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add preprint
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yuma-mizuno committed May 5, 2023
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5 changes: 5 additions & 0 deletions index.html
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Expand Up @@ -91,6 +91,11 @@ <h2>Research Interest</h2>

<h2 id="paper">Preprints</h2>
<ol>
<li>
Remarks on Nahm sums for symmetrizable matrices, arXiv:2305.02267.
Table 2 (<a href=modular_nahm_112.csv>modular_nahm_112.csv</a>),
Table 3 (<a href=modular_nahm_221.csv>modular_nahm_221.csv</a>).
</li>
<li>
Periodic Y-systems and Nahm sums: the rank 2 case, arXiv:2301.13239.
</li>
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69 changes: 69 additions & 0 deletions modular_nahm_112.csv
Original file line number Diff line number Diff line change
@@ -0,0 +1,69 @@
A,b,c,d,central_charge
"[1, 1, 0, 1, 2, 1, 0, 2, 4, ]","[1/2, 1, 0, ]",7/120,"[1, 1, 2, ]",17/10
"[1, 1, 0, 1, 2, 1, 0, 2, 4, ]","[1/2, 1, 4, ]",103/120,"[1, 1, 2, ]",17/10
"[1, 1, 0, 1, 3, 1, 0, 2, 2, ]","[1/2, -1, 0, ]",3/56,"[1, 1, 2, ]",12/7
"[1, 1, 0, 1, 3, 1, 0, 2, 2, ]","[1/2, 0, 0, ]",-1/56,"[1, 1, 2, ]",12/7
"[1, 1, 0, 1, 3, 1, 0, 2, 2, ]","[1/2, 1, 2, ]",19/56,"[1, 1, 2, ]",12/7
"[1, 1, 1, 1, 3, 2, 2, 4, 4, ]","[0, -1/2, 0, ]",-1/32,"[1, 1, 2, ]",3/2
"[1, 1, 1, 1, 3, 2, 2, 4, 4, ]","[1/2, -3/2, -2, ]",1/8,"[1, 1, 2, ]",3/2
"[1, 1, 1, 1, 3, 2, 2, 4, 4, ]","[1/2, -1/2, 0, ]",0,"[1, 1, 2, ]",3/2
"[1, 1, 1, 1, 3, 2, 2, 4, 4, ]","[1/2, 1/2, 2, ]",1/8,"[1, 1, 2, ]",3/2
"[1, 1, 1, 1, 3, 2, 2, 4, 4, ]","[1, 1/2, 2, ]",7/32,"[1, 1, 2, ]",3/2
"[1, 1, 0, 1, 4, 1, 0, 2, 1, ]","[1/2, -2, 1, ]",7/24,"[1, 1, 2, ]",7/4
"[1, 1, 0, 1, 4, 1, 0, 2, 1, ]","[1/2, 0, 0, ]",-1/48,"[1, 1, 2, ]",7/4
"[1, 1, 0, 1, 4, 1, 0, 2, 1, ]","[1/2, 0, 1, ]",1/24,"[1, 1, 2, ]",7/4
"[1, 1, 0, 1, 4, 1, 0, 2, 1, ]","[1/2, 2, 1, ]",7/24,"[1, 1, 2, ]",7/4
