Effective action of beta-deformed N=4 SYM theory and AdS/CFT

We compute the one-loop effective action in \N=1 conformal SU(N) gauge theory which is an exactly marginal deformation of the \N=4 SYM theory. We consider an abelian background of constant \N = 1 gauge field and single chiral scalar. While for finite N the effective action depends non-trivially on the deformation parameter \beta, this dependence disappears in the large N limit if the parameter \beta is real. This conclusion matches the strong-coupling prediction coming from the form of a D3-brane probe action in the dual supergravity background: for the simplest choice of the D3-brane position the probe action happens to be the same as for a D3-brane in AdS_5 x S^5 placed parallel to the boundary of AdS_5. This suggests that in the real \beta deformation case there exists a large N non-renormalization theorem for the 4-derivative term in the action.Comment: 15 pages, no figures. V2: comments, reference added. V3: the version to appear in PR

On Low-Energy Effective Action in N=2 Super Yang-Mills Theories on Non-Abelian Background

We compute the non-holomorphic corrections to low-energy effective action (higher derivative terms) in N=2, SU(2) SYM theory coupled to hypermultiplets on a non-abelian background for a class of gauge fixing conditions. A general procedure for calculating the gauge parameters depending contributions to one-loop superfield effective action is developed. The one-loop non-holomorphic effective potential is exactly found in terms of Euler dilogarithm function for specific choice of gauge parameters.Comment: LaTeX, 21 pages, typos corrected and references adde

On Low-Energy Effective Actions in N = 2, 4 Superconformal Theories in Four Dimensions

We study some aspects of low-energy effective actions in 4-d superconformal gauge theories on the Coulomb branch. We describe superconformal invariants constructed in terms of N=2 abelian vector multiplet which play the role of building blocks for the N=2,4 supersymmetric low-energy effective actions. We compute the one-loop effective actions in constant N=2 field strength background in N=4 SYM theory and in N=2 SU(2) SYM theory with four hypermultiplets in fundamental representation. Using the classification of superconformal invariants we then find the manifestly N=2 superconformal form of these effective actions. While our explicit computations are done in the one-loop approximation, our conclusions about the structure of the effective actions in N=2 superconformal theories are general. We comment on some applications to supergravity - gauge theory duality in the description of D-brane interactions.Comment: 18 pages, latex, comments/reference adde

Anti-D3 branes and moduli in non-linear supergravity

Anti-D3 branes and non-perturbative effects in flux compactifications spontaneously break supersymmetry and stabilise moduli in a metastable de Sitter vacua. The low energy 4D effective field theory description for such models would be a supergravity theory with non-linearly realised supersymmetry. Guided by string theory modular symmetry, we compute this non-linear supergravity theory, including dependence on all bulk moduli. Using either a constrained chiral superfield or a constrained vector field, the uplifting contribution to the scalar potential from the anti-D3 brane can be parameterised either as an F-term or Fayet-Iliopoulos D-term. Using again the modular symmetry, we show that 4D non-linear supergravities that descend from string theory have an enhanced protection from quantum corrections by non-renormalisation theorems. The superpotential giving rise to metastable de Sitter vacua is robust against perturbative string-loop and $\alpha'$ corrections.Comment: 33 page