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

We apply the localization technique to compute the free energy on four-sphere and the circular BPS Wilson loop in the four-dimensional $$ \mathcal{N} $$ N = ∈ superconformal Sp(2N) gauge theory containing vector multiplet coupled to four hypermultiplets in fundamental representation and one hypermultiplet in rank-2 antisymmetric representation. This theory is unique among similar $$ \mathcal{N} $$ N = ∈ superconformal models that are planar-equivalent to $$ \mathcal{N} $$ N = ∆ SYM in that the corresponding localization matrix model has the interaction potential containing single-trace terms only. We exploit this property to show that, to any order in large N expansion and an arbitrary ’t Hooft coupling λ, the free energy and the Wilson loop satisfy Toda lattice equations. Solving these equations at strong coupling, we find remarkably simple expressions for these observables which include all corrections in 1/N and 1/$$ \sqrt{\lambda } $$ λ . We also compute the leading exponentially suppressed $$ \mathcal{O}\left({e}^{-\sqrt{\lambda }}\right) $$ O e − λ corrections and consider a generalization to the case when the fundamental hypermultiplets have a non-zero mass. The string theory dual of this $$ \mathcal{N} $$ N = ∈ gauge theory should be a particular orientifold of AdS5 × S5 type IIB string and we discuss the string theory interpretation of the obtained strong-coupling results.

Section: Jhep01(2023)037mentioning

confidence: 99%

Section: Jhep01(2023)037mentioning

confidence: 99%

See 1 more Smart Citation

Exact strong coupling results in $$ \mathcal{N} $$ = 2 Sp(2N) superconformal gauge theory from localization

Beccaria

Korchemsky

Tseytlin

2023

“…Also the 2-and 3-point functions of single-trace scalar operators of the quiver theories can be studied at strong coupling. In fact, building on previous works that developed matrix-model techniques to study correlations functions in superconformal gauge theories [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], it has been shown in [40,41] that the 2-and 3-point functions of single-trace scalar operators in the planar limit can be written in terms of the elements of a Bessel operator at all values of the coupling constant. Exploiting these results, it is possible to find in an analytic way the leading behavior at strong coupling of these correlators and show that the corresponding normalized structure constants precisely agree with the predictions of the AdS/CFT correspondence in a Z M orbifold background [40,41].…”

Section: Jhep01(2023)119mentioning

confidence: 99%

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

Billó

Frau

Lerda

et al. 2023

Self Cite

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.

“…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].…”

Section: Ymmentioning

confidence: 99%

A derivation of the planar limit of $$ \mathcal{N} $$ = 2 chiral correlators

Fiol

Fukelman

2022

We derive analytically the terms of maximal transcendentality of the planar 2- and 3-point functions of single-trace chiral primary operators of $$ \mathcal{N} $$ N = 2 SQCD on ℝ4, to all orders in the ’t Hooft coupling. These results prove two conjectures we formulated in previous work. Furthermore, we also provide an explicit expression for the terms in the planar 2-point functions of these operators that contain products of two values of the ζ function.