A GLSM realization of derived equivalence in $U(1) \times U(2)$ models

TL;DR

This paper explores derived equivalences in Calabi--Yau varieties through GLSM models, analyzing B-brane behavior under RG flow and establishing new equivalences in anomalous $U(1) imes U(2)$ models.

Contribution

It generalizes band restriction rules to $U(2)$ GLSMs and demonstrates derived equivalences between Calabi--Yau varieties in anomalous models.

Findings

RG flow affects B-brane central charges in GLSMs.

Generalization of band restriction rules to $U(2)$ models.

New derived equivalences between Calabi--Yau varieties.

Abstract

This paper studies the derived equivalence between Calabi--Yau mixed branches using the B-brane hemisphere partition function in anomalous gauged linear sigma models (GLSMs). For a family of anomalous $U(2)$ GLSMs, we study the infrared behavior of B-branes under RG flow and the variation of FI parameters in the quantum K\"ahler moduli space. As characterized by the big and small window categories of the GLSM, the RG flow effect is analyzed according to the properties of their B-brane central charges as hemisphere partition functions. The result generalizes the band restriction rules in anomalous abelian GLSMs (Clingempeel--Floch--Romo) to some $U(2)$ models. As an application, we study a family of $U(1)\times U(k)$ models for $k=1,2$, which realize a Fano UV sigma model and two IR phases as mixed branches accompanied by local Calabi--Yau Higgs components. By applying the restriction rules, we establish new derived equivalences between Calabi--Yau varieties from these anomalous models.