Pith. sign in

REVIEW 2 cited by

Quantum spectrum and Gamma structures for quasi-homogeneous polynomials of general type

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2309.07446 v2 pith:3JU2EOSR submitted 2023-09-14 math.AG hep-th

Yefeng Shen , Ming Zhang This is my paper · ORCID
classification math.AGhep-th
keywords gammaquantumconjecturesfan-jarvis-ruan-wittengeneralspectrumstructurestheory
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

Let $W$ be a quasi-homogeneous polynomial of general type and $<J>$ be the cyclic symmetry group of $W$ generated by the exponential grading element $J$. We study the quantum spectrum and asymptotic behavior in Fan-Jarvis-Ruan-Witten theory of the Landau-Ginzburg pair $(W, <J>)$. Inspired by Galkin-Golyshev-Iritani's Gamma conjectures for quantum cohomology of Fano manifolds, we propose Gamma conjectures for Fan-Jarvis-Ruan-Witten theory of general type. We prove the quantum spectrum conjecture and the Gamma conjectures for Fermat homogeneous polynomials and the mirror simple singularities. The Gamma structures in Fan-Jarvis-Ruan-Witten theory also provide a bridge from the category of matrix factorizations of the Landau-Ginzburg pair (the algebraic aspect) to its analytic aspect. We will explain the relationship among the Gamma structures, Orlov's semiorthogonal decompositions, and the Stokes phenomenon.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantum spectrum and Gamma structure for standard flips

    math.AG 2025-02 conditional novelty 7.0 of 10

    For standard flips, the extremal quantum spectrum is shown to be compatible with the Gamma-class decomposition and with the semi-orthogonal decompositions of Orlov and Belmans-Fu-Raedschelders.

  2. A topological Chern character for matrix factorizations

    math.AG 2026-07 conditional novelty 6.0 of 10

    A topological Chern character from matrix-factorization K-theory to critical cohomology is constructed for global Landau-Ginzburg models, along with a Grothendieck-Riemann-Roch theorem.

Pith tools