We review recent works on supersymmetry breaking and gauge mediation. We survey our current understanding of dynamical supersymmetry breaking mechanisms and describe new model building tools using duality, meta-stability, and stringy construction. We discuss phenomenological constraints and their solutions, paying attentions to issues with gaugino masses and electroweak symmetry breaking.

We describe how to construct solutions to 11-dimensional supergravity corresponding to M5-branes wrapped on holomorphic 2-cycles embedded in C. These solutions preserve N = 1 supersymmetry in four dimensions. In the near-horizon limit they are expected to be dual to N = 1 large N gauge theories in four dimensions by Maldacena’s duality. USITP-00-19 DTP/00/111 hep-th/0012194 email: brinne@physto...

In the context of gauge/gravity duality, we try to understand better the proposed duality between the fractional D2-brane supergravity solutions of (Nucl. Phys. B 606 (2001) 18, hep-th/0101096) and a confining 2+ 1 dimensional gauge theory. Based on the similarities between this fractional D2-brane solution and D3-brane supergravity solutions with more firmly established gauge theory duals, we ...

We construct a holographic map between asymptotically AdS5 × S5 solutions of 10d supergravity and vacuum expectation values of gauge invariant operators of the dual QFT. The ingredients that enter in the construction are (i) gauge invariant variables so that the KK reduction is independent of any choice of gauge fixing; (ii) the non-linear KK reduction map from 10 to 5 dimensions (constructed p...

We give necessary and suucient conditions for uniqueness of the support vector solution for the problems of pattern recognition and regression estimation, for a general class of cost functions. We show that if the solution is not unique, all support vectors are necessarily at bound, and we give some simple examples of non-unique solutions. We note that uniqueness of the primal (dual) solution d...

We give necessary and sufficient conditions for uniqueness of the support vector solution for the problems of pattern recognition and regression estimation, for a general class of cost functions. We show that if the solution is not unique, all support vectors are necessarily at bound, and we give some simple examples of non-unique solutions. We note that uniqueness of the primal (dual) solution...

The multi-centre metrics are a family of euclidean solutions of the empty space Einstein equations with self-dual curvature. For this full class, we determine which metrics do exhibit an extra conserved quantity quadratic in the momenta, induced by a Killing-Stäckel tensor. Our results bring to light several metrics which correspond to classically integrable dynamical systems. They include, as ...

Note that Blaschke and his school only considered surfaces in 3-space and ignored the higher co-dimension case. In Sn this problem is still meaningful. It is known that the construction of Darboux pair of isothermic surfaces as well as dual Willmore surfaces has a generalization to Sn (see [4, 9] and [7]), and they still constitute solutions to the generalized Blaschke’s problem. Here we will s...

Let A be a dual Banach algebra with predual A∗ and consider the following assertions: (A) A is Connes-amenable; (B) A has a normal, virtual diagonal; (C) A∗ is an injective A-bimodule. For general A, all that is known is that (B) implies (A) whereas, for von Neumann algebras, (A), (B), and (C) are equivalent. We show that (C) always implies (B) whereas the converse is false for A = M(G) where G...

Let A be a dual Banach algebra with predual A∗ and consider the following assertions: (A) A is Connes-amenable; (B) A has a normal, virtual diagonal; (C) A∗ is an injective A-bimodule. For general A, all that is known is that (B) implies (A) whereas, for von Neumann algebras, (A), (B), and (C) are equivalent. We show that (C) always implies (B) whereas the converse is false for A = M(G) where G...