1 theories. Overall, the work provides a unifying framework for non-invertible symmetries in AD theories and deepens the connection between higher-form symmetry, duality defects, and conformal manifold structure.
Abstract
We demonstrate the presence of non-invertible symmetries in an infinite family of superconformal Argyres-Douglas theories. This class of theories arises from diagonal gauging of the flavor symmetry of a collection of multiple copies of $D_p(\mathrm{SU}(N))$ theories. The same set of theories that we study can also be realized from 6d $\mathcal{N}=(1,0)$ compactification on a torus. The main example in this class is the $(A_2, D_4)$ theory. We show in detail that this specific theory bears the same structures of non-invertible duality and triality defects as those of $\mathcal{N}=4$ super Yang-Mills with gauge algebra $\mathfrak{su}(2)$. We extend this result to infinitely many other Argyres-Douglas theories in the same family, including those with central charges $a=c$ whose conformal manifold is one dimensional, and those with $a\neq c$ whose conformal manifold has dimension larger than one. Our result is supported by examining certain special cases that can be realized in terms of theories of class $\mathcal{S}$.