Wilson loop correlators in $$ \mathcal{N} $$ = 2 superconformal quivers

Abstract

We complete the program of [1] about perturbative approaches for $$ \mathcal{N} $$ N = 2 superconformal quiver theories in four dimensions. We consider several classes of observables in presence of Wilson loops, and we evaluate them with the help of supersymmetric localization. We compute Wilson loop vacuum expectation values, correlators of multiple coincident Wilson loops and one-point functions of chiral operators in presence of them acting as superconformal defects. We extend this analysis to the most general case considering chiral operators and multiple Wilson loops scattered in all the possible ways among the vector multiplets of the quiver. Finally, we identify twisted and untwisted observables which probe the orbifold of AdS5 × S5 with the aim of testing possible holographic perspectives of quiver theories in $$ \mathcal{N} $$ N = 2.

Localization vs holography in 4d $$ \mathcal{N} $$ = 2 quiver theories

“…In the quiver theories there are sectors of BPS protected observables that can be profitably studied with supersymmetric localization techniques [9,10]. Examples of such observables are the partition function and the expectation value of circular Wilson loops [11][12][13][14][15][16][17][18][19]. In this paper we focus on another class of observables, namely the 2-and 3-point functions of a set of single-trace scalar operators.…”

Three-point functions in a $\mathcal{N}=2$ superconformal gauge theory and their strong-coupling limit

“…Indeed, as originally shown in [2], a generic N = 2 SYM theory in flat space can be mapped to a matrix model defined on a 4-sphere and the functional path-integral can be reduced to a finite dimensional integration over the elements of a matrix. Using this approach, many interesting results have been obtained in particular when the N = 2 theory is superconformal 1 , like for example the Wilson loop vacuum expectation value [4][5][6][7][8][9][10][11], the chiral/anti-chiral correlators [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28], the correlators of chiral operators and Wilson loops [29][30][31][32][33], the free energy [34][35][36] and the Bremsstrahlung function [37][38][39][40][41]. In the weak-coupling regime it is possible to check at the first perturbative orders that the results obtained with the matrix model agree with those obtained with standard Feynman diagrams (see for example [4,19,22,42,…”

Defect correlators in a $\mathcal{N}=2$ SCFT at strong coupling

“…In the future it would be interesting to further investigate this feature and understand if it holds for different observables, such as correlation functions among one chiral operator and a circular Wilson loop in different representations of the gauge group or to correlators among a Wilson loop and two chiral scalar operators, which have been considered in [42,43] for N = 4 SYM. Furthermore it would be interesting to study the same defect correlation function in the context of the 4d N = 2 quiver gauge theory arising as a Z M orbifold of N = 4 SYM, this way extending the perturbative analysis initiated in [27]. Moreover, as it was shown in [15], in the case of structure constants of chiral primary operators, the holographic dual geometry of this circular quiver gauge theory is known and simple enough to allow explicit computations at the Supergravity level.…”