"[1, 1, 0, 1, 4, 1, 0, 2, 1, ]","[1/2, 2, 2, ]",23/48,"[1, 1, 2, ]",7/4
"[1, 1, 0, 1, 4, 2, 0, 4, 4, ]","[1/2, 0, 0, ]",-1/168,"[1, 1, 2, ]",11/7
"[1, 1, 0, 1, 4, 2, 0, 4, 4, ]","[1/2, 0, 2, ]",47/168,"[1, 1, 2, ]",11/7
"[1, 1, 0, 1, 4, 2, 0, 4, 4, ]","[1/2, 2, 4, ]",143/168,"[1, 1, 2, ]",11/7
"[1, 1, 1, 1, 5, 4, 2, 8, 8, ]","[1/2, -1/2, 0, ]",1/120,"[1, 1, 2, ]",7/5
"[1, 1, 1, 1, 5, 4, 2, 8, 8, ]","[1/2, 3/2, 4, ]",49/120,"[1, 1, 2, ]",7/5
"[1, 1, 0, 1, 8, 1, 0, 2, 1, ]","[1/2, 0, 1, ]",7/120,"[1, 1, 2, ]",17/10
"[1, 1, 0, 1, 8, 1, 0, 2, 1, ]","[1/2, 4, 1, ]",103/120,"[1, 1, 2, ]",17/10
"[1, 1, 0, 1, 8, 2, 0, 4, 2, ]","[1/2, 0, 0, ]",-1/168,"[1, 1, 2, ]",11/7
"[1, 1, 0, 1, 8, 2, 0, 4, 2, ]","[1/2, 2, 0, ]",47/168,"[1, 1, 2, ]",11/7
"[1, 1, 0, 1, 8, 2, 0, 4, 2, ]","[1/2, 4, 2, ]",143/168,"[1, 1, 2, ]",11/7
"[2, 1, 1, 1, 2, 1, 2, 2, 2, ]","[-1, 0, 1, ]",1/8,"[1, 1, 2, ]",3/2
"[2, 1, 1, 1, 2, 1, 2, 2, 2, ]","[-1/2, 0, 0, ]",-1/32,"[1, 1, 2, ]",3/2
"[2, 1, 1, 1, 2, 1, 2, 2, 2, ]","[0, -1, 1, ]",1/8,"[1, 1, 2, ]",3/2
"[2, 1, 1, 1, 2, 1, 2, 2, 2, ]","[0, -1/2, 0, ]",-1/32,"[1, 1, 2, ]",3/2
"[2, 1, 1, 1, 2, 1, 2, 2, 2, ]","[0, 0, 1, ]",0,"[1, 1, 2, ]",3/2
"[2, 1, 1, 1, 2, 1, 2, 2, 2, ]","[0, 1, 1, ]",1/8,"[1, 1, 2, ]",3/2
"[2, 1, 1, 1, 2, 1, 2, 2, 2, ]","[1, 0, 1, ]",1/8,"[1, 1, 2, ]",3/2
"[2, 1, 1, 1, 2, 1, 2, 2, 2, ]","[1/2, 1, 2, ]",7/32,"[1, 1, 2, ]",3/2
"[2, 1, 1, 1, 2, 1, 2, 2, 2, ]","[1, 1/2, 2, ]",7/32,"[1, 1, 2, ]",3/2
"[2, 1, 1, 1, 4, 1, 2, 2, 2, ]","[0, 0, 1, ]",1/120,"[1, 1, 2, ]",7/5
"[2, 1, 1, 1, 4, 1, 2, 2, 2, ]","[0, 2, 1, ]",49/120,"[1, 1, 2, ]",7/5
"[2, 2, 1, 2, 4, 2, 2, 4, 3, ]","[-1, -1, -1, ]",1/48,"[1, 1, 2, ]",5/4
"[2, 2, 1, 2, 4, 2, 2, 4, 3, ]","[0, 0, 0, ]",-1/24,"[1, 1, 2, ]",5/4
"[2, 2, 1, 2, 4, 2, 2, 4, 3, ]","[0, 0, 1, ]",1/48,"[1, 1, 2, ]",5/4
"[2, 2, 1, 2, 4, 2, 2, 4, 3, ]","[0, 1, 2, ]",5/24,"[1, 1, 2, ]",5/4
"[2, 2, 1, 2, 4, 2, 2, 4, 3, ]","[1, 2, 3, ]",25/48,"[1, 1, 2, ]",5/4
"[1, 1, 1/2, 1, 2, 1, 1, 2, 3/2, ]","[0, 0, 0, ]",-1/18,"[1, 1, 2, ]",5/3
