We use fractional and wrapped branes to describe perturbative and non-perturbative properties of N = 1 super Yang-Mills living on their world-volume.

We obtain the supergravity dual of N = 1 gauge theory in 2+1 dimensions with a large number of unquenched massless flavors. The geometries found are obtained by solving the equations of motion of supergravity coupled to a suitable continuous distribution of flavor branes. The background obtained preserves two supersymmetries. We find that when N c ≥ 2N f the behavior of the solutions is compatible with having an asymptotically free dual gauge theory with dynamical quarks. On the contrary, when N c < 2N f the theory develops a Landau pole in the UV. We also find a new family of (unflavored) backgrounds generated by D5-branes that wrap a three-cycle of a cone with G 2 holonomy. 1 canoura@fpaxp1.usc.es 2 merlatti@fpaxp1.usc.es 3 alfonso@fpaxp1.usc.es

In this paper we investigate three-dimensional superconformal gauge theories with 𝒩 = 3 supersymmetry. Independently from specific models, we derive the shortening conditions for unitary representations of the Osp(3|4) superalgebra and we express them in terms of differential constraints on three-dimensional 𝒩 = 3 superfields. We find a ring structure underlying these short representations, which is just the direct generalization of the chiral ring structure of 𝒩 = 2 theories. When the superconformal field theory is realized on the worldvolume of an M2-brane such a superfield ring is the counterpart of the ring defined by the algebraic geometry of the eight-dimensional cone transverse to the brane. This and other arguments identify the 𝒩 = 3 superconformal field theory dual to M-theory compactified on AdS4×N0,1,0. It is an 𝒩 = 3 gauge theory with SU(N)×SU(N) gauge group coupled to a suitable set of hypermultiplets, with an additional Chern-Simons interaction. The AdS/CFT correspondence can be verified directly using the recently worked out Kaluza-Klein (KK) spectrum of N0,1,0 and we find a perfect match. We also note that besides the usual set of BPS conformal operators dual to the lightest KK states, we find that the composite operators corresponding to certain massive KK modes are organized into a massive spin-3/2 𝒩 = 3 multiplet that might be identified with the super-Higgs multiplet of a spontaneously broken 𝒩 = 4 theory. We investigate this intriguing and inspiring feature in a separate paper.

We refine the dictionary of the gauge/gravity correspondence realizing N = 1 super Yang-Mills by means of D5-branes wrapped on a resolved Calabi-Yau space. This is done by fixing an ambiguity on the correct interpretation of the holographic dual of the running gauge coupling and amounts to identify a specific 2-cycle in the dual ten-dimensional supergravity background. In doing so, we also discuss the role played in this context by gauge transformations in the relevant seven-dimensional gauged supergravity. While all nice properties of the duality are maintained, this modification of the dictionary has some interesting physical consequences and solves a puzzle recently raised in the literature. In this refined framework, it is also straightforward to see how the correspondence naturally realizes a geometric transition.

We study duals to field theories in two dimensions with N = (4, 4) SUSY. The string backgrounds reproduce certain non-perturbative aspects of the dual field theory with a large number of colors N c and a tunable number of flavors N f . Different aspects of the twodimensional field theory are discussed, among them the running of gauge couplings, the spectrum of mesons in Higgs and Coulomb branches, entanglement entropy and the nonrelativistic version of our string backgrounds.