Massless D-Branes on Calabi-Yau Threefolds and Monodromy

TL;DR

The paper develops a derived-category framework to classify massless B-type D-branes in Calabi–Yau threefold moduli spaces and to understand their associated monodromies. By treating masslessness via spherical and EZ-spherical objects, it shows that monodromy around discriminant loci is governed by autoequivalences such as $K_A$ and its composites, culminating in a general EZ-monodromy conjecture. A key result is that certain composed transforms reduce to a fiberwise cone-type autoequivalence $\mathbi{H}$, tying local masslessness to global monodromy via Fourier–Mukai kernels. The paper then illustrates these ideas through explicit geometric scenarios (points, curves, surfaces, exoflops), demonstrating how monodromy is realized as autoequivalences and how massless D-brane spectra reflect the underlying fibration geometry. Altogether, it provides a coherent mechanism linking massless D-branes, monodromy, and derived-category autoequivalences, with implications for mirror symmetry and nonperturbative phenomena such as enhanced gauge symmetry.

Abstract

We analyze the link between the occurrence of massless B-type D-branes for specific values of moduli and monodromy around such points in the moduli space. This allows us to propose a classification of all massless B-type D-branes at any point in the moduli space of Calabi-Yau's. This classification then justifies a previous conjecture due to Horja for the general form of monodromy. Our analysis is based on using monodromies around points in moduli space where a single D-brane becomes massless to generate monodromies around points where an infinite number become massless. We discuss the various possibilities within the classification.

Figures (3)

• Figure 1: Moduli Space for $y=0$.
• Figure 2: Full Moduli Space around $P_1$.
• Figure 3: Moduli Space for Elliptic Curve.

Theorems & Definitions (4)

• Conjecture 1
• Conjecture 2
• Conjecture 3
• Conjecture 4