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

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.