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We study the off-shell structure of the two-loop effective action in 6D, N = (1, 1) supersymmetric gauge theories formulated in N = (1, 0) harmonic superspace. The off-shell effective action involving all fields of 6D, N = (1, 1) supermultiplet is constructed by the harmonic superfield background field method, which ensures both manifest gauge covariance and manifest N = (1, 0) supersymmetry. We analyze the off-shell divergences dependent on both gauge and hypermultiplet superfields and argue that the gauge invariance of the divergences is consistent with the non-locality in harmonics. The two-loop contributions to the effective action are given by harmonic supergraphs with the background gauge and hypermultiplet superfields. The procedure is developed to operate with the harmonic-dependent superpropagators in the two-loop supergraphs within the superfield dimensional regularization. We explicitly calculate the gauge and the hypermultiplet-mixed divergences as the coefficients of 1 ε 2 and demonstrate that the corresponding expressions are non-local in harmonics. [ABSTRACT FROM AUTHOR]

We develop a novel bi-harmonic N = 4 superspace formulation of the N = 4 supersymmetric Yang-Mills theory (SYM) in four dimensions. In this approach, the N = 4 SYM superfield constraints are solved in terms of on-shell N = 2 harmonic superfields. Such an approach provides a convenient tool of constructing the manifestly N = 4 supersymmetric invariants and further rewriting them in N = 2 harmonic superspace. In particular, we present N = 4 superfield form of the leading term in the N = 4 SYM effective action which was known previously in N = 2 superspace formulation. [ABSTRACT FROM AUTHOR]

We elaborate on the low-energy effective action of 6D, N = (1, 1) supersymmetric Yang-Mills (SYM) theory in the N = (1, 0) harmonic superspace formulation. The theory is described in terms of analytic N = (1, 0) gauge superfield V ++ and analytic ω-hypermultiplet, both in the adjoint representation of gauge group. The effective action is defined in the framework of the background superfield method ensuring the manifest gauge invariance along with manifest N = (1, 0) supersymmetry. We calculate leading contribution to the one-loop effective action using the on-shell background superfields corresponding to the option when gauge group SU(N) is broken to SU (N-1) X Y (1) ⊂ SU(N). In the bosonic sector the effective action involves the structure ~ F4/X², where F4 is a monomial of the fourth degree in an abelian field strength FMN and X stands for the scalar fields from the ω-hypermultiplet. It is manifestly demonstrated that the expectation values of the hypermultiplet scalar fields play the role of a natural infrared cutoff. [ABSTRACT FROM AUTHOR]

Motivated by the recent interest in curved rigid supersymmetries, we construct a new type of , d = 1 supersymmetric systems by employing superfields defined on the cosets of the supergroup SU(2|1). The relevant worldline supersymmetry is a deformation of the standard supersymmetry by a mass parameter m. As instructive examples we consider, at the classical and quantum levels, the models associated with the supermultiplets (1, 4, 3) and (2, 4, 2) and find out interesting interrelations with some previous works on non-standard d = 1 supersymmetry. In particular, the d = 1 systems with ‘weak supersymmetry’ are naturally reproduced within our SU(2|1) superfield approach as a subclass of the (1, 4, 3) models. A generalization to the case implies the supergroup SU(2|2) as the candidate deformed worldline supersymmetry. [ABSTRACT FROM AUTHOR]

We overview applications of the harmonic superspace approach in models of N = 4supersymmetric mechanics, with emphasis on some recent results. [ABSTRACT FROM AUTHOR]

We explore a simple supersymmetric quantum mechanics (SQM) model describing the motion over complex manifolds in external gauge fields. The nilpotent supercharge Q of the model can be interpreted as a (twisted) exterior holomorphic derivative, such that the model realizes the twisted Dolbeault complex. The sum can be interpreted as the Dirac operator: the standard Dirac operator if the manifold is Kähler and the Dirac operator involving certain particular extra torsions for a generic complex manifold. Focusing on the Kähler case, we give new simple physical proofs of the two mathematical facts: (i) the equivalence of the twisted Dirac and twisted Dolbeault complexes and (ii) the Atiyah-Singer theorem. [ABSTRACT FROM AUTHOR]

We derive and discuss, at both the classical and quantum levels, generalized supersymmetric quantum mechanical sigma models describing the motion over an arbitrary real or an arbitrary complex manifold with extra torsions. We analyze the relevant vacuum states to make explicit the fact that their number is not affected by adding the torsion terms. [ABSTRACT FROM AUTHOR]

