Interaction of vortices in superconductors with kappa close to 2^(-1/2)

Using a perturbative approach to the infinitely degenerate Bogomolnyi vortex state for a superconductor with kappa = 2^(-1/2), T -> T_c, we calculate the interaction of vortices in a superconductor with kappa close to 2^(-1/2). We find, numerically and analytically, that depending on the material the interaction potential between the vortices varies with decreasing kappa from purely repulsive (as in a type-II superconductor) to purely attractive (as in a type-I superconductor) in two different ways: either vortices form a bound state and the distance between them changes gradually from infinity to zero, or this transition occurs in a discontinuous way as a result of a competition between minima at infinity and zero. We study the discontinuous transition between the vortex and Meissner states caused by the non-monotonous vortex interaction and calculate the corresponding magnetization jump.Comment: v1:original submit v2:changed formate of images (gave problems to some) v3:corrected fig v4v6 (was -v4v6) orthographic corrections (and U_lat/int) mismatch v4:more small orthographic corrections v5:converted to revtex4 and bibTex v6:Renamed images to submit to pr

Symmetries within domain walls

The comparison of symmetries in the interior and the exterior of a domain wall is relevant when discussing the correspondence between domain walls and branes, and also when studying the interaction of walls and magnetic monopoles. I discuss the symmetries in the context of an SU(N) times Z_2 model (for odd N) with a single adjoint scalar field. Situations in which the wall interior has less symmetry than the vacuum are easy to construct while the reverse situation requires significant engineering of the scalar potential.Comment: 5 pages. Added reference

Thermodynamic gauge-theory cascade

It is proposed that the cooling of a thermalized SU($N$) gauge theory can be formulated in terms of a cascade involving three effective theories with successively reduced (and spontaneously broken) gauge symmetries, SU($N$) $\to$ U(1)$^{N-1}$ $\to$ Z$_N$. The approach is based on the assumption that away from a phase transition the bulk of the quantum interaction inherent to the system is implicitly encoded in the (incomplete) classical dynamics of a collective part made of low-energy condensed degrees of freedom. The properties of (some of the) statistically fluctuating fields are determined by these condensate(s). This leads to a quasi-particle description at tree-level. It appears that radiative corrections, which are sizable at large gauge coupling, do not change the tree-level picture qualitatively. The thermodynamic self-consistency of the quasi-particle approach implies nonperturbative evolution equations for the associated masses. The temperature dependence of these masses, in turn, determine the evolution of the gauge coupling(s). The hot gauge system approaches the behavior of an ideal gas of massless gluons at asymptotically large temperature. A negative equation of state is possible at a stage where the system is about to settle into the phase of the (spontaneously broken) Z$_N$ symmetry.Comment: 25 pages, 6 figures, 1 reference added, minor corrections in text, errors in Sec. 3.2 corrected, PRD versio

Vortices and extreme black holes: the question of flux expulsion

It has been claimed that extreme black holes exhibit a phenomenon of flux expulsion for abelian Higgs vortices, irrespective of the relative width of the vortex to the black hole. Recent work by two of the authors showed a subtlety in the treatment of the event horizon, which cast doubt on this claim. We analyse in detail the vortex/extreme black hole system, showing that while flux expulsion can occur, it does not do so in all cases. We give analytic proofs for both expulsion and penetration of flux, in each case deriving a bound for that behaviour. We also present extensive numerical work backing up, and refining, these claims, and showing in detail how a vortex can end on a black hole in all situations. We also calculate the backreaction of the vortex on the geometry, and comment on the more general vortex-black hole system.Comment: 28 pages revtex, 10 figures, minor changes, reference adde