In the process of evaluating a "supersymmetric index", Bourget and Troost establish a rather elementary identity:
Nm∑d|Ngcd(d,m)∑l=1gcd[gcd(d,m),n+ldgcd(d,m)]
but later they compute this same supersymmetric index to be another formula:
N∑d|Ngcd[d,m,Nd,Nm,n]
and the finally they count it come other way and get yet another formula:
∑d|Nd−1∑t=0gcd[Ndm,Nmd,N(tm+nd)]
These formulae should be equivalent for any N,m,n with m dividing n... (and possibly other hypotheses missing) Is there a conceptual proof this result?
As a special case they show:
N∑d|N1=∑d|Nd∑l=1gcd(d,l)
The supersymmetrc index counts just about everthing in hep-th
- what could it be counting here?
I can venture a guess these have something to do with the Lie groups they mention:
(SU(N)/Zm)n
where the meaning of the n is unclear ( the paper says "dionic tilt"). In another section the Smith normal form is mentioned:
ZLZ≃n⨁i=1ZeiZ
This looks quite like the chinese remainder theorem
This post imported from StackExchange MathOverflow at 2016-06-23 20:58 (UTC), posted by SE-user john mangual