Abstract
We consider the mathcal{N} = 2 SYM theory with gauge group SU(N) and a matter content consisting of one multiplet in the symmetric and one in the anti-symmetric representation. This conformal theory admits a large-N ’t Hooft expansion and is dual to a particular orientifold of AdS5 × S5. We analyze this gauge theory relying on the matrix model provided by localization à la Pestun. Even though this matrix model has very non-trivial interactions, by exploiting the full Lie algebra approach to the matrix integration, we show that a large class of observables can be expressed in a closed form in terms of an infinite matrix depending on the ’t Hooft coupling λ. These exact expressions can be used to generate the perturbative expansions at high orders in a very efficient way, and also to study analytically the leading behavior at strong coupling. We successfully compare these predictions to a direct Monte Carlo numerical evaluation of the matrix integral and to the Padé resummations derived from very long perturbative series, that turn out to be extremely stable beyond the convergence disk |λ| < π2 of the latter.
Highlights
Symmetry is present,1 this matrix model encodes information on the observables of the theory in flat space
This conformal theory admits a large-N ’t Hooft expansion and is dual to a particular orientifold of AdS5 × S5. We analyze this gauge theory relying on the matrix model provided by localization à la Pestun. Even though this matrix model has very nontrivial interactions, by exploiting the full Lie algebra approach to the matrix integration, we show that a large class of observables can be expressed in a closed form in terms of an infinite matrix depending on the ’t Hooft coupling λ
These exact expressions can be used to generate the perturbative expansions at high orders in a very efficient way, and to study analytically the leading behavior at strong coupling. We successfully compare these predictions to a direct Monte Carlo numerical evaluation of the matrix integral and to the Padé resummations derived from very long perturbative series, that turn out to be extremely stable beyond the convergence disk |λ| < π2 of the latter
Summary
Symmetry is present, this matrix model encodes information on the observables of the theory in flat space In this way the partition function and the vacuum expectation value of the BPS Wilson loop have been computed [1, 3,4,5,6,7,8]. The second approach, instead, keeps the matrix integral over the full Lie algebra and exploits recursion relations [18] to evaluate correlation functions This technique, originally developed because of its effectiveness at finite N , has been applied to study the large-N and the large-charge sectors of gauge theories [40,41,42,43].
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