Estimates for a geometric flow for the Type IIB string

TL;DR

This paper establishes that uniform bounds on the metric and torsion 1-form imply bounds on all derivatives for a geometric flow relevant to Type IIB string theory, unifying it with Ricci flow.

Contribution

It introduces a formulation unifying the flow with Ricci flow, enabling derivative bounds from basic metric and torsion bounds in non-Kähler geometry.

Findings

All-order derivative bounds follow from uniform metric and torsion bounds.

The flow can be interpreted as a Type IIB string or Anomaly flow with source term.

A unifying formulation with Ricci flow was developed.

Abstract

It is shown that bounds of all orders of derivative would follow from uniform bounds for the metric and the torsion 1-form, for a flow in non-K\"ahler geometry which can be interpreted as either a flow for the Type IIB string or the Anomaly flow with source term and zero slope parameter. A key ingredient in the proof is a formulation of this flow unifying it with the Ricci flow, which was recently found.