The concept of the D-brane probe provides the link between gauge theory and geometry. It has proven to be one of the most important ideas among recent developments in string theory, shedding new light on strong coupling gauge theory dualities, providing a physical interpretation of previously obscure algebraic-geometric constructions, and resulting in examples of the AdS/CFT correspondence with...

The equations of motion of the massless sector of the two dimensional string theory, obtained by compactifying the heterotic string theory on an eight dimensional torus, is known to have an affine o(8, 24) symmetry algebra generating an O(8, 24) loop group. In this paper we study how various known discrete Sand T duality symmetries of the theory are embedded in this loop group. This allows us t...

for two given graphs g1 and g2, the ramseynumber r(g1,g2) is the smallest integer n such that for anygraph g of order n, either $g$ contains g1 or the complementof g contains g2. let tn denote a tree of order n andwm a wheel of order m+1. to the best of our knowledge, only r(tn,wm) with small wheels are known.in this paper, we show that r(tn,wm)=3n-2 for odd m with n>756m^{10}.

in today’s turbulent world, the continuity of criticalactivities in the event of disruptions, and also fast recovery and return tobusiness as usual, are vital for sustainable success of companies. maintainingcontinuous delivery of critical business processes in the event of disruptions isa matter of business continuity. business continuity management system (bcms)is concerned with the developme...

We classify biharmonic and harmonic homomorphisms f:(G,g1)⟶(G,g2) where G is a connected simply three-dimensional unimodular Lie group g1 g2 are left invariant Riemannian metrics.

We motivate and summarize our analysis of hep-th/0610276 in which we consider D7-brane probe embeddings in the Polchinski-Strassler background with N = 2 supersymmetry. The corresponding dual gauge theory is given by the N = 2 theory with fundamental matter. Based on a talk given by C. Sieg at the RTN Workshop 2006, Napoli. ∗[email protected], [email protected], [email protected], [email protected]...