"[1, 1, 1/2, 1, 2, 1, 1, 2, 3/2, ]","[0, 0, 1, ]",0,"[1, 1, 2, ]",5/3
"[1, 1, 1/2, 1, 2, 1, 1, 2, 3/2, ]","[0, 1, 1, ]",1/9,"[1, 1, 2, ]",5/3
"[1, 1, 1/2, 1, 2, 1, 1, 2, 3/2, ]","[1, 1, 2, ]",5/18,"[1, 1, 2, ]",5/3
"[1, 0, 1/2, 0, 2, 1, 1, 2, 2, ]","[0, 0, 0, ]",-5/88,"[1, 1, 2, ]",21/11
"[1, 0, 1/2, 0, 2, 1, 1, 2, 2, ]","[0, 0, 1, ]",-1/88,"[1, 1, 2, ]",21/11
"[1, 0, 1/2, 0, 2, 1, 1, 2, 2, ]","[0, 1, 2, ]",19/88,"[1, 1, 2, ]",21/11
"[1, 0, 1/2, 0, 2, 1, 1, 2, 2, ]","[1, 1, 2, ]",35/88,"[1, 1, 2, ]",21/11
"[2, 2, 2, 2, 5, 4, 4, 8, 8, ]","[0, -1/2, 0, ]",-1/42,"[1, 1, 2, ]",8/7
"[2, 2, 2, 2, 5, 4, 4, 8, 8, ]","[0, 1/2, 2, ]",5/42,"[1, 1, 2, ]",8/7
"[2, 2, 2, 2, 5, 4, 4, 8, 8, ]","[1, 3/2, 4, ]",17/42,"[1, 1, 2, ]",8/7
"[1, 1, 0, 1, 3, 1/2, 0, 1, 3/2, ]","[1/2, -1/2, 1/2, ]",1/40,"[1, 1, 2, ]",9/5
"[1, 1, 0, 1, 3, 1/2, 0, 1, 3/2, ]","[1/2, 1/2, -1/2, ]",1/40,"[1, 1, 2, ]",9/5
"[1, 1, 0, 1, 3, 1/2, 0, 1, 3/2, ]","[1/2, 1/2, 3/2, ]",9/40,"[1, 1, 2, ]",9/5
"[1, 1, 0, 1, 3, 1/2, 0, 1, 3/2, ]","[1/2, 3/2, 1/2, ]",9/40,"[1, 1, 2, ]",9/5
"[1, 1, 0, 1, 4, 1, 0, 2, 3/2, ]","[1/2, 0, -1, ]",3/56,"[1, 1, 2, ]",12/7
"[1, 1, 0, 1, 4, 1, 0, 2, 3/2, ]","[1/2, 0, 0, ]",-1/56,"[1, 1, 2, ]",12/7
"[1, 1, 0, 1, 4, 1, 0, 2, 3/2, ]","[1/2, 2, 1, ]",19/56,"[1, 1, 2, ]",12/7
"[3, 2, 2, 2, 4, 2, 4, 4, 4, ]","[-1/2, 0, 0, ]",-1/42,"[1, 1, 2, ]",8/7
"[3, 2, 2, 2, 4, 2, 4, 4, 4, ]","[-1/2, 1, 0, ]",5/42,"[1, 1, 2, ]",8/7
"[3, 2, 2, 2, 4, 2, 4, 4, 4, ]","[1/2, 2, 2, ]",17/42,"[1, 1, 2, ]",8/7
"[3/2, 1, 1, 1, 3, 2, 2, 4, 4, ]","[-1/2, -1/2, 0, ]",1/168,"[1, 1, 2, ]",10/7
"[3/2, 1, 1, 1, 3, 2, 2, 4, 4, ]","[0, -1/2, 0, ]",-5/168,"[1, 1, 2, ]",10/7
"[3/2, 1, 1, 1, 3, 2, 2, 4, 4, ]","[1/2, 1/2, 2, ]",25/168,"[1, 1, 2, ]",10/7
"[2, 1, 1, 1, 5/2, 3/2, 2, 3, 3, ]","[0, -1, -1, ]",1/168,"[1, 1, 2, ]",10/7
"[2, 1, 1, 1, 5/2, 3/2, 2, 3, 3, ]","[0, -1/2, 0, ]",-5/168,"[1, 1, 2, ]",10/7
