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

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

The Real Anatomy of Complex Linear Superfields

Recent work on classicication of off-shell representations of N-extended worldline supersymmetry without central charges has uncovered an unexpectedly vast number--trillions of even just (chromo)topology types--of so called adinkraic supermultiplets. Herein, we show by explicit analysis that a long-known but rarely used representation, the complex linear supermultiplet, is not adinkraic, cannot be decomposed locally, but may be reduced by means of a Wess-Zumino type gauge. This then indicates that the already unexpectedly vast number of adinkraic off-shell supersymmetry representations is but the proverbial tip of the iceberg.Comment: 21 pages, 4 figure

On 2D N=(4,4) superspace supergravity

We review some recent results obtained in studying superspace formulations of 2D N=(4,4) matter-coupled supergravity. For a superspace geometry described by the minimal supergravity multiplet, we first describe how to reduce to components the chiral integral by using ``ectoplasm'' superform techniques as in arXiv:0907.5264 and then we review the bi-projective superspace formalism introduced in arXiv:0911.2546. After that, we elaborate on the curved bi-projective formalism providing a new result: the solution of the covariant type-I twisted multiplet constraints in terms of a weight-(-1,-1) bi-projective superfield.Comment: 18 pages, LaTeX, Contribution to the proceedings of the International Workshop "Supersymmetries and Quantum Symmetries" (SQS'09), Dubna, July 29-August 3 200

Self-dual supersymmetric nonlinear sigma models

In four-dimensional N=1 Minkowski superspace, general nonlinear sigma models with four-dimensional target spaces may be realised in term of CCL (chiral and complex linear) dynamical variables which consist of a chiral scalar, a complex linear scalar and their conjugate superfields. Here we introduce CCL sigma models that are invariant under U(1) "duality rotations" exchanging the dynamical variables and their equations of motion. The Lagrangians of such sigma models prove to obey a partial differential equation that is analogous to the self-duality equation obeyed by U(1) duality invariant models for nonlinear electrodynamics. These sigma models are self-dual under a Legendre transformation that simultaneously dualises (i) the chiral multiplet into a complex linear one; and (ii) the complex linear multiplet into a chiral one. Any CCL sigma model possesses a dual formulation given in terms of two chiral multiplets. The U(1) duality invariance of the CCL sigma model proves to be equivalent, in the dual chiral formulation, to a manifest U(1) invariance rotating the two chiral scalars. Since the target space has a holomorphic Killing vector, the sigma model possesses a third formulation realised in terms of a chiral multiplet and a tensor multiplet. The family of U(1) duality invariant CCL sigma models includes a subset of N=2 supersymmetric theories. Their target spaces are hyper Kahler manifolds with a non-zero Killing vector field. In the case that the Killing vector field is triholomorphic, the sigma model admits a dual formulation in terms of a self-interacting off-shell N=2 tensor multiplet. We also identify a subset of CCL sigma models which are in a one-to-one correspondence with the U(1) duality invariant models for nonlinear electrodynamics. The target space isometry group for these sigma models contains a subgroup U(1) x U(1).Comment: 22 page

Conformal Invariance, N-extended Supersymmetry and Massless Spinning Particles in Anti-de Sitter Space

Starting with a manifestly conformal ($O(d,2)$ invariant) mechanics model in $d$ space and 2 time dimensions, we derive the action for a massless spinning particle in $d$-dimensional anti-de Sitter space. The action obtained possesses both gauge $N$-extended worldline supersymmetry and local $O(N)$ invarince. Thus we improve the old statement by Howe et al. that the spinning particle model with extended worldline supersymmetry admits only flat space-time background for $N > 2$ (spin greater one). The original $(d+2)$-dimensional model is characterized by rather unusual property that the corresponding supersymmetry transformations do not commute with the conformal ones, in spite of the explicit $O(d,2)$ invariance of the action.Comment: 13 pages, LaTe

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

Extended supersymmetric sigma models in AdS_4 from projective superspace

There exist two superspace approaches to describe N=2 supersymmetric nonlinear sigma models in four-dimensional anti-de Sitter (AdS_4) space: (i) in terms of N=1 AdS chiral superfields, as developed in arXiv:1105.3111 and arXiv:1108.5290; and (ii) in terms of N=2 polar supermultiplets using the AdS projective-superspace techniques developed in arXiv:0807.3368. The virtue of the approach (i) is that it makes manifest the geometric properties of the N=2 supersymmetric sigma-models in AdS_4. The target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations on the two-sphere of complex structures. The power of the approach (ii) is that it allows us, in principle, to generate hyperkahler metrics as well as to address the problem of deformations of such metrics. Here we show how to relate the formulation (ii) to (i) by integrating out an infinite number of N=1 AdS auxiliary superfields and performing a superfield duality transformation. We also develop a novel description of the most general N=2 supersymmetric nonlinear sigma-model in AdS_4 in terms of chiral superfields on three-dimensional N=2 flat superspace without central charge. This superspace naturally originates from a conformally flat realization for the four-dimensional N=2 AdS superspace that makes use of Poincare coordinates for AdS_4. This novel formulation allows us to uncover several interesting geometric results.Comment: 88 pages; v3: typos corrected, version published in JHE