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D-Branes and Quotient Singularities of Calabi-Yau Fourfolds

Kenji Mohri

TL;DR

This work examines a type IIB D1-brane at a Calabi–Yau fourfold orbifold, showing that worldvolume gauge anomalies are canceled by couplings to bulk RR chiral bosons and NSNS moduli. It develops a (0,2) gauged linear sigma model framework for the D1-brane and uses toric geometry to analyze the Higgs moduli space M_r, proving that for generic FI parameters M_r is a smooth fourfold birational to X_Γ but not necessarily Calabi–Yau. Calabi–Yau structure of M_r is tied to the existence of crepant resolutions of the orbifold; when such resolutions exist (class A), M_r can be Calabi–Yau, while for terminal or partially resolvable cases (classes B and C), M_r is typically non-CY. The results illuminate how bulk-brane couplings influence anomaly cancellation and moduli space geometry in two-dimensional (0,2) theories arising from D-branes at CY4 singularities, with implications for IR dynamics and the role of toric methods in D-brane gauge theories.

Abstract

We investigate a (0,2) gauge theory realized on the world volume of the type IIB D1-brane at the singular point of a Calabi-Yau fourfold. It is argued that the gauge anomaly can be canceled via coupling to the R-R chiral bosons in bulk IIB string. We find that for a generic choice of the Fayet-Iliopoulos parameters on the world volume, the Higgs moduli space is a smooth fourfold birational to the original Calabi-Yau fourfold, but is not necessarily a Calabi-Yau manifold.

D-Branes and Quotient Singularities of Calabi-Yau Fourfolds

TL;DR

This work examines a type IIB D1-brane at a Calabi–Yau fourfold orbifold, showing that worldvolume gauge anomalies are canceled by couplings to bulk RR chiral bosons and NSNS moduli. It develops a (0,2) gauged linear sigma model framework for the D1-brane and uses toric geometry to analyze the Higgs moduli space M_r, proving that for generic FI parameters M_r is a smooth fourfold birational to X_Γ but not necessarily Calabi–Yau. Calabi–Yau structure of M_r is tied to the existence of crepant resolutions of the orbifold; when such resolutions exist (class A), M_r can be Calabi–Yau, while for terminal or partially resolvable cases (classes B and C), M_r is typically non-CY. The results illuminate how bulk-brane couplings influence anomaly cancellation and moduli space geometry in two-dimensional (0,2) theories arising from D-branes at CY4 singularities, with implications for IR dynamics and the role of toric methods in D-brane gauge theories.

Abstract

We investigate a (0,2) gauge theory realized on the world volume of the type IIB D1-brane at the singular point of a Calabi-Yau fourfold. It is argued that the gauge anomaly can be canceled via coupling to the R-R chiral bosons in bulk IIB string. We find that for a generic choice of the Fayet-Iliopoulos parameters on the world volume, the Higgs moduli space is a smooth fourfold birational to the original Calabi-Yau fourfold, but is not necessarily a Calabi-Yau manifold.

Paper Structure

This paper contains 23 sections, 1 theorem, 79 equations.

Table of Contents

  1. Introduction
  2. Type IIB String on Orbifold
  3. General Aspect
  4. Resolvable Models
  5. Models with Terminal Singularity
  6. Partially Resolvable Models
  7. World Volume Theory
  8. Orbifold Projection
  9. (0,2) Gauged Linear Sigma Model
  10. Gauge Anomaly on World Volume
  11. Anomaly Polynomial
  12. Interaction with Bulk Closed String Fields
  13. Cancellation of Anomaly
  14. Toric Description of Higgs Moduli Space
  15. F-term Constraint
  16. ...and 8 more sections

Key Result

Lemma 1

The $n$ eigenvectors $\{v_{k}\}$ and these eigenvalues $\{b_{k}\}$ of $C_{S}$ are given by

Theorems & Definitions (4)

  • Claim 1
  • Claim 2
  • Lemma 1
  • Claim 3