Strong coupling expansions in N = 2 quiver gauge theories

We study the 3-point functions of gauge-invariant scalar operators in four dimensional N= 2 superconformal quiver theories using supersymmetric localization in the planar limit of a large number of colors. By exploiting a web of nontrivial relations, we show that the 3-point functions can be expressed in terms of the 2-point functions through exact Ward-like identities that are valid for all values of the coupling constant. In this way, using recent results about the 2-point functions, we are able to obtain the asymptotic strong-coupling expansion of the 3-point functions and of the corresponding structure constants in the planar limit. Our results extend to sub-leading orders what has been recently found at leading order, where a precise match with calculations within the AdS/CFT correspondence at the supergravity level is possible. Therefore, our findings can be interpreted also as a prediction for the sub-leading string corrections to these holographic calculations

Stringy instanton corrections to N=2 gauge couplings

We discuss a string model where a conformal four-dimensional N=2 gauge theory receives corrections to its gauge kinetic functions from "stringy" instantons. These contributions are explicitly evaluated by exploiting the localization properties of the integral over the stringy instanton moduli space. The model we consider corresponds to a setup with D7/D3-branes in type I' theory compactified on T4/Z2 x T2, and possesses a perturbatively computable heterotic dual. In the heteoric side the corrections to the quadratic gauge couplings are provided by a 1-loop threshold computation and, under the duality map, match precisely the first few stringy instanton effects in the type I' setup. This agreement represents a very non-trivial test of our approach to the exotic instanton calculus.Comment: 63 pages, 5 figures. V2: final version with minor corrections published on JHEP05(2010)10

Recent progress in the effective string theory description of LGTs.

In presence of a static pair of sources, the spectrum of low-lying states of any confining gauge theory in D space-time dimensions is described, at large source separations, by an effective string theory. Recently two important advances improved our understanding of this effective theory. First, it was realized that the form of the effective action is strongly constrained by the requirement of the Lorentz invariance of the gauge theory, which is spontaneously broken by the formation of a long confining flux tube in the vacuum. This constraint is strong enough to fix uniquely the first few subleading terms of the action. Second, it has been realized that the first of these allowed terms - a quartic polynomial in the field derivatives - is exactly the composite field $T\bar{T}$, built with the chiral components, $T$ and $\bar{T}$, of the energy-momentum tensor of the 2d QFT describing the infrared limit of the effective string. This irrelevant perturbation is quantum integrable and yields, through the thermodynamic Bethe Ansatz (TBA), the energy levels of the string which exactly coincide with the Nambu-Goto spectrum. In this talk we first review the general implications of these two results and then, as a test of the power of these methods, use them to construct the first few boundary corrections to the effective string action.Comment: Presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

Flux interactions on D-branes and instantons

We provide a direct world-sheet derivation of the couplings of NS-NS and R-R fluxes to various types of D-branes (including instantonic ones) by evaluating disk amplitudes among two open string vertex operators at a generic brane intersection and one closed string vertex representing the background fluxes. This world-sheet approach is in full agreement with the derivation of the flux couplings in the brane effective actions based on supergravity methods, but it is applicable also to more general brane configurations involving fields with twisted boundary conditions. As an application, we consider an orbifold compactification of Type IIB string theory with fractional D-branes preserving N=1 supersymmetry and study the flux-induced fermionic mass terms both on space-filling branes and on instantonic ones. Our results show the existence of a relation between the soft supersymmetry breaking and the lifting of some instanton fermionic zero-modes, which may lead to new types of non-perturbative couplings in brane-world models.Comment: 48 pages, 2 figures. One reference and some comments adde

Instanton effects in N=1 brane models and the Kahler metric of twisted matter

We consider locally consistent systems of magnetized D9 branes on an orbifolded six-torus which support N=1 gauge theories. In such realizations, the matter multiplets arise from "twisted" strings connecting different stacks of branes. The introduction of Euclidean 5 branes (E5) wrapped on the six-dimensional compact space leads to instanton effects. For instance, if the system is engineered so as to yield SQCD, a single E5 brane may account for the ADS/TVY superpotential. We discuss the subtle interplay that exists between the annuli diagrams with an E5 boundary and the holomorphicity properties of the effective low-energy action of the N=1 theory. The consistency of this picture allows to obtain information on the Kahler metric of the chiral matter multiplets arising from twisted strings.Comment: 33 pages, 4 figures. V2: improved discussion, clarifyng comments and references added. Version to be published in JHE

Instantons in N=2 magnetized D-brane worlds

In a toroidal orbifold of type IIB string theory we study instanton effects in N=2 super Yang-Mills theories engineered with systems of wrapped magnetized D9 branes and Euclidean D5 branes. We analyze the various open string sectors in this brane system and study the 1-loop amplitudes described by annulus diagrams with mixed boundary conditions, explaining their role in the stringy instanton calculus. We show in particular that the non-holomorphic terms in these annulus amplitudes precisely reconstruct the appropriate Kahler metric factors that are needed to write the instanton correlators in terms of purely holomorphic variables. We also explicitly derive the correct holomorphic structure of the instanton induced low energy effective action in the Coulomb branch.Comment: 40 pages, 5 figures, JHEP class. Some footnotes added and typos corrected. Version published in JHE

Non-perturbative effective interactions from fluxes

Motivated by possible implications on the problem of moduli stabilization and other phenomenological aspects, we study D-brane instanton effects in flux compactifications. We focus on a local model and compute non-perturbative interactions generated by gauge and stringy instantons in a N = 1 quiver theory with gauge group U(N_0) x U(N_1) and matter in the bifundamentals. This model is engineered with fractional D3-branes at a C^3/(Z_2 x Z_2) singularity, and its non-perturbative sectors are described by introducing fractional D-instantons. We find a rich variety of instanton-generated F- and D-term interactions, ranging from superpotentials and Beasley-Witten like multi-fermion terms to non-supersymmetric flux-induced instanton interactions.Comment: 37 pages, 7 figures. Final version published on JHEP. Section 4 modified in several points regarding string corrections in absence of fluxes; in particular, section 4.3 is removed. Some other minor changes and two references adde

N=4 Versus N=2 Phases, Hyperk\"Ahler Quotients and the 2D Topological Twist

We consider N=2 and N=4 supersymmetric gauge theories in two-dimensions, coupled to matter multiplets. In analogy with the N=2 case also in the N=4 case one can introduce Fayet-Iliopoulos terms.The associated three-parameters have the meaning of momentum-map levels in a HyperK\"ahler quotient construction. Differently from the N=2 case, however, the N=4 has a single phase corresponding to an effective $\sigma$-model. There is no Landau-Ginzburg phase. The main possible application of our N=4 model is to an effective Lagrangian construction of a $\sigma$-model on ALE-manifolds. We discuss the A and B topological twists of these models clarifying some issues not yet discussed in the literature, in particular the identification of the topological systems emerging from the twist. Applying our results to the case of ALE-manifolds we indicate how one can use the topologically twisted theories to study the K\"ahler class and complex structure deformations of these gravitational instantons.Comment: plain Latex, 77 pages, SISSA/151/93/E