[FtheoryTools] Added F-theory models on all toric hypersurfaces

[emikelsons]

1. I'm still not sure about the correct discete factors for the gauge groups, F12 I think I figured out, but I'm not sure about F14

2. For models 13,15 16 where the MW group has torsion, do we need to list the generators which correspond to the torsion part?(Also in the paper they only list the Weierstrass coordinates for these generators)

[emikelsons]

cc @HereAround @apturner

[HereAround]

Thank you @emikelsons for this great first PR!

Suggestion: Please let us add CI tests (see the test/literature_models.jl file).

Regarding your above questions, let us hear from @apturner to see how we should best proceed.

[HereAround]

@emikelsons and @apturner , as mentioned in slack, I ahve taken the liberty to take the next step in this PR. Hence, I began by adding CI-tests. Here is a summary of my actions and observations:

• Rebased to current master.
• Weierstrass forms of the newly added 1408_4808 models cannot be distinguished by our current index from their hypersurface counterparts. The information in the model json-files that is used to create the model index is identical. Hence, the index needs to be expanded and/or the model information. For now, I moved the Weierstrass counterparts to a separate folder, so they are not considered for the index. (Otherwise, we get an error "could not uniquely identify the model", which effectively means that we cannot even create a single new model.) This is of course only a temporary fix, so that I could demonstrate how the CI tests can be added.
• A couple of comments (related to the questions above by @emikelsons) prevented the creation of a new model index - the json files could then not be read-in to create the index. I have adjusted this, while making sure that we do not forget about these issues.
• Created a new model index.
• I noticed that the F1-model could not be created, because it lacks the information about the divisor classes D1 and D2. Those are the equivalent of D and \tilde(D) on page 17 of https://arxiv.org/pdf/1408.4808.pdf. I have (or do hope to have) added this information correctly. If I have not made a mistake, it now says that D1 (a.k.a. D in the notation of https://arxiv.org/pdf/1408.4808.pdf) is the divisor (class) of the model section s7, and likewise D2 (a.k.a. \tilde(D) in notation of https://arxiv.org/pdf/1408.4808.pdf) is the divisor (class) of the model section s9. With that change, the model could be created.
• For time reasons, I have not looked through all the other models. But they might also suffer from not having the D1, D2 information. This needs to be looked into.
• I noticed that the model description for the F1-model was very generic, and so I adjusted that too. This should also be checked for the other models.
• Finally, I added a first preliminary test for the F1-model. This test could be expanded. Also, similar tests should be added for all the remaining 1408_4808 models.

But first, let us see if the CI-tests complete with the changes I made.

[codecov]

Codecov Report

Merging #3568 (dc7c235) into master (f206830) will decrease coverage by 37.38%.
Report is 53 commits behind head on master.
The diff coverage is n/a.

Additional details and impacted files

@@             Coverage Diff             @@
##           master    #3568       +/-   ##
===========================================
- Coverage   81.72%   44.35%   -37.38%     
===========================================
  Files         573      565        -8     
  Lines       77488    76641      -847     
===========================================
- Hits        63330    33991    -29339     
- Misses      14158    42650    +28492     

see 473 files with indirect coverage changes

[HereAround]

I have just rebased to the latest master and extended the F1-test by also construction the F1 model over a concrete base. Hopefully, this is a useful foundation on which we can discuss the next steps in a few minutes during our zoom meeting @emikelsons and @apturner .

[apturner]

Based on Fig. 21 and Table 22, it seems this should actually be "global_gauge_quotients": [["Z2", [1, 3]], ["Z2", [2, 4]]], and the same is true for the WSF version

[apturner]

After further inspection, I believe this should be [["Z2", [1, 2, 3, 4]], ["Z2", [1, 4, 5]]]

[apturner]

In the order presented in the paper, this should be [["Z2", [1, 3]]]

[apturner]

As we discussed, I would put [["Z3", [1, 4]], ["Z2", [2, 3, 4]]] here

[apturner]

As discussed, this might be more clear as [["Z3", [1, 3]], ["Z2", [2, 3]]]

[apturner]

This looks good @emikelsons, thanks for all the work! The coordinate changes for the base gradings look good on models where you had to do that.

Really, we should make a new field to store the coordinates of the torsional generating sections, something like "torsion_sections", as we want to distinguish them from the U(1) generating sections. That could either be done now or in a subsequent PR.

[HereAround]

(I have just approved the run of the tests. This is likely necessary because this is @emikelsons first PR to OSCAR. Please ping me in once you want to run the tests again.)

[HereAround]

Just rebased onto the latest master. Let us see if the test now complete successfully.

[HereAround]

Since the F4-model was removed, we also seem to need to update the index, which I have done just now.

[HereAround]

Since the F4-model was moved, we can of course not execute its tests. That is why (or so I believe) the tests failed. I have just disabled the F4 tests.