N = 4 supergravity theory with local SU(2) × SU(2) invariance

N = 4 supergravity theory has been formulated in two different equivalent forms, which may be expected to become inequivalent when the internal symmetry is gauged. The extension of the first form to include local SO(4) internal symmetry is known. In this paper the extension of the second form to local SU(2) × SU(2) invariance is given, and is indeed inequivalent to the first form. The second form is in general parity non-conserving, while both forms have scalar field potentials that are unbounded from below.     

Supersymmetry and Superfields in Three Euclidean Dimensions

The simplest supersymmetry algebra and superspace in three-dimensional Euclidean (3dE) space is examined. Representations of the algebra are considered and the implications of restricting the space of states to states with positive definite norm are determined. A superspace is defined and superfields are introduced. Supersymmetric field theory models in 3dE are described in both superfield and component field forms. The relationship between these models and similar models in four-dimensional Minkowski space is described.     

Irreducible representations of the quantum analogue of SU(2)

We give the complete set of irreducible representations of U(SU(2))_q when q is a mth root of unity. In particular, we show that their dimensions are less or equal to m. Some of them are not highest-weight representations.     

Linearized N = 2 supergravity in terms of SU(2)-extended superfields

The linearized theory of N = 2 conformai supergravity is expressed in terms of a single irreducible SU(2)-extended superfield. In particular, in this way the origin of the N = 2 superconformal multiplet is established.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 5, pp. 93–95, May, 1986.     

The Branching Rules for SU(2N)⊃(SU(N)⊃O(N)⊃O(3))⊗SU(2) and the Highest Weight States for SU(N) and O(N)

Simple analytical recurrent formulae of the branching rules for group chain SU(2N)⊃(SU(N)⊃O(N)⊃O(3))⊗SU(2) are obtained. The highest weight states for the irreducible representations [2^al^b] or {nS} of group SU(N) and for the irreducible representations (2^α1^β) or (υS) of group O(N) are constructed respectively     

The unitary constructions of the N=4 SU (2) extended superconformal algebras

Unitary conditions for the N=4 SU (2) extended superconformal algebras (SUCAs) are derived. All highest weight unitary representations are identified and explicitly realized by free fermion and (twisted) boson constructions, which are essentially free theories.     

Twisted N=2 Supersymmetry with Central Charge and Equivariant Cohomology

We present an equivariant extension of the Thom form with respect to a vector field action, in the framework of the Mathai-Quillen formalism. The associated Topological Quantum Field Theories correspond to twisted N=2 supersymmetric theories with a central charge. We analyze in detail two different cases: topological sigma models and non-abelian monopoles on four-manifolds. Received: 2 April 1996 / Accepted: 15 July 1996     

SU(2) Charges as Angular Momentum in N = 1 Self-Dual Supergravity

The N = 1 self-dual supergravity has SL(2, ) symmetry. This symmetry results inSU(2) charges as the angular momentum. As innonsupersymmetric self-dual gravity, the currents arealso of their potentials and are therefore identically conserved. Thecharges are generally invariant and gauge covariantunder local SU(2) transforms and approach being rigid atspatial infinity. The Poisson brackets constitute the su(2) algebra and hence can be interpretedas the generally covariant conservative angularmomentum.     

Linearized N=2 Poincaré supergravity in terms of SU(2)-extended superfields

Linearized Poincaré N=2 supergravity is presented in terms of SU(2)-extended superfields. Thus, the connection of SU(2)-extended superfields with the structure of auxiliary fields in N=2 supergravity is established.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 31–34, October, 1986.     

Coherent states associated with the groups SU(N) and SU(N, 1)

The coherent-state basis is constructed for symmetric representations of the groups SU(N) and SU(N, 1) and its properties are studied. The evolution of coherent states is considered. A relationship between the SU(N) coherent states and the Glauber coherent states is established.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 83–89, January, 1990.     

SU(3) ⊗ SU(2) ⊗ U(1) from D = 11 supergravity

In this paper we show that D = 11 supergravity admits an infinite discrete class of solutions having the phenomenological group SU(3) ? SU(2) ? U(1) as a symmetry of the internal space M₇. These solutions lead, in dimensional reduction, to SU(3) ? SU(2) ? U(1) gauge fields.In general all these spaces produce a complete breaking of supersymmetry except in one case where N = 2 supersymmetry survives. The parameter which classifies the solutions is a rational number q/p which describes the embedding of the stability subgroup SU(2) ? U(1) ? U(1) of M₇ in SU(3) ? SU(2) ? U(1). For all q/p ≠ 1 the holonomy group is SO(7) and all supersymmetries are broken. For q/p = 1 the holonomy group is SU(3) and two supersymmetries survive. In this last case we can also find a solution with internal photon curl $\text{F}{}_{\mathrm{\alpha \beta \gamma \delta }}\text{≠ 0}$. It breaks all sypersymmetries.     

Spectral convexity for attractive SU(2N) fermions

We prove a general theorem on spectral convexity with respect to particle number for 2N degenerate components of fermions. The number of spatial dimensions is arbitrary, and the system may be uniform or constrained by an external potential. We assume only that the interactions are governed by an SU(2N)-invariant two-body potential whose Fourier transform is negative definite. The convexity result implies that the ground state is in a 2N-particle clustering phase. We discuss implications for light nuclei as well as asymmetric nuclear matter in neutron stars.     

The low-lying mass spectrum of the N = 1 SU(2) SUSY Yang-Mills theory with Wilson fermions

We analyze the low energy spectrum of bound states of the N = 1 SU(2) SUSY Yang-Mills Theory (SYM). This work continues the investigation of the non-perturbative properties of SYM by Monte Carlo simulations in the Wilson discretization with dynamical gluinos. The dynamics of the gluinos is included by the Two-Step Multi-Bosonic Algorithm (TSMB) for dynamical fermions. A new set of configurations has been generated on a lattice at and . The analysis also includes sets of configurations previously generated on a smaller ( ) lattice at and 0.1955. Guided by predictions from low energy Lagrangians, we consider spin-1/2, scalar and pseudoscalar particles. The spectrum of SYM is a challenging subject of investigation because of the extremely noisy correlators. In particular, meson-like correlators contain disconnected contributions. The larger time-extension of the lattice allows to observe two-state signals in the effective mass. Finite-volume effects are monitored by comparing results from the two lattice sizes.Received: 14 September 2004, Revised: 29 October 2004, Published online: 21 December 2004     

E2 transitions in the SU(3) formalism for N = Z nuclei of the sd and pf shells

We show that the SU(3) coupling scheme reproduces the data for E2 transitions in N = Z even-even nuclei both of the sd and the pf shells. The SU(3) results are compared with large-scale shell model calculations. Along the ground-state band-like structures, the increase of the B(E2) values with spin toward a maximum value and the subsequent fall with further increasing spin are reproduced rather well. The role of the quadrupole-quadrupole term of the nuclear residual interaction is stressed.