We consider $mathcal{N}=2$ superconformal quiver gauge theories in four dimensions and evaluate the chiral/anti-chiral correlators of single-trace operators. We show that it is convenient to form particular twisted and untwisted combinations of these
operators suggested by the dual holographic description of the theory. The various twisted sectors are orthogonal and the correlators in each sector have always the same structure, as we show at the lowest orders in perturbation theory with Feynman diagrams. Using localization we then map the computation to a matrix model. In this way we are able to obtain formal expressions for the twisted correlators in the planar limit that are valid for all values of the t Hooft coupling $lambda$, and find that they are proportional to $1/lambda$ at strong coupling. We successfully test the correctness of our extrapolation against a direct numerical evaluation of the matrix model and argue that the $1/lambda$ behavior qualitatively agrees with the holographic description.
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 $AdS_{5}times S^{5}$. We analyze this gauge theory relying on the matrix model provided by localization a 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 $lambda$. 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 Pade resummations derived from very long perturbative series, that turn out to be extremely stable beyond the convergence disk $|lambda|<pi^2$ of the latter.
We study non-perturbative effects in supersymmetric U(N) gauge theories in eight dimensions realized by means of D(-1)/D7-brane systems with non-trivial world-volume fluxes turned on. Using an explicit string construction in terms of vertex operators
, we derive the action for the open strings ending on the D(-1)-branes and exhibit its BRST structure. The space of vacua for these open strings is shown to be in correspondence with the moduli space of generalized ADHM gauge connections which trigger the non-perturbative corrections in the eight-dimensional theory. These corrections are computed via localization and turn out to depend on the curved background used to localize the integrals on the instanton moduli space, and vanish in flat space. Finally, we show that for specific choices of the background the instanton partition functions reduce to weighted sums of the solid partitions of the integers.
We consider a class of N=2 conformal SU(N) SYM theories in four dimensions with matter in the fundamental, two-index symmetric and anti-symmetric representations, and study the corresponding matrix model provided by localization on a sphere S4, which
also encodes information on flat-space observables involving chiral operators and circular BPS Wilson loops. We review and improve known techniques for studying the matrix model in the large-N limit, deriving explicit expressions in perturbation theory for these observables. We exploit both recursive methods in the so-called full Lie algebra approach and the more standard Cartan sub-algebra approach based on the eigenvalue distribution. The sub-class of conformal theories for which the number of fundamental hypermultiplets does not scale with N differs in the planar limit from the N=4 SYM theory only in observables involving chiral operators of odd dimension. In this case we are able to derive compact expressions which allow to push the small t Hooft coupling expansion to very high orders. We argue that the perturbative series have a finite radius of convergence and extrapolate them numerically to intermediate couplings. This is preliminary to an analytic investigation of the strong coupling behavior, which would be very interesting given that for such theories holographic duals have been proposed.
We show that the Gukov-Witten monodromy defects of supersymmetric Yang-Mills theory can be realized in perturbative string theory by considering an orbifold background of the Kanno-Tachikawa type and placing stacks of fractional D3-branes whose world
-volume partially extends along the orbifold directions. In particular, we show that turning on a constant background value for some scalar fields in the closed string twisted sectors induces a non-trivial profile for the gauge field and one of the complex scalars of the world-volume theory, and that this profile exactly matches the singular behavior that one expects for a Gukov-Witten surface defect in the $mathcal{N}=4$ super Yang-Mills theory. To keep the presentation as simple as possible, in this work we restrict our analysis to surface defects corresponding to a $mathbb{Z}_2$ orbifold and defer the study of the most general case to a companion paper.
We consider the 1/2 BPS circular Wilson loop in a generic N=2 SU(N) SYM theory with conformal matter content. We study its vacuum expectation value, both at finite $N$ and in the large-N limit, using the interacting matrix model provided by localizat
ion results. We single out some families of theories for which the Wilson loop vacuum expectation values approaches the N=4 result in the large-N limit, in agreement with the fact that they possess a simple holographic dual. At finite N and in the generic case, we explicitly compare the matrix model result with the field-theory perturbative expansion up to order g^8 for the terms proportional to the Riemann value zeta(5), finding perfect agreement. Organizing the Feynman diagrams as suggested by the structure of the matrix model turns out to be very convenient for this computation.
We study the two-point correlation functions of chiral/anti-chiral operators in $N=2$ supersymmetric Yang-Mills theories on $R^4$ with gauge group SU(N) and $N_f$ massless hypermultiplets in the fundamental representation. We compute them in perturba
tion theory, using dimensional regularization up to two loops, and show that field-theory observables built out of dimensionless ratios of two-point renormalized correlators on $R^4$ are in perfect agreement with the same quantities computed using localization on the four-sphere, even in the non-conformal case $N_f ot=2N$.
We study half-BPS surface operators in four dimensional N=2 SU(N) gauge theories, and analyze their low-energy effective action on the four dimensional Coulomb branch using equivariant localization. We also study surface operators as coupled 2d/4d qu
iver gauge theories with an SU(N) flavour symmetry. In this description, the same surface operator can be described by different quivers that are related to each other by two dimensional Seiberg duality. We argue that these dual quivers correspond, on the localization side, to distinct integration contours that can be determined by the Fayet-Iliopoulos parameters of the two dimensional gauge nodes. We verify the proposal by mapping the solutions of the twisted chiral ring equations of the 2d/4d quivers onto individual residues of the localization integrand.
We consider conformal N=2 super Yang-Mills theories with gauge group SU(N) and Nf=2N fundamental hypermultiplets in presence of a circular 1/2-BPS Wilson loop. It is natural to conjecture that the matrix model which describes the expectation value of
this system also encodes the one-point functions of chiral scalar operators in presence of the Wilson loop. We obtain evidence of this conjecture by successfully comparing, at finite N and at the two-loop order, the one-point functions computed in field theory with the vacuum expectation values of the corresponding normal-ordered operators in the matrix model. For the part of these expressions with transcendentality zeta(3), we also obtain results in the large-N limit that are exact in the t Hooft coupling lambda.
We study half-BPS surface operators in 5d N=1 gauge theories compactified on a circle. Using localization methods and the twisted chiral ring relations of coupled 3d/5d quiver gauge theories, we calculate the twisted chiral superpotential that govern
s the infrared properties of these surface operators. We make a detailed analysis of the localization integrand, and by comparing with the results from the twisted chiral ring equations obtain constraints on the 3d and 5d Chern-Simons levels so that the instanton partition function does not depend on the choice of integration contour. For these values of the Chern-Simons couplings, we comment on how the distinct quiver theories that realize the same surface operator are related to each other by Aharony-Seiberg dualities.
