Abstract
We study the two-dimensional chiral algebra associated with the simplest Argyres-Douglas type theory with an exactly marginal coupling, i.e., the (A3, A3) theory. Near a cusp in the space of the exactly marginal deformations (i.e., the conformal manifold), the theory is well-described by the SU(2) gauge theory coupled to isolated Argyres-Douglas theories and a fundamental hypermultiplet. In this sense, the (A3, A3) theory is an Argyres-Douglas version of the mathcal{N} = 2 SU(2) conformal QCD. By studying its Higgs branch and Schur index, we identify the minimal possible set of chiral algebra generators for the (A3, A3) theory, and show that there is a unique set of closed OPEs among these generators. The resulting OPEs are consistent with the Schur index, Higgs branch chiral ring relations, and the BRST cohomology conjecture. We then show that the automorphism group of the chiral algebra we constructed contains a discrete group G with an S3 subgroup and a homomorphism G → S4 × Z2. This result is consistent with the S-duality of the (A3, A3) theory.
Highlights
Constructed by wrapping M5-branes on a Riemann surface [10,11,12] as well as by considering type II string theory on a Calabi-Yau singularity [13, 14]
We study the two-dimensional chiral algebra associated with the simplest Argyres-Douglas type theory with an exactly marginal coupling, i.e., the (A3, A3) theory
By studying its Higgs branch and Schur index, we identify the minimal possible set of chiral algebra generators for the (A3, A3) theory, and show that there is a unique set of closed OPEs among these generators
Summary
As shown in [38] and further studied in [39,40,41], the conformal manifold of the (A3, A3). Since the beta function for the SU(2) gauging vanishes, the gauge coupling τ θ π It was shown in [38] that the Seiberg-Witten curve of the (A3, A3) theory is invariant under two duality transformations T and S, which act on the gauge coupling τ as. The duality group acts on the space of τ as PSL(2, Z). In addition to changing the value of τ , the S-duality permutes operators of the same scaling dimensions It permutes the flavor U(1) currents through the symmetric group S3. This is the (A3, A3) counterpart of the SO(8) triality associated with the S-duality of the N = 2 SU(2) gauge theory with four flavors studied in [35].10
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