"[2, 1, 1, 1, 5/2, 3/2, 2, 3, 3, ]","[1, 0, 1, ]",25/168,"[1, 1, 2, ]",10/7
72 changes: 72 additions & 0 deletions modular_nahm_221.csv
Original file line number Diff line number Diff line change
@@ -0,0 +1,72 @@
A,b,c,d,central_charge
"[1, 0, 1, 0, 2, 2, 1/2, 1, 2, ]","[0, 0, 0, ]",-7/88,"[2, 2, 1, ]",15/11
"[1, 0, 1, 0, 2, 2, 1/2, 1, 2, ]","[1, 0, 0, ]",1/88,"[2, 2, 1, ]",15/11
"[1, 0, 1, 0, 2, 2, 1/2, 1, 2, ]","[1, 0, 1, ]",9/88,"[2, 2, 1, ]",15/11
"[1, 0, 1, 0, 2, 2, 1/2, 1, 2, ]","[1, 2, 2, ]",49/88,"[2, 2, 1, ]",15/11
"[1, 1, 1, 1, 2, 2, 1/2, 1, 2, ]","[0, 0, -1/2, ]",-3/56,"[2, 2, 1, ]",9/7
"[1, 1, 1, 1, 2, 2, 1/2, 1, 2, ]","[1, 0, -1/2, ]",1/56,"[2, 2, 1, ]",9/7
"[1, 1, 1, 1, 2, 2, 1/2, 1, 2, ]","[1, 2, 1/2, ]",9/56,"[2, 2, 1, ]",9/7
"[1, 1, 0, 1, 4, 4, 0, 2, 3, ]","[1, 0, -1/2, ]",1/48,"[2, 2, 1, ]",5/4
"[1, 1, 0, 1, 4, 4, 0, 2, 3, ]","[1, 4, 3/2, ]",25/48,"[2, 2, 1, ]",5/4
"[2, 1, 0, 1, 2, 2, 0, 1, 2, ]","[0, 1, 0, ]",-1/36,"[2, 2, 1, ]",4/3
"[2, 1, 0, 1, 2, 2, 0, 1, 2, ]","[2, 1, 0, ]",11/36,"[2, 2, 1, ]",4/3
"[2, 1, 0, 1, 2, 2, 0, 1, 2, ]","[2, 3, 1, ]",23/36,"[2, 2, 1, ]",4/3
"[2, 1, 2, 1, 2, 0, 1, 0, 2, ]","[1, 0, 0, ]",-1/36,"[2, 2, 1, ]",4/3
"[2, 1, 2, 1, 2, 0, 1, 0, 2, ]","[1, 2, 0, ]",11/36,"[2, 2, 1, ]",4/3
"[2, 1, 2, 1, 2, 0, 1, 0, 2, ]","[3, 2, 1, ]",23/36,"[2, 2, 1, ]",4/3
"[2, 2, 2, 2, 4, 4, 1, 2, 3, ]","[-1, -2, -3/2, ]",1/24,"[2, 2, 1, ]",1
"[2, 2, 2, 2, 4, 4, 1, 2, 3, ]","[-1, 0, 1/2, ]",1/24,"[2, 2, 1, ]",1
"[2, 2, 2, 2, 4, 4, 1, 2, 3, ]","[0, -1, -1, ]",-1/48,"[2, 2, 1, ]",1
"[2, 2, 2, 2, 4, 4, 1, 2, 3, ]","[0, 0, -1/2, ]",-1/24,"[2, 2, 1, ]",1
"[2, 2, 2, 2, 4, 4, 1, 2, 3, ]","[0, 0, 0, ]",-5/96,"[2, 2, 1, ]",1
"[2, 2, 2, 2, 4, 4, 1, 2, 3, ]","[0, 2, 3/2, ]",7/24,"[2, 2, 1, ]",1
"[2, 2, 2, 2, 4, 4, 1, 2, 3, ]","[1, 0, -1/2, ]",1/24,"[2, 2, 1, ]",1
"[2, 2, 2, 2, 4, 4, 1, 2, 3, ]","[1, 0, 1/2, ]",1/24,"[2, 2, 1, ]",1
"[2, 2, 2, 2, 4, 4, 1, 2, 3, ]","[2, 2, 1/2, ]",7/24,"[2, 2, 1, ]",1