Abstract: We present the first example of super Landau model with both worldline supersymmetry and non-trivial target space supersymmetry . The model also reveals a hidden second supersymmetry which, together with the manifest one, close on a worldline . We start from an off-shell action in bi-harmonic , superspace and come to the component action with four bosonic and four fermionic fields. Its bosonic core is the action of generalized Landau model on considered some time ago by Elvang and Polchinski. At each Landau level the wave functions are shown to form “atypical” ()-dimensional multiplets of the worldline supergroup . Some states have negative norms, but this trouble can be evaded by redefining the inner product, like in other super Landau models. We promote the action to the most general form compatible with off-shell worldline supersymmetry and find the corresponding background gauge field to be generic self-dual on and the target superspace metric to remain flat. [Copyright &y& Elsevier]

It is a brief review of a new class of N = 2supersymmetric Landau models which generalize the superplane Landau model by extending it to an arbitrary magnetic field on any two-dimensional manifold M. Using an off-shell N = 2 superfield formalism, it is shown that these models are characterized by two independent potentials given on M. The relevant Hamiltonians are factorizable and in the special case, when both the Gauss curvature and the magnetic field are constant over M, admit infinite series of factorization chains, which implies the integrability of the associated systems. For the particular model with the ℂℙ bosonic manifold, the spectrum and eigenvectors are explicitly given. [ABSTRACT FROM AUTHOR]

Abstract: We construct the manifestly supersymmetric off-shell superfield “master” action for any number n of the supermultiplets described by harmonic analytic superfields , , subjected to the most general harmonic constraints. The action consists of the sigma-model and Wess–Zumino parts. We present the general expressions for the target space metric, torsion and background gauge fields. The generic target space geometry is shown to be weak HKT (hyper-Kähler with torsion), with the strong HKT and HK ones as particular cases. The background gauge fields obey the self-duality condition. Our formulation suggests that the weak HKT geometry is fully specified by the two primary potentials: an unconstrained scalar potential which is the projection of the superfield sigma-model Lagrangian, and a charge 3 harmonic analytic potential coming from the harmonic constraint on . The reductions to the strong HKT and HK geometries amount to simple restrictions on the underlying potentials. We also show, using the superfield approach, that the most general bosonic target geometry of the , sigma models, of which the weak HKT geometry is a particular case, naturally comes out after adding the mirror multiplets with different transformation laws under supersymmetry and symmetry. Thus the minimal dimension of the target spaces exhibiting such a “weakest” geometry is 8, which corresponds to a pair of the mutually mirror multiplets. [Copyright &y& Elsevier]

We report on the new approach to constructing superconformal extensions of the Calogerotype systems with an arbitrary number of involved particles. It is based upon the superfield gauging of non-Abelian isometries of some supersymmetric matrix models. Among its applications, we focus on the new N = 4 superconformal system yielding the U(2)-spin Calogero model in the bosonic sector, and the one-particle case of this system, which is a new OSp(4|2) superconformal mechanics with nondynamical U(2) spin variables. The characteristic feature of thesemodels is that the strength of the conformal inverse-square potential is quantized. [ABSTRACT FROM AUTHOR]

We review a recent progress in constructing and studying superextensions of the Landau problem of a quantum particle moving on the two-sphere S2. These are the superspherical and superflag Landau models describing a nonrelativistic particle on the supermanifolds SU(2|1)/U(1|1) and SU(2|1)/[U(1) x U(1)]. Though in both models, under the “naive” definition of the inner product, there are negative-norm states, all norms can be made positive-definite by introducing a nontrivial “metric” in the space of states. So both models are unitary. The superflag model is shown to be quantum-equivalent to the supersphere model for the special choice of the intrinsic parameters. We also address the planar limit of the superspherical model, in which there arises the hidden world-line N =2 supersymmetry. An analog of this phenomenon in the superflag model is a dynamical enhancement of its SU(2|1) symmetry to SU(2|2). [ABSTRACT FROM AUTHOR]

We elaborate on a new model of the higher spin (HS) particle which makes manifest the classical equivalence of the HS particle of the unfolded formulation and the HS particle model with a bosonic counterpart of supersymmetry. Both these models emerge as two different gauges of the new master system. Physical states of the master model are massless HS multiplets described by complex HS fields which carry an extra U(1) charge q. The latter fully characterizes the given multiplet by fixing the minimal helicity at q/2. We construct the twistorial formulation of the master model and discuss symmetries of the new HS multiplets within its framework. [ABSTRACT FROM AUTHOR]

