[en] We study the locality properties of the vortex operators in compact U(1) Maxwell-Chern-Simons and SU(N) Yang-Mills-Chern-Simons theories in 2+1 dimensions. We find that these theories do admit local vortex operators and thus in the UV regularized versions should contain stable magnetic vortices. In the continuum limit however the energy of these vortex excitations generically is logarithmically UV divergent. Nevertheless the classical analysis shows that at small values of the CS coefficient κ the vortices become light. It is conceivable that they in fact become massless and condense due to quantum effects below some small κ. If this happens the magnetic symmetry breaks spontaneously and the theory is confining

[en] We demonstrate by explicit construction that while the untwisted Harrington-Shepard caloron A_μ is manifestly periodic in Euclidean time, with a period β=1/T, when transformed to the Weyl (A₀=0) gauge, the caloron gauge field A_i is periodic only up to a large gauge transformation, with the winding number equal to the caloron's topological charge. This helps clarify the tunneling interpretation of these solutions, and their relation to Chern-Simons numbers and winding numbers

[en] It is known that self-duality equations for multi-instantons on a line in four dimensions are equivalent to minimal surface equations in three dimensional Minkowski space. We extend this equivalence beyond the equations of motion and show that topological number, instanton moduli space and anti-self-dual solutions have representations in terms of minimal surfaces. The issue of topological charge is quite subtle because the surfaces that appear are non-compact. This minimal surface/instanton correspondence allows us to define a metric on the configuration space of the gauge fields. We obtain the minimal surface representation of an instanton with arbitrary charge. The trivial vacuum and the BPST instanton as minimal surfaces are worked out in detail. BPS monopoles and the geodesics are also discussed. (author)

[en] We show that correlators of some local operators in gauge theories are sensitive to the presence of the instantons even at high temperature where the latter are bound into instanton-antiinstanton 'molecules'. We calculate correlation functions of such operators in the deconfined phase of the 2+1 dimensional Georgi-Glashow model and discuss analogous quantities in the chirally symmetric phase of QCD. We clarify the mechanism by which the instanton-antiinstanton molecules contribute to the anomaly of axial U(1) at high temperature. (author)

[en] We show that the apparently periodic Charap-Duff Yang-Mills 'instantons' in time-compactified Euclidean Schwarzschild space are actually time independent. For these solutions, the Yang-Mills potential is constant along the time direction (no barrier) and therefore, there is no tunneling. We also demonstrate that the solutions found to date are three-dimensional monopoles and dyons. We conjecture that there are no time-dependent solutions in the Euclidean Schwarzschild background

[en] In three dimensions, there are two distinct mass-generating mechanisms for gauge fields: adding the usual Proca/Pauli-Fierz, or the more esoteric Chern-Simons (CS), terms. Here, we analyse the three-term models where both types are present and their various limits. Surprisingly, in the tensor case, these seemingly innocuous systems are physically unacceptable. If the sign of the Einstein term is 'wrong', as is in fact required in the CS theory, then the excitation masses are always complex; with the usual sign, there is a (known) region of the two mass parameters where reality is restored, but instead a ghost problem arises, while for the 'pure mass' two-term system without an Einstein action, complex masses are unavoidable. This contrasts with the smooth behaviour of the corresponding vector models. Separately, we show that the 'partial masslessness' exhibited by (plain) massive spin-2 models in de Sitter backgrounds is shared by the three-term system: it also enjoys a reduced local gauge invariance when this mass parameter is tuned to the cosmological constant. (letter to the editor)

[en] We study static vortex type solutions of pure gravity for D ≥ (4+1). Non-singular vortex solutions can be obtained by considering periodic Kaluza-Klein monopoles. We also show that away from the center of the vortices the space is described by the gravitational instantons derived from minimal surfaces. (author)

[en] We show that, in the weak field limit, at large separations, in sharp contrast to General Relativity (GR), all massive gravity theories predict distance-dependent spin alignments for spinning objects. For all separations GR requires anti-parallel spin orientations with spins pointing along the line joining the sources. Hence total spin is minimized in GR. On the other hand, while massive gravity at small separations (m_gr⩽1.62) gives the same result as GR, for large separations (m_gr>1.62) the spins become parallel to each other and perpendicular to the line joining the objects. Namely, the potential energy is minimized when the total spin is maximized in massive gravity for large separations. We also compute the spin–spin interactions in quadratic gravity theories and find that while at large separations GR result is intact, at small separations, spins become perpendicular to the line joining sources and anti-parallel to each other

[en] New massive gravity provides a nonlinear extension of the Fierz-Pauli mass for gravitons in 2+1 dimensions. Here we construct a Weyl-invariant version of this theory. When the Weyl symmetry is broken, the graviton gets a mass in analogy with the Higgs mechanism. In (anti)-de Sitter backgrounds, the symmetry can be broken spontaneously, but in flat backgrounds radiative corrections, at the two-loop level, break the Weyl symmetry a la Coleman-Weinberg mechanism. We also construct the Weyl-invariant extensions of some other higher-derivative models, such as the Gauss-Bonnet theory (which reduces to the Maxwell theory in three dimensions) and the Born-Infeld type gravities.

[en] We construct the conserved charges (mass and angular momentum) of the Chern-Simons modified general relativity in asymptotically flat and anti-de Sitter (AdS) spacetimes. Our definition is based on background Killing symmetries and reduces to the known expressions in the proper limits