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The purpose of this article is to demonstrate that i) the framework ofelliptic hypergeometric integrals (EHIs) can be extended by input fromsupersymmetric gauge theory, and ii) analyzing the hyperbolic limit of the EHIsin the extended framework leads to a rich structure containing sharpmathematical problems of interest to supersymmetric quantum field theorists.Both of the above items have already been discussed in the theoretical physicsliterature. Item i was demonstrated by Dolan and Osborn in 2008. Item ii wasdiscussed in the present author's Ph.D. Thesis in 2016, wherein crucialelements were borrowed from the 2006 work of Rains on the hyperbolic limit ofcertain classes of EHIs. This article contains a concise review of thesedevelopments, along with minor refinements and clarifying remarks, writtenmainly for mathematicians interested in EHIs. In particular, we work with arepresentation-theoretic definition of a supersymmetric gauge theory, so thatreaders without any background in gauge theory - but familiar with therepresentation theory of semi-simple Lie algebras - can follow the discussion.

The Hyperbolic Asymptotics of Elliptic Hypergeometric Integrals Arising in Supersymmetric Gauge Theory