Abstract
We study the integral Bailey lemma associated with the An-root system and identities for elliptic hypergeometric integrals generated thereby. Interpreting integrals as superconformal indices of four-dimensional mathcal{N} = 1 quiver gauge theories with the gauge groups being products of SU(n + 1), we provide evidence for various new dualities. Further confirmation is achieved by explicitly checking that the ‘t Hooft anomaly matching conditions holds. We discuss a flavour symmetry breaking phenomenon for supersymmetric quantum chromodynamics (SQCD), and by making use of the Bailey lemma we indicate its manifestation in a web of linear quivers dual to SQCD that exhibits full s-confinement.
Highlights
In many cases these dualities can be understood from the point of view of symmetries of higher-dimensional theories
We study the integral Bailey lemma associated with the An-root system and identities for elliptic hypergeometric integrals generated thereby
We discuss a flavour symmetry breaking phenomenon for supersymmetric quantum chromodynamics (SQCD), and by making use of the Bailey lemma we indicate its manifestation in a web of linear quivers dual to SQCD that exhibits full s-confinement
Summary
For general n it was defined in [13] Following these works we shall call the functions β(w, t) and α(z, t) a Bailey pair with respect to the parameter t, if they are related to each other as β(w, t) = M (t)wzα(z, t). After the substitution of explicit expressions for the operators, change of the integration orders on the left-hand side (i.e. integrating first over the “internal” variable z), one can see that the relation (2.6) is true due to the following An-elliptic beta integral evaluation formula proposed in [15]. Yields the left- and right-hand sides of the elliptic beta integral (2.7) after dividing by we do not obtain a proof of the explicit integral evaluation formula, since it was used already for proving the Bailey lemma itself.
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