Abstract
As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625) of strong-coupling expansion of non-planar corrections in mathcal{N} = 2 4d superconformal models we consider two special theories with gauge groups SU(N) and Sp(2N). They contain N-independent numbers of hypermultiplets in rank 2 antisymmetric and fundamental representations and are planar-equivalent to the corresponding mathcal{N} = 4 SYM theories. These mathcal{N} = 2 theories can be realised on a system of N D3-branes with a finite number of D7-branes and O7-plane; the dual string theories should be particular orientifolds of AdS5 × S5 superstring. Starting with the localization matrix model representation for the mathcal{N} = 2 partition function on S4 we find exact differential relations between the 1/N terms in the corresponding free energy F and the frac{1}{2} -BPS Wilson loop expectation value leftlangle mathcal{W}rightrangle and also compute their large ’t Hooft coupling (λ » 1) expansions. The structure of these expansions is different from the previously studied models without fundamental hypermultiplets. In the more tractable Sp(2N) case we find an exact resummed expression for the leading strong coupling terms at each order in the 1/N expansion. We also determine the exponentially suppressed at large λ contributions to the non-planar corrections to F and leftlangle mathcal{W}rightrangle and comment on their resurgence properties. We discuss dual string theory interpretation of these strong coupling expansions.
Highlights
N -independent numbers of hypermultiplets in rank 2 antisymmetric and fundamental representations and are planar-equivalent to the corresponding N = 4 SYM theories
Starting with the localization matrix model representation for the N = 2 partition function on S4 we find exact differential relations between the 1/N terms in the corresponding free energy
As in the case of the SA-orientifold [4] the structure of the localization matrix model implies that the leading 1/N corrections to the Wilson loop expectation value can be expressed in terms of the corresponding corrections to the gauge theory free energy F (λ, N ) = − log Z on 4-sphere
Summary
Let us summarise the main results of this paper starting with the SU(N ) case. As in the case of the SA-orientifold [4] the structure of the localization matrix model implies that the leading 1/N corrections to the Wilson loop expectation value can be expressed in terms of the corresponding corrections to the gauge theory free energy F (λ, N ) = − log Z on 4-sphere. Similar relations between higher order 1/N terms Fn in free energy (1.21) and Wn in (1.28) are expected in general, with the dominant large λ term in Fn determining the strong coupling asymptotics of Wn. In particular, λ3/2 W3 = − 4! Combining the leading terms in (1.32), (1.33) and (1.34) suggests that the dominant (at each order in 1/N ) strong coupling terms in ∆ W in (1.28) exponentiate as This may be compared with similar exponentiation of the leading large λ terms in the N = 4 SYM case: as one finds from (1.1) in SU(N ) case [1] and from (1.29) in the Sp(2N ). 1 4 in the definition of λ g2 N YM (assuming one keeps only the leading large λ term at each order in 1/N ).
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