"[2, 2, 2, 2, 4, 4, 1, 2, 3, ]","[3, 4, 5/2, ]",25/24,"[2, 2, 1, ]",1
"[1, 1, 1, 1, 2, 2, 1/2, 1, 3/2, ]","[0, 0, 0, ]",-5/72,"[2, 2, 1, ]",4/3
"[1, 1, 1, 1, 2, 2, 1/2, 1, 3/2, ]","[1, 0, 1/2, ]",1/72,"[2, 2, 1, ]",4/3
"[1, 1, 1, 1, 2, 2, 1/2, 1, 3/2, ]","[1, 2, 3/2, ]",25/72,"[2, 2, 1, ]",4/3
"[1, 0, 1, 0, 2, 2, 1/2, 1, 5/2, ]","[0, 0, -1/2, ]",-5/72,"[2, 2, 1, ]",4/3
"[1, 0, 1, 0, 2, 2, 1/2, 1, 5/2, ]","[1, 0, -1, ]",1/8,"[2, 2, 1, ]",4/3
"[1, 0, 1, 0, 2, 2, 1/2, 1, 5/2, ]","[1, 0, 0, ]",1/72,"[2, 2, 1, ]",4/3
"[1, 0, 1, 0, 2, 2, 1/2, 1, 5/2, ]","[1, 2, 1, ]",25/72,"[2, 2, 1, ]",4/3
"[1, 1, 1, 1, 3, 3, 1/2, 3/2, 5/2, ]","[0, -1, -1, ]",-1/40,"[2, 2, 1, ]",6/5
"[1, 1, 1, 1, 3, 3, 1/2, 3/2, 5/2, ]","[1, -2, -3/2, ]",9/40,"[2, 2, 1, ]",6/5
"[1, 1, 1, 1, 3, 3, 1/2, 3/2, 5/2, ]","[1, 0, -1/2, ]",1/40,"[2, 2, 1, ]",6/5
"[3/2, 1/2, 1, 1/2, 3/2, 1, 1/2, 1/2, 1, ]","[-3/2, -1/2, 1/2, ]",1/8,"[2, 2, 1, ]",3/2
"[3/2, 1/2, 1, 1/2, 3/2, 1, 1/2, 1/2, 1, ]","[-1/2, -3/2, 1/2, ]",1/8,"[2, 2, 1, ]",3/2
"[3/2, 1/2, 1, 1/2, 3/2, 1, 1/2, 1/2, 1, ]","[-1/2, 1/2, 0, ]",-1/32,"[2, 2, 1, ]",3/2
"[3/2, 1/2, 1, 1/2, 3/2, 1, 1/2, 1/2, 1, ]","[-1/2, 1/2, 1/2, ]",0,"[2, 2, 1, ]",3/2
"[3/2, 1/2, 1, 1/2, 3/2, 1, 1/2, 1/2, 1, ]","[1/2, -1/2, 0, ]",-1/32,"[2, 2, 1, ]",3/2
"[3/2, 1/2, 1, 1/2, 3/2, 1, 1/2, 1/2, 1, ]","[1/2, -1/2, 1/2, ]",0,"[2, 2, 1, ]",3/2
"[3/2, 1/2, 1, 1/2, 3/2, 1, 1/2, 1/2, 1, ]","[1/2, 3/2, 1/2, ]",1/8,"[2, 2, 1, ]",3/2
"[3/2, 1/2, 1, 1/2, 3/2, 1, 1/2, 1/2, 1, ]","[1/2, 3/2, 1, ]",7/32,"[2, 2, 1, ]",3/2
"[3/2, 1/2, 1, 1/2, 3/2, 1, 1/2, 1/2, 1, ]","[3/2, 1/2, 1/2, ]",1/8,"[2, 2, 1, ]",3/2
"[3/2, 1/2, 1, 1/2, 3/2, 1, 1/2, 1/2, 1, ]","[3/2, 1/2, 1, ]",7/32,"[2, 2, 1, ]",3/2
"[3/2, 1/2, 1, 1/2, 3/2, 1, 1/2, 1/2, 3/2, ]","[-1/2, 1/2, -1/2, ]",1/168,"[2, 2, 1, ]",10/7
"[3/2, 1/2, 1, 1/2, 3/2, 1, 1/2, 1/2, 3/2, ]","[-1/2, 1/2, 0, ]",-5/168,"[2, 2, 1, ]",10/7
"[3/2, 1/2, 1, 1/2, 3/2, 1, 1/2, 1/2, 3/2, ]","[1/2, -1/2, -1/2, ]",1/168,"[2, 2, 1, ]",10/7
