Work

The point insertion technique and open r-spin theories II: intersection theories in genus-zero

Year: 2026

Type: article

Abstract: Recent works have initiated the study of open r -spin and open Fan–Jarvis–Ruan–Witten (FJRW) intersection theories, and related them to integrable hierarchies and mirror symmetry. This paper uses a new technique, the point insertion technique , to define new open r -spin and open FJRW intersection theories. These new constructions provide candidates for theories whose existence was conjectured before: 1. Hori predicted the existence of open r -spin theory with ⌊ r 2 ⌋ types of boundary states. The previously constructed open r -spin theory (Buryak–Clader–Tessler 2018) has only boundary states of one type. In this work we describe ⌊ r 2 ⌋ open r -spin theories, labelled by h ∈ { 0 , … , ⌊ r 2 ⌋ − 1 } , where the h th one has h + 1 types of boundary states. We prove that the h = 0 theory is equivalent to the previous construction, and calculate all intersection numbers for all these theories. 2. Aleshkin and Liu conjectured the existence of a quintic Fermat FJRW theory. We construct such an FJRW theory, and provide evidence that this is the conjectured theory.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2026.111044

Authors: Ran J. Tessler, Yizhen Zhao

Institutions: Weizmann Institute of Science, Institut de Mathématiques de Jussieu-Paris Rive Gauche

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,790

Funders: Israel Science Foundation, European Research Council, Islamic Scholarship Fund