Decomposition of N = 1 superconformal minimal models and their fractional quantum Hall wavefunctions

Journal article

N = 1 superconformal minimal models are the first series of unitary conformal field theories (CFTs) extending beyond Virasoro algebra. Using coset constructions, we characterize CFTs in N = 1 superconformal minimal models using combinations of a parafermion theory, an Ising theory and a free boson theory. Supercurrent operators in the original theory also becomes sums of operators from each constituent theory. If we take our N = 1 superconformal theories as the neutral part of the edge theory of a fractional quantum Hall state, we present a systematic way of calculating its ground state wavefunction using free field methods. Each ground state wavefunction is known previously as a sum of polynomials with distinct clustering behaviours. Based on our decomposition, we find explicit expressions for each summand polynomial. A brief generalization to S3 minimal models using coset construction is also included.

Authors: Hu, Y; Ning, S; Zhou, Y

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Journal of High Energy Physics
• Volume: 2026
• Issue: 3
• Article number: 115
• Publication date: 2026-03-12
• Acceptance date: 2026-01-26
• DOI: 10.1007/jhep03(2026)115
• EISSN: 1029-8479
• ISSN: 1126-6708
• Language: English
• Keywords: Topological States of Matter; Conformal and W Symmetry; Supersymmetric Gauge Theory