Near zero modes in condensate phases of the Dirac theory on the honeycomb lattice

We investigate a number of fermionic condensate phases on the honeycomb lattice, to determine whether topological defects (vortices and edges) in these phases can support bound states with zero energy. We argue that topological zero modes bound to vortices and at edges are not only connected, but should in fact be \emph{identified}. Recently, it has been shown that the simplest s-wave superconducting state for the Dirac fermion approximation of the honeycomb lattice at precisely half filling, supports zero modes inside the cores of vortices (P. Ghaemi and F. Wilczek, 2007). We find that within the continuum Dirac theory the zero modes are not unique neither to this phase, nor to half filling. In addition, we find the \emph{exact} wavefunctions for vortex bound zero modes, as well as the complete edge state spectrum of the phases we discuss. The zero modes in all the phases we examine have even-numbered degeneracy, and as such pairs of any Majorana modes are simply equivalent to one ordinary fermion. As a result, contrary to bound state zero modes in $p_x+i p_y$ superconductors, vortices here do \emph{not} exhibit non-Abelian exchange statistics. The zero modes in the pure Dirac theory are seemingly topologically protected by the effective low energy symmetry of the theory, yet on the original honeycomb lattice model these zero modes are split, by explicit breaking of the effective low energy symmetry.Comment: Final version including numerics, accepted for publication in PR

Italy’s constitutional referendum: yet another reform to improve the country’s governability

Italy will hold a constitutional referendum on 20-21 September which proposes to reduce the size of both chambers of the Italian parliament. Matthew E. Bergman provides the background to the vote and assesses the potential political consequences

Winding effects on brane/anti-brane pairs

We study a brane/anti-brane configuration which is separated along a compact direction by constructing a tachyon effective action which takes into account transverse scalars. Such an action is relevant in the study of HQCD model of Sakai and Sugimoto of chiral symmetry breaking, where the size of the compact circle sets the confinement scale. Our approach is motivated by string theory orbifold constructions and gives a route to model inhomogeneous tachyon decay. We illustrate the techniques involved with a relatively simple example of a harmonic oscillator on a circle. We will then repeat the analysis for the Sakai-Sugimoto model and show that by integrating out the winding modes will provide us with a renormalized action with a lower energy than that of truncating to zero winding sector.Comment: 21 pages, 3 figures. v3: discussion and references added, published versio

Slow Dynamics in Glasses

Minimalist theories of complex systems are broadly of two kinds: mean-field and axiomatic. So far all theories of complex properties absent from simple systems and intrinsic to glasses are axiomatic. Stretched Exponential Relaxation (SER) is the prototypical complex temporal property of glasses, discovered by Kohlrausch 150 years ago, and now observed almost universally in microscopically homogeneous, complex non-equilibrium materials, including luminescent electronic (Coulomb) glasses. Critical comparison of alternative axiomatic theories with both numerical simulations and experiments strongly favors dynamical trap models over static percolative or energy landscape models. PACS: 61.20.Lc; 67.40.F