Abstract
In the reduction of 4d dualities to 3d there are non-perturbative effects arising from monopoles acting as instantons. This mechanism has been reproduced in string theory by engineering the theories in a IIA brane setup. Nevertheless there are limiting cases of the 4d dualities where the dual theories are actually confined phases of the UV gauge theories. In these cases the monopoles are absent and the mechanism of reduction of the 4d duality has to be modified. In this paper we investigate such modification in the brane setup. The main observation behind our analysis is that in the 4d case the superpotential of the confined theories can been obtained also as the "exotic" contribution of a D0 brane, a stringy instanton. When considering these configurations we reproduce the field theory results in the brane setup. We study both the unitary and the symplectic case. As a further check we study the reduction of the 4d superconformal index to the 3d partition function for these theories.
Highlights
The main observation behind our analysis is that in the 4d case the superpotential of the confined theories can been obtained from the “exotic” contribution of a D0 brane, a stringy instanton
The stack of D(p+4) branes corresponds to the non-abelian gauge theory and the Dp branes reproduce the effect of the gauge instantons
The gauge instanton effect discussed above can be captured in a different way in string theory, without requiring to UV complete the confining phase to an SU(2) gauge theory
Summary
The main observation behind our analysis is that in the 4d case the superpotential of the confined theories can been obtained from the “exotic” contribution of a D0 brane, a stringy instanton. In this case there is a different prescription for the reduction to 3d [15, 16] and the effective IR confined theory on the circle has the same field content and superpotential of the 4d parent. The second term in (2.2) has been interpreted as a gauge instanton in field theory, by UV completing the s-confining phase to SU(N ) SQCD with N + 2 flavors.
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