Abstract
We consider mathcal{N} = 2 superconformal quiver gauge theories in four dimensions and evaluate the chiral/anti-chiral correlators of single-trace operators. We show that it is convenient to form particular twisted and untwisted combinations of these operators suggested by the dual holographic description of the theory. The various twisted sectors are orthogonal and the correlators in each sector have always the same structure, as we show at the lowest orders in perturbation theory with Feynman diagrams. Using localization we then map the computation to a matrix model. In this way we are able to obtain formal expressions for the twisted correlators in the planar limit that are valid for all values of the ‘t Hooft coupling λ, and find that they are proportional to 1/λ at strong coupling. We successfully test the correctness of our extrapolation against a direct numerical evaluation of the matrix model and argue that the 1/λ behavior qualitatively agrees with the holographic description.
Highlights
Localization allows one to map the partition function and other protected observables of a supersymmetric gauge theory defined on a four-sphere to quantities in a matrix model [3]; when the quantum theory is conformal, this matrix model captures the corresponding observables in flat space
We successfully test the correctness of our extrapolation against a direct numerical evaluation of the matrix model and argue that the 1/λ behavior qualitatively agrees with the holographic description
While the matrix model associated to the N = 4 SYM theory is Gaussian, the one for N = 2 theories has a complicated potential with contributions at any order in the gauge coupling constant g
Summary
Localization allows one to map the partition function and other protected observables of a supersymmetric gauge theory defined on a four-sphere to quantities in a matrix model [3]; when the quantum theory is conformal, this matrix model captures the corresponding observables in flat space. In the specific instance of orientifold theory with gauge group SU(N ) and matter in the symmetric and anti-symmetric representations, which was dubbed E theory in [15], significant progress has been made in extracting exact results from the localization matrix model in the large-N limit and in exploring the strong-coupling regime [46,47,48,49]. In the weak-coupling regime, the constituent fields of the quiver theories can be given a simple interpretation in terms of open strings attached to fractional D3- branes in the orbifold background [23]; the adjoint fields arise from open strings starting and ending on the same fractional brane, while the bi- fundamental matter field correspond to open string stretching between two different branes This open-string description has a closed-string counterpart in terms of boundary states (for a review see for instance [51]). Rather we consider (un)twisted combinations which are precisely constructed according to the Cardy formula
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