Non-perturbative studies of N=2 conformal quiver gauge theories

Abstract

We study N = 2 super-conformal field theories in four dimensions that correspond to mass-deformed linear quivers with n gauge groups and (bi-)fundamental matter. We describe them using Seiberg-Witten curves obtained from an M-theory construction and via the AGT correspondence. We take particular care in obtaining the detailed relation between the parameters appearing in these descriptions and the physical quantities of the quiver gauge theories. This precise map allows us to efficiently reconstruct the non-perturbative prepotential that encodes the effective IR properties of these theories. We give explicit expressions in the cases n = 1, 2, also in the presence of an Ω-background in the Nekrasov-Shatashvili limit. All our results are successfully checked against those of the direct microscopic evaluation of the prepotentialà la Nekrasov using localization methods.

Modular properties of surface operators in $$ \mathcal{N} $$ = 2 SU(2) SQCD

“…where q 0 = e πiτ 0 , such that τ 0 = θ π + 8πi g 2 is the bare complexified gauge coupling and f 0 is the prepotential in the massless limit. After adding the classical and the 1 loop terms to the instanton contribution obtained via the SW analysis (see [34] for example) which matches the localization results obtained in the previous section we have :…”

“…Let us first analyse the case when the masses of the flavours are set to zero. In this limit, the Gaiotto curve is such that φ 2 (t) takes the form [34]…”

“…We will now consider the case when all the masses are turned on. The Gaiotto form of the SW curve is still x 2 = φ 2 (t), where [34]:…”

Modular anomaly equations and S-duality in N = 2 $$ \mathcal{N}=2 $$ conformal SQCD

“…Skipping several intermediate steps which are similar to those described in [26], we find that the four dimensional SW curve for the SU(3) superconformal theory is…”

“…We engineer such a theory using the NS5 − D4 brane set up of Type IIA string theory [15], and closely follow the notations and conventions of [26].…”