Strong coupling expansions in $$ \mathcal{N} $$ = 2 quiver gauge theories

Abstract

We study the 3-point functions of gauge-invariant scalar operators in four dimensional $$ \mathcal{N} $$ N = 2 superconformal quiver theories using supersymmetric localization in the planar limit of a large number of colors. By exploiting a web of nontrivial relations, we show that the 3-point functions can be expressed in terms of the 2-point functions through exact Ward-like identities that are valid for all values of the coupling constant. In this way, using recent results about the 2-point functions, we are able to obtain the asymptotic strong-coupling expansion of the 3-point functions and of the corresponding structure constants in the planar limit. Our results extend to sub-leading orders what has been recently found at leading order, where a precise match with calculations within the AdS/CFT correspondence at the supergravity level is possible. Therefore, our findings can be interpreted also as a prediction for the sub-leading string corrections to these holographic calculations.

Wilson loop correlators at strong coupling in $$ \mathcal{N} $$ = 2 quiver gauge theories

“…It would also be interesting to examine the subleading corrections in the coupling in the planar limit of the theory, as already done for 2-and 3-point functions of chiral scalar operators, the v.e.v of a Wilson loop and the free energy [8,32]. In order to determine these contributions, the knowledge of the subleading orders of the generating function G(s α , ℓ, x), defined in (B.33), are required.…”

“…However, more recently, mainly by exploiting supersymmetric localization techniques [1] also the strong coupling regime of some N = 2 gauge theories in the large-N limit has been investigated. In the context of theories with eight supercharges many BPS observables have been analysed using localization techniques both at weak and strong coupling, such as correlation functions between chiral/anti-chiral scalar operators [2][3][4][5][6][7][8][9][10][11][12], correlators between a chiral operator and a Wilson loop [13][14][15][16][17], the vacuum expectation value of BPS Wilson loops [18][19][20] and the free energy [21][22][23][24].…”

“…This is the X-matrix, a semi-infinite matrix whose elements are a convolution of Bessel functions of the first kind. As a matter of fact, as shown in [8,29,30,32], it is possible to express the partition function, and also 2-and 3-point functions of chiral scalar operators, in terms of this semi-infinite matrix. Furthermore, in recent papers [8,32] the features of the X-matrix have been employed to work out a systematic strong coupling expansion in inverse powers of the't Hooft coupling.…”

“…of a single Wilson loop. Instead, one of the main novelty of this work is that we only concentrate on the orbifold fixed point of the theory where, as mentioned above, the strong coupling regime of the theory can be successfully investigated using supersymmetric localization and the techniques of [8,32]. Moreover, following the analysis carried out in [28] for chiral/anti-chiral operators, it turns out to be convenient to introduce a new basis of Wilson loop operators, namely, generalizing [15,38], we consider untwisted and twisted combinations of the Wilson loops associated to the different nodes of the quiver.…”

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

“…This way the computation of the vacuum expectation value of an observable in the N = 2 SYM theory which, in principle, should be performed by computing an infinite dimensional path integral, can be carried out via the evaluation of a finite dimensional integration over the elements of a matrix. When the N = 2 theory is conformal, this method led to several results such as the computation of correlation functions among chiral and anti-chiral scalar operators [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], the vacuum expectation value of Wilson loops [17][18][19][20][21][22] and the free energy of the theory [23,24].…”