loom

loom generates a spectral network in a representation of \(\mathfrak{g} = \mathrm{A}_n, \mathrm{D}_n, \mathrm{E}_6\), or \(\mathrm{E}_7\). For more detail, see

• Spectral networks [Gaiotto, Moore, Neitzke (2012)]
• ADE Spectral Networks [Longhi, Park (2016)]

loom is an open-source project.

The source code of loom can be found at https://github.com/plonghi/loom-py3.

List of contributors to loom in the order of the date of their first contribution:

If you have any question using this website and/or loom, please contact one of the contributors or post it on the GitHub issues page.

How to use loom using a web user interface

• We recommend using Mozilla Firefox or Google Chrome for best experience. Microsoft Internet Explorer is not supported.
• See How to use loom web UI for a detailed guide.
• Go to the configuration page to generate spectral networks.
• In the configuration page input the data for a 4d \(\mathcal{N} = 2\) class \(\mathcal{S}\) theory to study.
• loom will grow each \(\mathcal{S}\)-wall by producing data points as many as (number of steps) \(\times\) (number of iterations). loom stops growing an S-wall when it either reaches the maximum number of data points or when the S-wall reaches the mass limit.
• When given a single phase (in radian), loom generates a single spectral network. To generate a family of spectral network, input [(start phase), (end phase), (number of phase)].
• Configuration data can be saved as a file, which can be loaded at the configuration page.
• After having a configuration ready, click "Generate spectral networks" button, which will show the progress of generating spectral networks.
• "Plot spectral networks" button will be activated when the data is ready. Click the button and wait for a few moment, which can take from a few seconds to a few minutes according to the size of the data and the internet speed.
• In the plot page, you can download the data and the plot by clicking "Download data" and "Download plot" buttons.

Examples of spectral networks

• Pure \(\mathrm{SU}(2)\) gauge theory at the origin of the Coulomb branch
  
• Pure \(\mathrm{SU}(3)\) gauge theory at the origin of the Coulomb branch
  
• Semiclassical limit of pure \(\mathrm{SO}(8)\) gauge theory
  
• An Argyres-Douglas fixed point theory from pure \(\mathrm{SU}(3)\) gauge theory, with the minimal BPS spectrum
  
• An Argyres-Douglas fixed point theory from pure \(\mathrm{SU}(3)\) gauge theory, with the maximal BPS spectrum
  
• Pure \(\mathrm{SO}(6)\) gauge theory at the origin of the Coulomb branch
  
• Pure \(\mathrm{SO}(8)\) gauge theory at the origin of the Coulomb branch
  
• Pure \(\mathrm{E}_6\) gauge theory at the origin of the Coulomb branch
  
• An Argyres-Douglas fixed point theory from pure \(\mathrm{SO}(8)\) gauge theory, with the minimal BPS spectrum
  
• An Argyres-Douglas fixed point theory from pure \(\mathrm{SO}(8)\) gauge theory, with the maximal and symmetric BPS spectrum