"[3/2, 1/2, 1, 1/2, 3/2, 1, 1/2, 1/2, 3/2, ]","[1/2, -1/2, 0, ]",-5/168,"[2, 2, 1, ]",10/7
"[3/2, 1/2, 1, 1/2, 3/2, 1, 1/2, 1/2, 3/2, ]","[1/2, 3/2, 1/2, ]",25/168,"[2, 2, 1, ]",10/7
"[3/2, 1/2, 1, 1/2, 3/2, 1, 1/2, 1/2, 3/2, ]","[3/2, 1/2, 1/2, ]",25/168,"[2, 2, 1, ]",10/7
"[3/2, 1/2, 2, 1/2, 3/2, 2, 1, 1, 4, ]","[-1/2, 1/2, 0, ]",-1/42,"[2, 2, 1, ]",8/7
"[3/2, 1/2, 2, 1/2, 3/2, 2, 1, 1, 4, ]","[-1/2, 1/2, 1, ]",5/42,"[2, 2, 1, ]",8/7
"[3/2, 1/2, 2, 1/2, 3/2, 2, 1, 1, 4, ]","[1/2, -1/2, 0, ]",-1/42,"[2, 2, 1, ]",8/7
"[3/2, 1/2, 2, 1/2, 3/2, 2, 1, 1, 4, ]","[1/2, -1/2, 1, ]",5/42,"[2, 2, 1, ]",8/7
"[3/2, 1/2, 2, 1/2, 3/2, 2, 1, 1, 4, ]","[1/2, 3/2, 2, ]",17/42,"[2, 2, 1, ]",8/7
"[3/2, 1/2, 2, 1/2, 3/2, 2, 1, 1, 4, ]","[3/2, 1/2, 2, ]",17/42,"[2, 2, 1, ]",8/7
"[4, 4, 2, 4, 5, 2, 1, 1, 1, ]","[0, 0, 1/2, ]",-1/40,"[2, 2, 1, ]",6/5
"[4, 4, 2, 4, 5, 2, 1, 1, 1, ]","[4, 4, 1/2, ]",31/40,"[2, 2, 1, ]",6/5
"[4, 4, 4, 4, 6, 6, 2, 3, 4, ]","[0, -1, -1, ]",-1/60,"[2, 2, 1, ]",4/5
"[4, 4, 4, 4, 6, 6, 2, 3, 4, ]","[2, 1, 0, ]",11/60,"[2, 2, 1, ]",4/5
"[5/2, 3/2, 1, 3/2, 5/2, 1, 1/2, 1/2, 1, ]","[-1/2, 1/2, 1/2, ]",1/120,"[2, 2, 1, ]",7/5
"[5/2, 3/2, 1, 3/2, 5/2, 1, 1/2, 1/2, 1, ]","[1/2, -1/2, 1/2, ]",1/120,"[2, 2, 1, ]",7/5
"[5/2, 3/2, 1, 3/2, 5/2, 1, 1/2, 1/2, 1, ]","[3/2, 5/2, 1/2, ]",49/120,"[2, 2, 1, ]",7/5
"[5/2, 3/2, 1, 3/2, 5/2, 1, 1/2, 1/2, 1, ]","[5/2, 3/2, 1/2, ]",49/120,"[2, 2, 1, ]",7/5
"[5/2, 3/2, 2, 3/2, 5/2, 2, 1, 1, 2, ]","[-1/2, 1/2, 0, ]",-1/42,"[2, 2, 1, ]",8/7
"[5/2, 3/2, 2, 3/2, 5/2, 2, 1, 1, 2, ]","[1/2, -1/2, 0, ]",-1/42,"[2, 2, 1, ]",8/7
"[5/2, 3/2, 2, 3/2, 5/2, 2, 1, 1, 2, ]","[1/2, 3/2, 0, ]",5/42,"[2, 2, 1, ]",8/7
"[5/2, 3/2, 2, 3/2, 5/2, 2, 1, 1, 2, ]","[3/2, 1/2, 0, ]",5/42,"[2, 2, 1, ]",8/7
"[5/2, 3/2, 2, 3/2, 5/2, 2, 1, 1, 2, ]","[3/2, 5/2, 1, ]",17/42,"[2, 2, 1, ]",8/7
"[5/2, 3/2, 2, 3/2, 5/2, 2, 1, 1, 2, ]","[5/2, 3/2, 1, ]",17/42,"[2, 2, 1, ]",8/7

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