Non-perturbative gauge/gravity correspondence in $ \mathcal{N} $ = 2 theories

Abstract

We derive the exact supergravity profile for the twisted scalar field emitted by a system of fractional D3 branes at a Z 2 orbifold singularity supporting N = 2 quiver gauge theories with unitary groups and bifundamental matter. At the perturbative level this twisted field is "dual" to the gauge coupling but it is corrected non-perturbatively by an infinite tower of fractional D-instantons. The explicit microscopic description allows to derive the gravity profile from disk amplitudes computing the emission rate of the twisted scalar field in terms of chiral correlators in the dual gauge theory. We compute these quantum correlators using multi-instanton localization techniques and/or Seiberg-Witten analysis. Finally, we discuss a non-perturbative relation between the twisted scalar and the effective coupling of the gauge theory for some simple choices of the brane set ups.

S-duality and the prepotential of N = 2 ⋆ $$ \mathcal{N}={2}^{\star } $$ theories (II): the non-simply laced algebras

“…The columns display, respectively, the moduli in a ADHM-like notation organized as supersymmetric pairs, their statistics, their transformation properties with respect to the gauge and instanton symmetry groups and finally Q 2 -eigenvalues λ φ , where Q is the supersymmetry charge used in the localization approach. See also [30] where similar tables have been given for other brane systems.…”

Resumming instantons in 𝒩 = 2* theories with arbitrary gauge groups

“…These proceedings are based on the papers 1 where we studied N = 2 SYM theories with a gauge algebra g ∈ {Ã r , B r , C r , D r , E 6,7,8 , F 4 , G 2 }, extending previous results obtained in 2 for the unitary groups. a Our motivation is to shed light on the general structure of N = 2 SYM theories at low energy and show that the constraints imposed by S-duality take the form of a recursion relation which allows one to determine the prepotential at a non-perturbative level and resum all instanton contributions.…”

“…where α L and α S are, respectively, the long and the short roots of g. For the root system Ψ g , we follow the standard conventions 1 (see also the Appendix), so that n g = 1 for g =Ã r , D r , E 6,7,8 , n g = 2 for g = B r , C r , F 4 ,…”

Chiral trace relations in Ω-deformed N = 2 $$ \mathcal{N}=2 $$ theories

“…The deformed partition function as well the chiral traces may be computed systematically by localization, see for instance [93] and references therein. Here, we briefly discuss the illustrative case of the N = 2 * gauge theory with gauge group U(N ).…”