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Yukawa couplings in intersecting D-brane models

D. Cremades, L. E. Ibanez, F. Marchesano

TL;DR

This work computes Yukawa couplings among chiral fields in toroidal Type IIA compactifications with D6-branes at angles, showing that disc worldsheet instantons yield couplings expressible as products of Jacobi theta functions depending on Kahler moduli and open-string moduli, while remaining independent of complex structure. It provides an explicit MSSM-like example with calculable Yukawa textures, and demonstrates that the method extends to elliptically fibered Calabi–Yau geometries, where results match mirrors such as D3-branes at ${\bf C}^3/{\bf Z}_3$ singularities. A key conceptual insight is the connection between these Yukawa computations and Fukaya’s category, illustrating how the A∞-structure of the Fukaya category emerges from worldsheet instantons in intersecting D-brane setups, thereby linking string phenomenology with homological mirror symmetry. Overall, the paper offers a calculable framework for Yukawa textures in brane-world models and reveals a deep mathematical interpretation within the Fukaya/homological mirror symmetry paradigm.

Abstract

We compute the Yukawa couplings among chiral fields in toroidal Type II compactifications with wrapping D6-branes intersecting at angles. Those models can yield realistic standard model spectrum living at the intersections. The Yukawa couplings depend both on the Kahler and open string moduli but not on the complex structure. They arise from worldsheet instanton corrections and are found to be given by products of complex Jacobi theta functions with characteristics. The Yukawa couplings for a particular intersecting brane configuration yielding the chiral spectrum of the MSSM are computed as an example. We also show how our methods can be extended to compute Yukawa couplings on certain classes of elliptically fibered CY manifolds which are mirror to complex cones over del Pezzo surfaces. We find that the Yukawa couplings in intersecting D6-brane models have a mathematical interpretation in the context of homological mirror symmetry. In particular, the computation of such Yukawa couplings is related to the construction of Fukaya's category in a generic symplectic manifold.

Yukawa couplings in intersecting D-brane models

TL;DR

This work computes Yukawa couplings among chiral fields in toroidal Type IIA compactifications with D6-branes at angles, showing that disc worldsheet instantons yield couplings expressible as products of Jacobi theta functions depending on Kahler moduli and open-string moduli, while remaining independent of complex structure. It provides an explicit MSSM-like example with calculable Yukawa textures, and demonstrates that the method extends to elliptically fibered Calabi–Yau geometries, where results match mirrors such as D3-branes at singularities. A key conceptual insight is the connection between these Yukawa computations and Fukaya’s category, illustrating how the A∞-structure of the Fukaya category emerges from worldsheet instantons in intersecting D-brane setups, thereby linking string phenomenology with homological mirror symmetry. Overall, the paper offers a calculable framework for Yukawa textures in brane-world models and reveals a deep mathematical interpretation within the Fukaya/homological mirror symmetry paradigm.

Abstract

We compute the Yukawa couplings among chiral fields in toroidal Type II compactifications with wrapping D6-branes intersecting at angles. Those models can yield realistic standard model spectrum living at the intersections. The Yukawa couplings depend both on the Kahler and open string moduli but not on the complex structure. They arise from worldsheet instanton corrections and are found to be given by products of complex Jacobi theta functions with characteristics. The Yukawa couplings for a particular intersecting brane configuration yielding the chiral spectrum of the MSSM are computed as an example. We also show how our methods can be extended to compute Yukawa couplings on certain classes of elliptically fibered CY manifolds which are mirror to complex cones over del Pezzo surfaces. We find that the Yukawa couplings in intersecting D6-brane models have a mathematical interpretation in the context of homological mirror symmetry. In particular, the computation of such Yukawa couplings is related to the construction of Fukaya's category in a generic symplectic manifold.

Paper Structure

This paper contains 19 sections, 78 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Intersecting brane models and Yukawa couplings
  3. D-branes wrapping intersecting cycles
  4. The rôle of worldsheet instantons
  5. Yukawa couplings in intersecting D-brane models
  6. The general form of Yukawa couplings in toroidal models
  7. Computing Yukawas on a $T^2$
  8. Adding a B-field and Wilson lines
  9. Orientifolding the torus
  10. The non-coprime case
  11. Higher dimensional tori
  12. Physical interpretation
  13. An MSSM-like example
  14. The model
  15. Yukawa couplings
  16. ...and 4 more sections

Figures (1)

  • Figure 1: The Standard Model at intersecting D-branes. a) Four stacks of branes, baryonic, left, right and leptonic are needed to get all quark and leptons at the intersections. b) The SM branes may be wrapping cycles on a, e.g., CY manifold, with appropriate intersections so as to yield the SM chiral spectrum.