Narrow Results

Axion electrodynamics is deduced from the local duality invariant electrodynamics (LDIE) with a new perspective on both formalism and the physical interpretation. First, the delicate issue of duality rotation symmetry in the Maxwell action is critically reviewed and the generalized Maxwell field equations invariant under local duality rotation are derived. In the alternative approach, a generalization is made to Sudbery’s pseudo-vector action such that it is local duality invariant. Variational principle is used to derive the Euler–Lagrange equations of motion. The gauge potential for local duality rotation, termed duroton, under the assumption that it is a gradient of the axion field leads to the dual symmetric axion electrodynamics. The absence of the magnetic monopole in Maxwell equations motivates to impose a natural condition to deduce the standard axion electrodynamics. The present derivation offers the possibility for new physical interpretation of the axions and the monopoles.

New actions in D = 2 and D = 3 are proposed that are dual equivalent to known theories displaying well-defined chirality and helicity, respectively, along with new interpolating actions mapping continuously through the original dualities. The new chiral action in D = 2 is a second-order theory displaying the chiral constraint dynamically. In D = 3 the helicity constraint is imposed a la Siegel displaying a continuous mapping between the Maxwell–Chern–Simons and the self-dual model. It is also shown that the resulting theories introduce new versions of the Hull noton to take care of the symmetry aspects of the original models. The new interpolating formulation is then reexamined as a condensed phase for the discussion of duality under the light of the dual mechanisms — Julia–Toulouse and Higgs — establishing new interpolating actions in the dilute phase, according to these mechanisms.

By generalizing the Hodge dual operator to the case of soldered bundles, and working in the context of the teleparallel equivalent of general relativity, an analysis of the duality symmetry in gravitation is performed. Although the basic conclusion is that, at least in the general case, gravitation is not dual symmetric, there is a particular theory in which this symmetry shows up. It is a self dual (or anti-self dual) teleparallel gravity in which, due to the fact that it does not contribute to the interaction of fermions with gravitation, the purely tensor part of torsion is assumed to vanish. The ensuing fermionic gravitational interaction is found to be chiral. Since duality is intimately related to renormalizability, this theory may eventually be more amenable to renormalization than teleparallel gravity or general relativity.

We discuss the consequences of a duality-invariant Einstein–Planck (DIEP) relation on the equation of state of micro black holes. The results are analogous to those obtained from the "world-crystal" model, but with some significative differences, as for instance a limiting vanishing value for temperature for very small black holes. The model leads to a total evaporation of micro black holes but with the final stage being very slow.

Starting from a generalized black hole entropy with logarithmic area corrections, in this paper we obtain (for positive value of the coefficient of the correction term) a generalized equation of state for black holes with two dual branches. In one of them (the usual one for macro black holes) T ≃ 1/M, with T temperature and M mass. In the other one, for micro black holes, instead, T ≃ M. We compare the equilibrium and stability between macro black holes and electromagnetic radiation in a finite box with reflecting walls, with the dual situation corresponding to micro black holes and cosmic string loops, also in a finite box. In this model, the dual phenomenon of evaporation of unstable macro black holes into a stable gas of electromagnetic radiation would be the condensation of unstable gas of cosmic string loops into stable micro black holes.

We discuss general conditions which are imposed on the form of actions for duality-symmetric theories by the requirement of manifest duality symmetry and space-time invariance.