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We study curved domain wall solutions for gauged supergravity theories obtained by gauging some of the isometries of the manifold spanned by the scalars of vector and hypermultiplets. We first consider the case obtained by compactifying M-theory on a Calabi-Yau threefold in the presence of G-fluxes. It is found that supersymmetry allows for the construction of domain wall configurations with curved worldvolume and a cosmological constant. However it turns out that the equations of motion, if one insists on the supersymmetric ansatz for the scalars and warp factor, rule out solutions with a cosmological constant and allows only for Ricci-flat worldvolumes. Moreover, in the absence of flux, there are non-supersymmetric solutions with worldvolumes given by Einstein manifolds. We also generalize our results to all five dimensional gauged supergravity., Nucl. Phys. version, minor changes

The formalism of non-commutative geometry of A. Connes is used to construct models in particle physics. The physical space-time is taken to be a product of a continuous four-manifold by a discrete set of points. The treatment of Connes is modified in such a way that the basic algebra is defined over the space of matrices, and the breaking mechanism is planted in the Dirac operator. This mechanism is then applied to three examples. In the first example the discrete space consists of two points, and the two algebras are taken respectively to be those of $2\times 2$ and $1\times 1$ matrices. With the Dirac operator containing the vacuum breaking $SU(2)\times U(1)$ to $U(1)$, the model is shown to correspond to the standard model. In the second example the discrete space has three points, two of the algebras are identical and consist of $5\times 5$ complex matrices, and the third algebra consists of functions. With an appropriate Dirac operator this model is almost identical to the minimal $SU(5)$ model of Georgi and Glashow. The third and final example is the left-right symmetric model $SU(2)_L\times SU(2)_R\times U(1)_{B-L}.$, 25 pages, ZU-TH-30/1992 and ETH/TH/92-41

Topological theories of gravity are constructed in odd-dimensional space-times of dimensions 2n + 1, using the Chern-Simons (2n + 1)-forms and with the gauge groups ISO(1, 2n) or SO(1, 2n + 1) or SO(2, 2n). In even dimensions the presence of a scalar field in the fundamental representation of the gauge group is needed, besides the gauge field. Supersymmetrization of the de Sitter groups can be performed up to a maximal dimension of seven, but there is no limit on the super-Poincare groups. The different phases of the topological theory are investigated. It is argued that these theories are finite. It is shown that the graviton propagates in a perturbative sense around a non-trivial background.

Using a general construction of the modular invariant partition function for four-dimensional strings with twisted, orbifold-like, boundary conditions, we discuss the equivalence of their Neveu-Schwarz-Ramond and Green-Schwarz formulations. Four-dimensional GS strings are found to be equivalent to the class of NSR theories on orbifolds based on the canonical, free supercurrent, with underlying N = 2 linear world-sheet supersymmetry. This equivalence provides interesting insights on the consistency conditions for all order modular invariance to be applied on four-dimensional Green-Schwarz strings.

We propose a topological action for 1 + 1 dimensional gravity based on the gauge symmetry SO(1,2) or its contraction ISO(1,1). The construction employs, besides the gauge multiplet, a scalar multiplet and is closely related to the Liouville action and induced gravity action. The theory is solvable at both the classical and quantum levels and has a renormalizable perturbation expansion. The only contributions that could be non-vanishing are those which are one-loop. The partition function is computed exactly and is related to the moduli space measure, implying a cancellation among the one-loop contributions. It is argued that if the theory is formulated on space-times admitting classical solutions then the quantum theory escapes the planckian domain to the classical domain. We give the generalizations to include matter interactions and supersymmetrization. Matter fields of any dimensions can be quantized and the interactions introduced are renormalizable.

We start from the covariant action for the induced two-dimensional gravity and derive the equation of motion. We show that the underlying symmetry for the equation of motion is an SL(2, R ) Kac-Moody current algebra, and give the explicit connection with the Wess-Zumino-Witten model. We also construct the energy-moment tensor and work out the operator product expansion.

The gauge hierarchy at the tree level in supergravity GUTS is examined. General criteria on the superpotential are given which guarantee the hierarchy to all orders in the gravitational coupling constant κ. Thus for theories obeying these criteria the light Higgs VEVs are protected from both the Planck and GUT masses. An effective potential for these light fields is constructed.

In a new approach to supergravity we consider the gauge theory of the 14-dimensional supersymmetry group. The theory is constructed from 14×4 gauge fields, 4 gauge fields being associated with each of the 14 generators of supersymmetry. The gauge fields corresponding to the 10 generators of the Poincare subgroup are those normally associated with general relativity, and the gauge fields corresponding to the 4 generators of supersymmetry transformations are identified with a Rarita-Schwinger spinor. The transformation laws of the gauge fields and the Lagrangian of lowest degree are uniquely constructed from the supersymmetry algebra. The resulting action is shown to be invariant under these gauge transformations if the translation associated field strength vanishes. It is shown that the second-order form of the action, which is the same as that previously proposed, is invariant without constraint.

We develop a simple and unified formalism to construct four-dimensional string models consistent with modular invariance. The boundary conditions are allowed to be twisted for fermions while bosons are either twisted or shifted. We show that the generalized GSO projection conditions follow from our solution to the modular invariance of the total partition function. The Green-Schwarz strings and the Neveu-Schwarz-Ramond strings are treated in a unified way. We give the conditions needed to preserve world-sheet supersymmetry and to characterize N = 1, 2, 4 space-time supersymmetry. Our formalism is general enough to contain the fermionic, lattice, and orbifold constructions of four-dimensional strings and we provide its connection to some of them.

We study the formulation of string theories in four dimensions with explicit space-time supersymmetry, allowing the string coordinates to have both shifted and twisted, orbifold-like, boundary conditions. The theories we construct are automatically tachyon-free and can have gauge groups of small ranks. As an example, we recover the Z 3 orbifold model. We describe the construction of superstring theories with rank eight gauge groups, illustrated by an SO(10) ⊗ SU(3) ⊗ U(1) model.