Harmonic space and quaternionic manifolds

We find a principle of harmonic analyticity underlying the quaternionic (quaternion-K\"ahler) geometry and solve the differential constraints which define this geometry. To this end the original $4n$-dimensional quaternionic manifold is extended to a bi-harmonic space. The latter includes additional harmonic coordinates associated with both the tangent local $Sp(1)$ group and an extra rigid $SU(2)$ group rotating the complex structures. Then the constraints can be rewritten as integrability conditions for the existence of an analytic subspace in the bi-harmonic space and solved in terms of two unconstrained potentials on the analytic subspace. Geometrically, the potentials have the meaning of vielbeins associated with the harmonic coordinates. We also establish a one-to-one correspondence between the quaternionic spaces and off-shell $N=2$ supersymmetric sigma-models coupled to $N=2$ supergravity. The general $N=2$ sigma-model Lagrangian when written in the harmonic superspace is composed of the quaternionic potentials. Coordinates of the analytic subspace are identified with superfields describing $N=2$ matter hypermultiplets and a compensating hypermultiplet of $N=2$ supergravity. As an illustration we present the potentials for the symmetric quaternionic spaces.Comment: 44 pages, LATEX, JHU-TIPAC-920023, ENSLAPP-L-405-92, MPI-Ph/92-8

Non-BPS Brane Dynamics And Dual Tensor Gauge Theory

The action for the long wavelength oscillations of a non-BPS p=3 brane embedded in N=1, D=5 superspace is determined by means of the coset method. The D=4 world volume Nambu-Goldstone boson of broken translation invariance and the two D=4 world volume Weyl spinor Goldstinos of the completely broken supersymmetry describe the excitations of the brane into the broken space and superspace directions. The resulting action is an invariant synthesis of the Akulov-Volkov and Nambu-Goto actions. The D=4 antisymmetric tensor gauge theory action dual to the p=3 brane action is determined.Comment: 15 pages, no figure

Bulk and boundary g2g_2 factorized S-matrices

We investigate the $g_2$-invariant bulk (1+1D, factorized) $S$-matrix constructed by Ogievetsky, using the bootstrap on the three-point coupling of the vector multiplet to constrain its CDD ambiguity. We then construct the corresponding boundary $S$-matrix, demonstrating it to be consistent with $Y(g_2,a_1\times a_1)$ symmetry.Comment: 7 page

Quantum Deformed su(m∣n)su(m|n) Algebra and Superconformal Algebra on Quantum Superspace

We study a deformed $su(m|n)$ algebra on a quantum superspace. Some interesting aspects of the deformed algebra are shown. As an application of the deformed algebra we construct a deformed superconformal algebra. {}From the deformed $su(1|4)$ algebra, we derive deformed Lorentz, translation of Minkowski space, $iso(2,2)$ and its supersymmetric algebras as closed subalgebras with consistent automorphisms.Comment: 27 pages, KUCP-59, LaTeX fil

Nonlinear realization of local symmetries of AdS space

Coset methods are used to construct the action describing the dynamics associated with the spontaneous breaking of the local symmetries of AdS_{d+1} space due to the embedding of an AdS_d brane. The resulting action is an SO(2,d) invariant AdS form of the Einstein-Hilbert action, which in addition to the AdS_d gravitational vielbein, also includes a massive vector field localized on the brane. Its long wavelength dynamics is the same as a massive Abelian vector field coupled to gravity in AdS_d space.Comment: 17 page

A Higgs Mechanism for Gravity. Part II: Higher Spin Connections

We continue the work of hep-th/0503024 in which gravity is considered as the Goldstone realization of a spontaneously broken diffeomorphism group. We complete the discussion of the coset space Diff(d,R)/SO(1,d-1) formed by the d-dimensional group of analytic diffeomorphisms and the Lorentz group. We find that this coset space is parameterized by coordinates, a metric and an infinite tower of higher-spin-like or generalized connections. We then study effective actions for the corresponding symmetry breaking which gives mass to the higher spin connections. Our model predicts that gravity is modified at high energies by the exchange of massive higher spin particles.Comment: 17 pages; discussion on local Poincare invariance and matter currents added; references adde

Three form potential in (special) minimal supergravity superspace and supermembrane supercurrent

This contribution begins the study of the complete superfield Lagrangian description of the interacting system of D=4 N=1 supergravity (SUGRA) and supermembrane. Firstly, we review a 'three form supergravity' by Ovrut and Waldram, which we prefer to call 'special minimal supergravity'. This off-shell formulation of simple SUGRA is appropriate for our purposes as the supermembrane action contains the so-called Wess-Zumino term given by the integral over a three form potential in superspace, C3. We describe this formulation in the frame of Wess--Zumino superfield approach, showing how the basic variations of minimal SUGRA are restricted by the conditions of the existence of a three-form potential C3 in its superspace. In this language the effect of dynamical generation of cosmological constant, known to be characteristic for this formulation of SUGRA, appears in its superfield form, first described by Ogievetsky and Sokatchev in their formulation of SUGRA as a theory of axial vector superfield. Secondly, we vary the supermembrane action with respect to the special minimal SUGRA superfields (basic variations) and obtain the supercurrent superfields as well as the supergravity superfield equations with the supermembrane contributions.Comment: 18 pages, no figures. V2: Important references added. The abstract and presentation have been changed to reflect the overloop with that. Submitted to the QTS7 Proceedings. J. Phys. style use

Colliders and Brane Vector Phenomenology

Brane world oscillations manifest themselves as massive vector gauge fields. Their coupling to the Standard Model is deduced using the method of nonlinear realizations of the spontaneously broken higher dimensional space-time symmetries. Brane vectors are stable and weakly interacting, and therefore escape particle detectors unnoticed. LEP and Tevatron data on the production of a single photon in conjunction with missing energy are used to delineate experimentally excluded regions of brane vector parameter space. The additional region of parameter space accessible to the LHC as well as a future lepton linear collider is also determined by means of this process.Comment: 12 pages, 13 figure

Supermembrane interaction with dynamical D=4 N=1 supergravity. Superfield Lagrangian description and spacetime equations of motion

We obtain the complete set of equations of motion for the interacting system of supermembrane and dynamical D=4 N = 1 supergravity by varying its complete superfield action and writing the resulting superfield equations in the special gauge where the supermembrane Goldstone field is set to zero. We solve the equations for auxiliary fields and discuss the effect of dynamical generation of cosmological constant in the Einstein equation of interacting system and its renormalization due to some regular contributions from supermembrane. These two effects (discussed in late 70th and 80th, in the bosonic perspective and in the supergravity literature) result in that, generically, the cosmological constant has different values in the branches of the spacetime separated by the supermembrane worldvolume.Comment: 23 pages, no figures. V2 two references added, 24 page