Abstract: Elaborating on previous work [F. Delduc, E. Ivanov, Nucl. Phys. B 753 (2006) 211, hep-th/0605211; F. Delduc, E. Ivanov, Nucl. Phys. B 770 (2007) 179, hep-th/0611247], we show how the linear and nonlinear chiral multiplets of supersymmetric mechanics with the off-shell content can be obtained by gauging three distinct two-parameter isometries of the “root” multiplet actions. In particular, two different gauge groups, one Abelian and one non-Abelian, lead, albeit in a disguised form in the second case, to the same (unique) nonlinear chiral multiplet. This provides an evidence that no other nonlinear chiral multiplets exist. General sigma model type actions are discussed, together with the restricted potential terms coming from the Fayet–Iliopoulos terms associated with Abelian gauge superfields. As in our previous work, we use the manifestly supersymmetric language of , harmonic superspace. A novel point is the necessity to use in parallel the λ and τ gauge frames, with the “bridges” between these two frames playing a crucial role. It is the harmonic analyticity which, though being non-manifest in the τ frame, gives rise to both linear and nonlinear chirality constraints. [Copyright &y& Elsevier]

Abstract: Using an , superfield approach, we construct an supersymmetric action of the self-interacting off-shell multiplet . This action is found to be invariant under the exceptional superconformal group with the R-symmetry subgroup . The general supersymmetric action is a sum of the superconformal action and the previously known free bilinear action. We show that the general action is also superconformal, but with respect to redefined superfield transformation laws. The scalar potential can be generated by two Fayet–Iliopoulos superfield terms which preserve supersymmetry but break the superconformal and symmetries. [Copyright &y& Elsevier]

Abstract: Exploiting the gauging procedure developed by us in hep-th/0605211, we study the relationships between the models of mechanics based on the off-shell multiplets and . We make use of the off-shell , harmonic superspace approach as most adequate for treating this circle of problems. We show that the most general sigma-model type superfield action of the multiplet can be obtained in a few non-equivalent ways from the actions invariant under certain three-parameter symmetries, through gauging the latter by the appropriate non-propagating gauge multiplets. We discuss in detail the gauging of both the Pauli–Gürsey symmetry and the Abelian three-generator shift symmetry. We reveal the origin of the known mechanisms of generating potential terms for the multiplet , as well as of its superconformal properties. A new description of this multiplet in terms of unconstrained harmonic analytic gauge superfield is proposed. It suggests, in particular, a novel mechanism of generating the potential terms via coupling to the fermionic off-shell multiplet . [Copyright &y& Elsevier]

Abstract: We argue that off-shell dualities between supermultiplets with different sets of physical bosonic components and the same number of fermionic ones are related to gauging some symmetries in the actions of the supermultiplets with maximal sets of physical bosons. Our gauging procedure uses off-shell superfields and so is manifestly supersymmetric. We focus on supersymmetric mechanics and show that various actions of the multiplet amount to some gauge choices in the gauged superfield actions of the linear or nonlinear multiplets. In particular, the conformally invariant superpotential is generated by the Fayet–Iliopoulos term of the gauge superfield. We find a new nonlinear variant of the multiplet , such that its simplest superfield action produces the most general 4-dim hyper-Kähler metric with one triholomorphic isometry as the bosonic target metric. We also elaborate on some other instructive examples of superfield gaugings, including a non-Abelian gauging which relates the free linear multiplet to a self-interacting multiplet. [Copyright &y& Elsevier]

It is shown how the static-gauge world-volume superfield actions of diverse superbranes on the AdSd + 1 superbackgrounds can be systematically derived from nonlinear realizations of the appropriate AdS supersymmetries. The latter are treated as superconformal symmetries of flat Minkowski superspaces of the bosonic dimension d. Examples include the N = 1AdS4 supermembrane, which is associated with the 1/2 partial breaking of the OSp(1|4) supersymmetry down to the N = 1, d = 3 Poincaré supersymmetry, and the T-duality related L3-brane on AdS5 and scalar 3-brane on AdS5 × S1, which are associated with two different patterns of 1/2 breaking of the SU(2, 2|1) supersymmetry. Another (closely related) topic is the AdS/CFT equivalence transformation. It maps the world-volume actions of the codimension-one AdSd + 1 (super)branes onto the actions of the appropriate Minkowski (super)conformal field theories in the dimension d.© 2005 Pleiades Publishing, Inc. [ABSTRACT FROM AUTHOR]

Abstract: We study the invariant Q-deformation of Euclidean gauge theories in the harmonic superspace formulation. This deformation preserves chirality and Grassmann harmonic analyticity but breaks to supersymmetry. The action of the deformed gauge theory is an integral over the chiral superspace, and only the purely chiral part of the covariant superfield strength contributes to it. We give the component form of the supersymmetric action for the gauge groups U(1) and . In the U(1) and U(2) cases, we find the explicit nonlinear field redefinition (Seiberg–Witten map) relating the deformed gauge multiplet to the undeformed one. This map exists in the general case as well, and we use this fact to argue that the deformed gauge theory can be nonlinearly reduced to a theory with the gauge group . [Copyright &y& Elsevier]

