1993/05/23 by Ezer Melzer · 9 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #hep-th
paper · pdf · doi:10.1142/s0217751x94000510
published as Int.J.Mod.Phys.A9:1115-1136,1994 · 24/15 pages in harvmac, Stony Brook preprint ITP-SB-93-29
arxiv created 1993/05/23 · openalex publication_date 1994/03/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a "natural finitization" of the fermionic q-series (certain generalizations of the Rogers–Ramanujan sums) which were recently conjectured to be equal to Virasoro characters of the unitary minimal conformal field theory (CFT) ℳ (p, p + 1). Within the quasi-particle interpretation of the fermionic q-series this finitization amounts to introducing an ultraviolet cutoff, which — contrary to a lattice spacing — does not modify the linear dispersion relation. The resulting polynomials are conjectured (proven, for p = 3, 4) to be equal to corner transfer matrix (CTM) sums which arise in the computation of order parameters in regime III of the r = p + 1 RSOS model of Andrews, Baxter and Forrester. Following Schur's proof of the Rogers–Ramanujan identities, these authors have shown that the infinite lattice limit of the CTM sums gives what later became known as the Rocha–Caridi formula for the Virasoro characters. Thus we provide a proof of the fermionic q-series representation for the Virasoro characters for p = 4 (the case p = 3 is "trivial"), in addition to extending the remarkable connection between CFT and off-critical RSOS models. We also discuss finitizations of the CFT modular-invariant partition functions.