Coloured supersymmetry

Supersymmetry Without Supersymmetry

We present four-dimensional M -theory vacua with N > 0 supersymmetry which, from the perspective of perturbative Type IIA string theory, have N = 0. Such vacua can appear when the compactifying 7-manifold is a U(1) fibration. The missing superpartners are Dirichlet 0-branes. Someone unable to detect Ramond-Ramond charge would thus conclude that these worlds have no unbroken supersymmetry. In pa...

Supersymmetry without Supersymmetry

We investigate the possibility that supersymmetry is not a fundamental symmetry of nature, but emerges as an accidental approximate global symmetry at low energies. This can occur if the visible sector is nonsupersymmetric at high scales, but flows toward a strongly-coupled superconformal fixed point at low energies; or, alternatively, if the visible sector is localized near the infrared brane ...

Coloured Spectacles

Properly Coloured Hamiltonian Paths in Edge-coloured Complete Graphs

We consider edge-coloured complete graphs. A path or cycle Q is called properly coloured (PC) if any two adjacent edges of Q differ in colour. Our note is inspired by the following conjecture by B. Bollobás and P. Erdős (1976) : if G is an edge-coloured complete graph on n vertices in which the maximum monochromatic degree of every vertex is less than bn/2c, then G contains a PC Hamiltonian cyc...

Large 2-Coloured Matchings in 3-Coloured Complete Hypergraphs

We prove the generalized Ramsey-type result on large 2-coloured matchings in a 3-coloured complete 3-uniform hypergraph, supporting a conjecture by A. Gyárfás.