Topological spin transport of photons: the optical Magnus Effect and Berry Phase

The paper develops a modified geometrical optics (GO) of smoothly inhomogeneous isotropic medium, which takes into account two topological phenomena: Berry phase and the optical Magnus effect. By using the analogy between a quasi-classical motion of a quantum particle with a spin and GO of an electromagnetic wave in smoothly inhomogeneous media, we have introduced the standard gauge potential associated with the degeneracy in the wave momentum space. This potential corresponds to the Dirac-monopole-like field (Berry curvature), which causes the topological spin (polarization) transport of photons. The deviations of waves of right-hand and left-hand helicity occur in the opposite directions and orthogonally to the principal direction of motion. This produces a spin current directed across the principal motion. The situation is similar to the anomalous Hall effect for electrons. In addition, a simple scheme of the experiment allowing one to observe the topological spin splitting of photons has been suggested.Comment: 4 pages, 1 figur

The microscopic dynamics of quantum space as a group field theory

We provide a rather extended introduction to the group field theory approach to quantum gravity, and the main ideas behind it. We present in some detail the GFT quantization of 3d Riemannian gravity, and discuss briefly the current status of the 4-dimensional extensions of this construction. We also briefly report on recent results obtained in this approach and related open issues, concerning both the mathematical definition of GFT models, and possible avenues towards extracting interesting physics from them.Comment: 60 pages. Extensively revised version of the contribution to "Foundations of Space and Time: Reflections on Quantum Gravity", edited by G. Ellis, J. Murugan, A. Weltman, published by Cambridge University Pres

Quantum Attractor Flows

Motivated by the interpretation of the Ooguri-Strominger-Vafa conjecture as a holographic correspondence in the mini-superspace approximation, we study the radial quantization of stationary, spherically symmetric black holes in four dimensions. A key ingredient is the classical equivalence between the radial evolution equation and geodesic motion of a fiducial particle on the moduli space M^*_3 of the three-dimensional theory after reduction along the time direction. In the case of N=2 supergravity, M^*_3 is a para-quaternionic-Kahler manifold; in this case, we show that BPS black holes correspond to a particular class of geodesics which lift holomorphically to the twistor space Z of M^*_3, and identify Z as the BPS phase space. We give a natural quantization of the BPS phase space in terms of the sheaf cohomology of Z, and compute the exact wave function of a BPS black hole with fixed electric and magnetic charges in this framework. We comment on the relation to the topological string amplitude, extensions to N>2 supergravity theories, and applications to automorphic black hole partition functions.Comment: 43 pages, 6 figures; v2: typos and references added; v3: published version, minor change

Explicit Actions for Electromagnetism with Two Gauge Fields with Only one Electric and one Magnetic Physical Fields

We extend the work of Mello et al. based in Cabbibo and Ferrari concerning the description of electromagnetism with two gauge fields from a variational principle, i.e. an action. We provide a systematic independent derivation of the allowed actions which have only one magnetic and one electric physical fields and are invariant under the discrete symmetries $P$ and $T$. We conclude that neither the Lagrangian, nor the Hamiltonian, are invariant under the electromagnetic duality rotations. This agrees with the weak-strong coupling mixing characteristic of the duality due to the Dirac quantization condition providing a natural way to differentiate dual theories related by the duality rotations (the energy is not invariant). Also the standard electromagnetic duality rotations considered in this work violate both $P$ and $T$ by inducing Hopf terms (theta terms) for each sector and a mixed Maxwell term. The canonical structure of the theory is briefly addressed and the 'magnetic' gauge sector is interpreted as a ghost sector.Comment: v2: 12 pages; References added, discussion concerning degrees of freedom corrected; v3: is now used the standard normalization of 1/4 in the actions; the possibility of theta being a pseudo-scalar implied a title changing; eq (23) added; signs corrected in equations (39,45-47); references adde