Wandering in five-dimensional curved superspace

This is a brief review of the superspace formulation for five-dimensional N=1 matter-coupled supergravity recently developed by the authors.Comment: 10 pages, LaTeX, Contribution to the proceedings of the Third Workshop of the RTN project "Constituents, Fundamental Forces and Symmetries of the Universe," Valencia, October 1-5, 2007; V2: typo above eq. (26) correcte

Comments on N = 2 supersymmetric sigma models in projective superspace

For the most general off-shell N = 2 supersymmetric sigma model in projective superspace, we elaborate on its formulation in terms of N = 1 chiral superfields. A universal (model-independent) expression is obtained for the holomorphic symplectic two-form, which determines the second supersymmetry transformation. This two-form is associated with the two complex structures of the hyperkahler target space, which are complimentary to the one used to realize the target space as a Kahler manifold.Comment: 7 pages; V2: reference [18] correcte

Exact propagators in harmonic superspace

Within the background field formulation in harmonic superspace for quantum N = 2 super Yang-Mills theories, the propagators of the matter, gauge and ghost superfields possess a complicated dependence on the SU(2) harmonic variables via the background vector multiplet. This dependence is shown to simplify drastically in the case of an on-shell vector multiplet. For a covariantly constant background vector multiplet, we exactly compute all the propagators. In conjunction with the covariant multi-loop scheme developed in hep-th/0302205, these results provide an efficient (manifestly N = 2 supersymmetric) technical setup for computing multi-loop quantum corrections to effective actions in N = 2 supersymmetric gauge theories, including the N = 4 super Yang-Mills theory.Comment: Latex, 12 pages; V2: a reference added; V3: typos in eq. (3) corrected, the version to appear in PLB; V4: typos in eq. (47) correcte

Relaxed super self-duality and effective action

A closed-form expression is obtained for a holomorphic sector of the two-loop Euler-Heisenberg type effective action for N = 2 supersymmetric QED derived in hep-th/0308136. In the framework of the background-field method, this sector is singled out by computing the effective action for a background N = 2 vector multiplet satisfying a relaxed super self-duality condition. The approach advocated in this letter can be applied, in particular, to the study of the N = 4 super Yang-Mills theory on its Coulomb branch.Comment: 8 pages, latex; V2: comments, references added, typos correcte

Supersymmetric Nonlinear Sigma Model in AdS_5

We construct the supersymmetric nonlinear sigma model in a fixed AdS_5 background. We use component fields and find that the complex bosons must be the coordinates of a hyper-Kahler manifold that admits a Killing vector satisfying an inhomogeneous tri-holomorphic condition. We propose boundary conditions that map the on-shell bulk hypermultiplets into off-shell chiral multiplets on 3-branes that foliate the bulk. The supersymmetric AdS_5 isometries reduce to superconformal transformations on the brane fields.Comment: Latex, 7 pages. Published versio

On N = 2 supergravity and projective superspace: Dual formulations

The superspace formulation for four-dimensional N = 2 matter-coupled supergravity recently developed in arXiv:0805.4683 makes use of a new type of conformal compensator with infinitely many off-shell degrees of freedom: the so-called covariant weight-one polar hypermultiplet. In the present note we prove the duality of this formulation to the known minimal (40+40) off-shell realization for N = 2 Poincare supergravity involving the improved tensor compensator. Within the latter formulation, we present new off-shell matter couplings realized in terms of covariant weight-zero polar hypermultiplets. We also elaborate upon the projective superspace description of vector multiplets in N = 2 conformal supergravity. An alternative superspace representation for locally supersymmetric chiral actions is given. We present a model for massive improved tensor multiplet with both ``electric'' and ``magnetic'' types. of mass terms.Comment: 18 pages, LaTeX, no figures; V2: typos corrected, comments adde

Self-dual effective action of N = 4 SYM revisited

More evidence is provided for the conjectured correspondence between the D3-brane action in AdS_5 x S^5 and the low-energy effective action for N = 4 SU(N) SYM on its Coulomb branch, where the gauge group SU(N) is spontaneously broken to SU(N-1) x U(1) and the dynamics is described by a single N = 2 vector multiplet corresponding to the U(1) factor of the unbroken group. Using an off-shell formulation for N = 4 SYM in N = 2 harmonic superspace, within the background-field quantization scheme we compute the two-loop quantum correction to a holomorphic sector of the effective action, which is a supersymmetric completion of interactions of the form \Omega ((F^+)^2 |Y|^{-4}) (F^+)^2(F^-)^2 |Y|^{-4}, with F^\pm the (anti) self-dual components of the U(1) gauge field strength, and Y the complex scalar belonging to the vector multiplet. In the one-loop approximation, \Omega was shown in hep-th/9911221 to be constant. It is demonstrated in the present paper that \Omega \propto (F^+)^2 |Y|^{-4} at the two-loop order. The corresponding coefficient proves to agree with the F^6 coefficient in the D3-brane action, after implementing the nonlinear field redefinition which was sketched in hep-th/9810152 and which relates the N = 2 vector multiplet component fields with those living on the D3-brane. In the approximation considered, our results are consistent with the conjecture of hep-th/9810152 that the N = 4 SYM effective action is self-dual under N = 2 superfield Legendre transformation, and also with the stronger conjecture of hep-th/0001068 that it is self-dual under supersymmetric U(1) duality rotations.Comment: 0+37 pages, 1 figure, latex; V2: references, comments added; V3: comments, references adde

Three-dimensional (p,q) AdS superspaces and matter couplings

We introduce N-extended (p,q) AdS superspaces in three space-time dimensions, with p+q=N and p>=q, and analyse their geometry. We show that all (p,q) AdS superspaces with X^{IJKL}=0 are conformally flat. Nonlinear sigma-models with (p,q) AdS supersymmetry exist for p+q4 the target space geometries are highly restricted). Here we concentrate on studying off-shell N=3 supersymmetric sigma-models in AdS_3. For each of the cases (3,0) and (2,1), we give three different realisations of the supersymmetric action. We show that (3,0) AdS supersymmetry requires the sigma-model to be superconformal, and hence the corresponding target space is a hyperkahler cone. In the case of (2,1) AdS supersymmetry, the sigma-model target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations of the two-sphere of complex structures.Comment: 52 pages; V3: minor corrections, version published in JHE