Weyl gravity has been advanced in the recent past as an alternative to General Relativity (GR). The theory has had some success in fitting galactic rotation curves without the need for copious amounts of dark matter. To check the viability of Weyl gravity, we propose two additional classical tests of the theory: the deflection of light and time delay in the exterior of a static spherically symmetric source. The result for the deflection of light is remarkably simple: besides the usual positive (attractive) Einstein deflection of 4GM/r 0 we obtain an extra deflection term of −γr 0 where γ is a constant and r 0 is the radius of closest approach. With a negative γ, the extra term can increase the deflection on large distance scales (galactic or greater) and therefore imitate the effect of dark matter. Notably, the negative sign required for γ is opposite to the sign of γ used to fit galactic rotation curves. The experimental constraints show explicitly that the magnitude of γ is of the order of the inverse Hubble length something already noted as an interesting numerical coincidence in the fitting of galactic rotation curves [9].

We study the properties of soliton solutions in an analogue of the Skyrme model in 2ϩ1 dimensions whose Lagrangian contains the Skyrme term and the mass term, but no usual kinetic term. The model admits a symmetry under area-preserving diffeomorphisms. We solve the dynamical equations of motion analytically for the case of spinning isolated baryon-type solitons. We take fully into account the induced deformation of the spinning Skyrmions and the consequent modification of its moment of inertia to give an analytical example of related numerical behavior found by Piette, Schroers, and Zakrzewski. We solve the equations of motion also for the case of an infinite, open string, and a closed annular string. In each case, the solitons are of finite extent, so called ''compactons,'' being exactly the vacuum outside a compact region. We end with indications on the scattering of baby Skyrmions, as well as some considerations as the properties of solitons on a curved space. ͓S0556-2821͑97͒03512-1͔

We study the quantum phase transition from a Dirac spin liquid to an antiferromagnet driven by condensing monopoles with spin quantum numbers. We describe the transition in field theory by tuning a fermion interaction to condense a spin-Hall mass, which in turn allows the appropriate monopole operators to proliferate and confine the fermions. We compute various critical exponents at the quantum critical point (QCP), including the scaling dimensions of monopole operators by using the state-operator correspondence of conformal field theory. We find that the degeneracy of monopoles in QED3 is lifted and yields a non-trivial monopole hierarchy at the QCP. In particular, the lowest monopole dimension is found to be smaller than that of QED3 using a large N f expansion where 2N f is the number of fermion flavors. For the minimal magnetic charge, this dimension is 0.39N f at leading order. We also study the QCP between Dirac and chiral spin liquids, which allows us to test a conjectured duality to a bosonic CP 1 theory. Finally, we discuss the implications of our results for quantum magnets on the Kagome lattice.

Abstract. We study the theory of Weyl conformal gravity with matter degrees of freedom in a conformally invariant interaction. Specifically, we consider a triplet of scalar fields and SO(3) non-abelian gauge fields, i.e. the Georgi-Glashow model conformally coupled to Weyl gravity. We show that the equations of motion admit solutions spontaneously breaking the conformal symmetry and the gauge symmetry, providing a mechanism for supplying a scale in the theory. The vacuum solution corresponds to anti-de-Sitter space-time, while localized soliton solutions correspond to magnetic monopoles in asymptotically anti-de-Sitter space-time. The resulting effective action gives rise to Einstein gravity and the residual U (1) gauge theory. This mechanism strengthens the reasons for considering conformally invariant mattergravity theory, which has shown promising indications concerning the problem of missing matter in galactic rotation curves.

Paranjape Responds: Brown 1 calculates the expectation value of the covariant, symmetric, stress-energy tensor V kV in the limit of infinite fermion mass. However, since T* v is not conserved, neither is the corresponding angular momentum operator J.I consider, in a rotationally symmetric gauge, the expectation value of the conserved, canonical angular momentum M, which is the generator of rotations. 2 Therefore, Brown has performed, in a simplifying limit, an independent calculation of a different quantity, which in no way reflects on my calculation,The only criticism Brown makes of my Letter 2 is that my angular momentum is not gauge invariant. I consider fermions interacting with a rotationally symmetric magnetic flux tube. I introduce the usual Lagrangean formalism for this system, at the expense of incorporating some redundancies in the description, the gauge freedom. The set of gauge transformations parametrize a family of quantum systems, the Dirac field minimally coupled to the gauge field. One can easily see that in any gauge, there exists a conserved angular momentum operator, and these operators are all unitarily related to each other. In the firstquantized picture (it is trivial to translate everything to the second-quantized picture), under a gauge transformation, the wave function transforms to i//- •• i//' = e /A t//, and the Hamiltonian transforms as H-+H' ^ei\ He -i\ So^ if A/-A/' =