Asymptotically free scaling solutions in non-Abelian Higgs models

Asymptotically free models and discrete non-Abelian groups

We study the two-dimensional renormalization-group flow induced by perturbations that reduce the global symmetry of the O(3) σ-model to the discrete symmetries of Platonic solids. We estimate the value of the correlation length at which differences in the behaviour of the various models should be expected. For the icosahedron model with nearest-neighbor interactions, we find ξ & 200. We provide...

Asymptotically Good Codes Over Non-Abelian Groups

In this paper, we show that good structured codes over non-Abelian groups do exist. Specifically, we construct codes over the smallest non-Abelian group D6 and show that the performance of these codes is superior to the performance of Abelian group codes of the same alphabet size. This promises the possibility of using non-Abelian codes for multi-terminal settings where the structure of the cod...

Abelian versus Non-Abelian Higgs Model in Three Dimensions

We study the phase structure of the abelian Higgs model in three dimensions based on perturbation theory and a set of gauge independent gap equations for Higgs boson and vector boson masses. Contrary to the non-abelian Higgs model, the vector boson mass vanishes in the symmetric phase. In the Higgs phase the gap equations yield masses consistent with perturbation theory. The phase transition is...

Scaling BPS solutions and pure-Higgs states

Depending on the value of the coupling, BPS states of type II string theory compactified on a Calabi-Yau manifold can be described as multicenter supergravity solutions or as BPS states in a quiver gauge theory. While states that spread into the Coulomb-branch states can be mapped one-to-one to supergravity states, this is not automatically so for the majority of Higgs-branch states. In this pa...

Higgs Bundles and Non-abelian Hodge Theory