Dynamically broken supergravity and the hierarchy problem

We propose a scenario for grand unified models based on local supersymmetry. We give arguments that condensates of strongly interacting gauge theories might break local supersymmetry. The gravitino mass induces mass splittings in the low energy theory and allows us to understand a hierarchy of M_p = 10¹⁹ GeV to M_w = 10² GeV naturally.     

N=1 supergravity theories coupled to matter and duality transformations

The most general action for chiral and complex linear superfields coupled to theN=1 old minimal supergravity is given. Scalar potentials for pure complex linear and mixed cases are found. A condition for the breakdown of the duality transformation, which transforms a theory with complex linear superfields to one with chiral scalar superfields, is obtained. When this condition is satisfied, the potentials and couplings cannot be transformed, in general, into a Kähler form; examples are given. Some aspects of vanishing cosmological constant are considered in this context.     

N = 4 Supersymmetric (Dyonic) Hypermultiplets in String Theory

In four-dimensional N = 4 supersymmetric gauge theory, we obtain an exact metric on the moduli space of quantum vacua and analyze the spectra of BPS states in weak as well as in strong coupling regions. Identifying the hypermultiplet of the dyonic state as a string stretched between D₃-brane probe and a 7-brane, we demonstrate that the two hypermultiplets, which become massless at two singularities in supersymmetric theory, correspond to open strings beginning on the D₃-brane and ending on the respective 7-brane.     

Gravitating Dyons and Dyonic Black Holes in SU(2) and SU(5) Theories

The study of gravitating dyons and dyonic black holes in SU(2) and SU(5) theories has been undertaken and it has been shown that gravitating fundamental dyonic solutions and dyonic black holes are stable in both the cases.     

Geometry ofN=1 supergravity (II)

The supergravity torsion and curvature constraints are shown to be a particular case of constraints arising in a general geometrical situation. For this purpose, a theorem is proved which describes the necessary and sufficient conditions that the given geometry can be realized on a surface as one induced by the geometry of the ambient space. The proof uses the theory of nonlinear partial differential equations in superspace, Spencer cohomologies, etc. This theorem generalizes various theorems, well known in mathematics (e.g., the Gauss—Codazzi theorem), and may be of its own interest.     

Multiplets of linearized SO(2) supergravity

A set of fields for SO(2) supergravity theories is presented on which the gauge algebra closes at the linearized level. The Poincaré Lagrangian and three higher-order invariants are constructed. One of them, an extension of the Weyl Lagrangian, is manifestly invariant under chiral U(2) transformations. Several aspects of our results are discussed, like the particle content of the various Lagrangians and the ghost interactions that occur in the quantised Poincaré action.     

Phenomenological SU(1, 1) supergravity

We investigate the structure of phenomenological supergravity models which permit the hierarchy problem to be “solved” in the sense that $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and m_W are determined dynamically to be exp [-O(1)/α] × m_P. Such models must have a flat hidden sector potential, which is only possible if the theory has an underlying SU(1, 1) invariance. Flat SU(1, 1) theories necessarily have a zero cosmological constant and the hidden sector is an Einstein space with . The SU(1, 1) invariance is necessarily broken down to U(1) by the gravitino mass. If $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ is the only source of SU(1, 1) breaking then the tree-level gaugino masses are small and $\text{A =}\text{3}\text{2}$, while values of A up to 3 and non-zero gaugino masses are possible if other sources of SU(1, 1) breaking are tolerated. Yukawa couplings may scale as some power of $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{m}{}_{\mathrm{<mtext>P</mtext>}}$ in these models where $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ is generated dynamically, which may explain the hierarchy of Higgs-fermion Yukawa couplings: $\text{m}{}_{\mathrm{<mtext>f</mtext>}}\text{m}{}_{\mathrm{<mtext>W</mtext>}}\text{=}\text{O}\text{(}\text{m}{}_{\mathrm{<mtext>W</mtext>}}\text{m}{}_{\mathrm{<mtext>P</mtext>}}\text{)}{}^{\mathrm{\lambda >0}}$? These models also permit the spontaneous violation of CP in the Yukawa coupling matrix. Numerical studies yield 20 GeV < m_t < 100 GeV in these phenomenological SU(1, 1) supergravity models. Speculations are presented about their relation to a fundamental theory based on extended supergravity.     

Properties of SO(8) extended supergravity

The conjectured SU(8) invariance of the field equations of SO(8) extended supergravity is used to elucidate the general structure of the extended theories. Due to the representation content of the spinless fields this does not lead to a complete determination of the theory, as was the case for N = 4. The non-polynomial modifications by spinless fields are given in terms of a number of SU(8) covariant tensors, for which various identities are derived and discussed.     

Higher-derivative supergravity in U(l) superspace

The complete structure of curvature squared terms is analyzed in the context of chirally extended supergravity, with special emphasis on the gravitationally induced Fayet–Iliopoulos D–term. Coupling of (chiral) matter is discussed in relation with a possible extension to supergravity of the equivalence mechanism between and General Relativity coupled to a scalar. Received: 9 June 1997 / Revised version: 12 September 1997 / Published online: 26 February 1998     

Quartic ghost interactions of O(N) supergravity

The quartic ghost couplings of O(N) (N ? 8) supergravity are obtained to order κ². These additional interactions which are necessary for unitarity are formally the same for all N. This pattern may be useful in the search for auxilliary fields of O(N > 2) supergravity.     

A new solution of d = 11 supergravity with internal isometry group SU(3) × SU(2) × U(1)

A new solution of the bosonic sector of D = 11 supergravity is presented in which the internal space has the topology CP² × S² × S¹ and the internal isometry group is SU(3) × SU(2) × U(1).     

Extended supergravity with local SO(5) invariance

We present a version of N = 5 supergravity with local SO(5) invariance and a lowest order calculation for N = 8 supergravity with local SO(8). The implications of these results and related aspects are discussed.