2020/06/24 by Songyuan Li, Jan Troost · 11 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Cohomology #Conjecture #Frobenius algebra #Genus #Orbifold #Quotient #Structure constants #Symmetric group #Topological quantum field theory #Topology (electrical circuits) #hep-th
paper · pdf · doi:10.1007/jhep10(2020)201
published in Journal of High Energy Physics 2020(10) (Springer Nature) · 33 pages. v2: Remarks on proof added
openalex created_date 2020/06/19 · arxiv created 2020/06/24 · openalex publication_date 2020/10/01 · arxiv updated 2020/12/02 · openalex updated_date 2026/08/06
A bstract We analyze topological orbifold conformal field theories on the symmetric product of a complex surface M . By exploiting the mathematics literature we show that a canonical quotient of the operator ring has structure constants given by Hurwitz numbers. This proves a conjecture in the physics literature on extremal correlators. Moreover, it allows to leverage results on the combinatorics of the symmetric group to compute more structure constants explicitly. We recall that the full orbifold chiral ring is given by a symmetric orbifold Frobenius algebra. This construction enables the computation of topological genus zero and genus one correlators, and to prove the vanishing of higher genus contributions. The efficient description of all topological correlators sets the stage for a proof of a topological AdS/CFT correspondence. Indeed, we propose a concrete mathematical incarnation of the proof, relating Gromow-Witten theory in the bulk to the cohomology of the Hilbert scheme on the boundary.