An approach to linear programming duality is proposed which relies on quadratic penalization, so that the relation between solutions to the penalized primal and dual problems becomes affine. This yields a new proof of Levin’s duality theorem for capacity-constrained optimal transport as an infinite-dimensional application.

The total space of the spinor bundle on the four dimensional sphere S4 is a quaternionic line bundle that admits a metric of Spin(7) holonomy. We consider octonionic Yang-Mills instanton on this eight dimensional gravitational instanton. This is a higher dimensional generalization of (anti-)self-dual instanton on the Eguchi-Hanson space. We propose an ansatz for Spin(7) Yang-Mills field and der...

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...

Spherically and cylindrically symmetric solutions of SU (3) Yang-Mills theory are found, whose gauge potentials have confining properties. The spherically symmetric solutions give field distributions which have a spherical surface on which the gauge fields become infinite (which is similiar to bag models of confinement), and the other solution has a potential which increases at large distances....

We find new solutions to 11-dimensional supergravity describing M5-branes wrapped on holomorphic 2-cycles embedded in C. These solutions preserve N = 1 supersymmetry in four dimensions. They are dual to N = 1 gauge theories in four dimensions by Maldacena’s duality. USITP-00-19 DTP/00/111 hep-th/0012194 email: [email protected] email: [email protected] email: [email protected] email: Douglas.Smith...

We study the supersymmetric extension of the gauged O(3) sigma model in 2+1 dimensions and find the supersymmetry algebra. We also discuss soliton solutions in case the Maxwell term is replaced by the Born-Infeld term. We show that by appropriate choice of the potential, the self-dual equations in the Born-Infeld case coincide with those of the Maxwell’s case.

Using the κ-symmetric action for a D3-brane, we study the interaction between its world-volume fermions and a bosonic type IIB supergravity background preserving 4-dimensional Lorentz invariance. We find that the renormalizable terms in the action include only coupling between the fermions and the 3-form flux in the combination (∗6G(3) − iG(3)), which is zero for a class of supersymmetric and n...

We consider stochastic volatility models under parameter uncertainty and investigate how model derived prices of European options are affected. We let the pricing parameters evolve dynamically in time within a specified region, and formalise the problem as a control problem where the control acts on the parameters to maximise/minimise the option value. Through a dual representation with backwar...

Three dimensional spacelike warped anti-de Sitter space is studied in the context of Einstein theories of gravity and string theory, where there is no gravitational Chern-Simons term in the action. We propose that it is holographically dual to a two-dimensional conformal field theory with equal left and right moving central charges. Various checks of the central charges are offered, based on th...