Fermat Surface Calabi-Yau With Branes and Strings - Part 1
A red up left quark on a 1-fold Calabi-Yau manifold in 1 complex compact dimension or 2 real compact dimensions with open string endpoints connected via Dirichlet boundary conditions to intersections between 2 D-branes resulting from intersections between 4 D6-brane stacks and the C-Y manifold, thus, a fermion. For this particular video, the string is attached to a baryonic brane and a left weak brane.
This is an introductory video of my Calabi-Yau manifold and strings interactive visualization via the Unity game engine "compute shaders" and using DirectCompute GP-GPU massively parallel computing. Whereas my strings on branes on C-Y informatics based interactive visualizations are novel (as far as I know), my work is a derivative of and hopefully a synthesis of and a visualization extension of the research and publications of several string theory researchers, mathematicians and 3D/4D graphics programmers and others; including:
Andrew J. Hanson
Ji-Ping Sha
Konstantine I. Ishkov
Jeff H. Ma
Barton Zwiebach
Angel M. Uranga
Louis E. Ibanez
I. Antoniadis
D. Cremades
and many more.
For clarity, my C-Y visualizations follow the lead of Andrew J. Hanson, et.al., regarding parametric terminology and phase-space patch color scheme.
My work is not intended to be a rigorous publication in physics and mathematics, but rather as a tool that some might find helpful for visualizing how superstring theory may describe the standard model and how all of the standard model particles can be rendered as open strings attached to the Calabi-Yau manifold. Any mistakes are my own. (and there are bound to be some)
My intent here is not to present a single model as the way the universe works, but rather to help visualize an umbrella of related theories in a way that is plausible and consistent. Of course there are a near infinite number of such plausible and consistent models, so the specifics of what is used in these visualizations must be understood to only be a possible way to model and visualize rather than "the way".
My visualizations are based on open strings in type IIA superstring theory with the full standard model symmetry groups. Whereas the 3-fold quintic C-Y may be the best representation for the standard model, my simulation handles any number of degrees of freedom (dimensions) from 1-9. For visualization simplicity, I usually work with a 1-fold even though that does not have enough degrees of freedom or symmetry to enable the full standard model. All of the standard model 1st generation particles and antiparticles can be visualized here via plausible D-brane connections, except for the Higgs boson. The graviton is also not modeled. The model used here has 48 D-brane intersections on which the standard model fermion strings can be attached. The standard model has 48 fermions across three generations, so this model has the right number of "degrees of constraint" for all three generations but does not present a string visualization for the second and third generation fermions. Some models employ non-orthogonal D-branes stacks which wrap in cycles around the Calabi-Yau orbifold. Those models are not considered in this visualization tool.
In addition to the C-Y manifolds visualization, my simulation also displays the intersection branes "projected" onto a 2D quiver diagram. There are two variations of these quivers. In one variation, the D-branes lines are drawn in orthogonal space as a type of legend. In the other variation, the quiver is drawn to show the approximate topology of the D-branes across all of the C-Y "patches" in 2D phase space. Currently, string attachment points are not correctly handled in this quiver representation.
My informatic simulation displays two variations of the same data. The one on the right is composed of a point cloud of 2M particles. The one on the left is a triangle mesh created from the point cloud data on the GPU via massively parallel computation. The point coordinates are calculated via parametric equations of the Fermat surfaces and mathematically determined intersections between D6-branes and the C-Y manifold and between those intersection "lines".
My computing hardware is a Dell Alienware Aurora gaming tower computer running Windows 11. My GPU is an NVIDIA GeForce GTX 1080 .
The GPU parallel particle engine used is the TCParticles engine by Arthur Brusse. Many thanks to him for this wonderfully extensible engine for Unity.
My actual Unity simulation was developed to be compatible with the HTC Vive Pro Eye with eye-tracking and VR. Most of the text you will see on my screen-grabs is actually "gaze targets", where I can change parameters just by gazing at the text in VR. All of these have keyboard equivalent so that I can change parameters via keyboard when I am not viewing in VR. The VR hand controllers can also be used to navigate in stereoscopic 3D in VR via the headset.
More to come in subsequent videos and descriptions.