Strong-coupling results for $\mathcal{N}=2$ superconformal quivers and holography

Abstract

We consider 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.

The planar limit of the $\mathcal{N} = 2$ $\mathbf{E}$-theory: numerical calculations and the large $λ$ expansion

“…The result of this procedure is fairly complicated and we do not present it explicitly here. Finally, inserting χ 2k+1 (x) into equation (3.13) gives D kl as a series in µ: 15 .…”

“…5 11.64760271190(0±6) e 10 15.5647287113(94±21) e 10. 5 20.6471553368(9±4) e 11 27.225974672885(68±15) e 11.5 35.726290419555(6±8) e 12 46.69392596735(85±24) e 12.5 60.8297166581(16±11) e 13 79.033540756198(14±11) e 13.5 102.460855469831(90±14) e 14 132.595289990373(00±26) e 14.5 171.34185630862(66±11) e 15 221.1466338982(52±31) e 15.5 285.1504476051873(00±31) e 16 367.3861937408442(07±28) Table 5: The numerical values of F that we used for numerical fitting. The range of our sampling points is (0, L), where in practice we take L = 12000.…”

“…There are two localization schemes in the literature; in this paper we use the full Lie algebra localization[3,15,9,13,11].…”

The planar limit of $$ \mathcal{N} $$ = 2 chiral correlators

“…More specifically, it was argued in [5,6] that supersymmetric localization reduces the evaluation of closely related n-point functions on S 4 to matrix model computations; then, a Gram-Schmidt orthogonalization procedure applied to these S 4 correlators yields the correlators on R 4 [7][8][9][10][11][12]. Other approaches use the 4d analog [1] of the tt ˚equations [13][14][15][16], the large R-charge expansion [17][18][19][20][21][22][23] or holography [24,25].…”

Wilson loops in Large Symmetric Representations through a Double-Scaling Limit

“…In particular, it would be interesting to study the double-scaling limit for Wilson loops in symmetric representations in quiver gauge theories, also including correlation functions involving CPO's. Such correlation functions can be computed from a matrix model [43] and it would be interesting to study its potential applications to Wilson loops.…”