Modified elliptic gamma functions and 6d superconformal indices
  We construct a modified double elliptic gamma function which is well defined when one of the base parameters lies on the unit circle. A model consisting of 6d hypermultiplets coupled to a gauge field theory living on a 4d defect is proposed whose superconformal index uses the double elliptic gamma function and obeys W(E7)-group symmetry. 
V. P. Spiridonov
hep-th