We find, at the Lagrangian off-shell level, the explicit equivalence transformation which relates the conformal mechanics of De Alfaro, Fubini and Furlan to the conformal mechanics describing the radial motion of the charged massive particle in the Bertotti–Robinson AdS2×S2 background. Thus we demonstrate the classical equivalence of these two systems which are usually regarded as essentially different “old” and “new” conformal mechanics models. We also construct a similar transformation for N=2, SU(1,1&z.sfnc;1) superconformal mechanics in N=2 superfield formulation. Performing this transformation in the action of the N=2 superconformal mechanics, we find an off-shell superfield action of N=2 superextension of Bertotti–Robinson particle. Such an action has not been given before. We show its on-shell equivalence to the AdS2 superparticle action derived from the spontaneous partial breaking of SU(1,1&z.sfnc;1) superconformal symmetry treated as the N=2 AdS2 supersymmetry. [Copyright &y& Elsevier]

Nonlinear realizations superfield techniques, pertinent to the description of partial breaking of global N=2 supersymmetry in a flat d=4 super-Minkowski background, are generalized to the case of partially broken N=1 AdS5 supersymmetry SU(2,2&z.sfnc;1). We present, in an explicit form, off-shell manifestly N=1, d=4 supersymmetric minimal Goldstone superfield actions for two patterns of partial breaking of SU(2,2&z.sfnc;1) supersymmetry. They correspond to two different nonlinear realizations of the latter, in the supercosets with the AdS5 and AdS5×S1 bosonic parts. The relevant worldvolume Goldstone supermultiplets are accommodated, respectively, by improved tensor and chiral N=1, d=4 superfields. The second action is obtained from the first one by dualizing the improved tensor Goldstone multiplet into a chiral Goldstone one. In the bosonic sectors, the first and second actions yield static-gauge Nambu–Goto actions for a L3-brane on AdS5 and a scalar 3-brane on AdS5×S1. [Copyright &y& Elsevier]

We consider partial spontaneous breaking of N=1 AdS4 supersymmetry OSp(1&z.sfnc;4) down to N=1, d=3 Poincare´ supersymmetry in the nonlinear realizations framework. We construct the corresponding worldvolume Goldstone superfield action and show that it describes the N=1 AdS4 supermembrane. It enjoys OSp(1&z.sfnc;4) supersymmetry realized as a field-dependent modification of N=1, d=3 superconformal symmetry and goes into the superfield action of ordinary N=1, D=4 supermembrane in the flat limit. Its bosonic core is the Maldacena-type conformally invariant action of the AdS4 membrane. We show how to reproduce the latter action within a nonlinear realization of the AdS4 group SO(2,3). The same universal nonlinear realizations techniques can be used to construct conformally-invariant worldvolume actions for (D−2)-branes in generic AdSD spaces. [Copyright &y& Elsevier]

We compute the one-loop holomorphic effective action of the massless Cartan sector of N = 2 SYM theory in the Coulomb branch, taking into account the contributions both from the charged hypermultiplets and off-diagonal components of the gauge superfield. We use the manifestly supersymmetric harmonic superfields diagram techniques adapted to N = 2 supersymmetry with the central charges induced by Cartan generators. The (anti)holomorphic part proves to be proportional to the central charges and it has the generic form of Seiberg's action obtained by integrating U(1)[sub R] anomaly. It vanishes for N = 4 SYM theory, i.e. the coupled system of N = 2 gauge superfield and hypermultiplet in the adjoint representation. [ABSTRACT FROM AUTHOR]

The local Sugawara constructions of the “small” N=4 SCA in terms of supercurrents of N=2 extensions of the affine (formula available within PDF) and (formula available within PDF) algebras are investigated. The associated super mKdV type hierarchies induced by N=4 SKdV ones are defined. In the (formula available within PDF) case the existence of two nonequivalent Sugawara constructions is found. The “long” one involves all the affine (formula available within PDF) currents, while the “short” one deals only with those from the subalgebra (formula available within PDF) . As a consequence, the (formula available within PDF) -valued affine superfields carry two nonequivalent mKdV type super-hierarchies induced by the correspondence between “small” N=4 SCA and N=4 SKdV hierarchy. However, only the first hierarchy possesses genuine global N=4 supersymmetry. We discuss peculiarities of the realization of this N=4 supersymmetry on the affine supercurrents. [ABSTRACT FROM AUTHOR]

Deals with the Korteweg-de Vries hierarchy and its supersymmetric extensions. Examples of integrable systems; Algebra of spinor and harmonic derivatives; Modification of the Poisson structure; Integration measure of the full harmonic superspace; Conserved charges.