Electromagnetism, metric deformations, ellipticity and gauge operators on conformal 4-manifolds

On Riemannian signature conformal 4-manifolds we give a conformally invariant extension of the Maxwell operator on 1-forms. We show the extension is in an appropriate sense injectively elliptic, and recovers the invariant gauge operator of Eastwood and Singer. The extension has a natural compatibility with the de Rham complex and we prove that, given a certain restriction, its conformally invariant null space is isomorphic to the first de Rham cohomology. General machinery for extending this construction is developed and as a second application we describe an elliptic extension of a natural operator on perturbations of conformal structure. This operator is closely linked to a natural sequence of invariant operators that we construct explictly. In the conformally flat setting this yields a complex known as the conformal deformation complex and for this we describe a conformally invariant Hodge theory which parallels the de Rham result.Comment: 30 pages, LaTe

Causes of Appreciation and Volatility of the Dollar with Comment by Jacob Frenkel

In 1981 real interest rates in the United States increased spectacularly, and the dollar appreciated in real terms by about 20 percent. Since the end of 1981, long-term real interest rates have remained in the range of 5-10 percent, with nominal long rates above short rates. The dollar appreciated further, but more gradually, until early 1985. This paper argues that these movements in real interest rates and the real exchange rate are due to the shift in the high-employment deficit by some $200 billion that was announced in the 1981 budget program. This requires an increase in real interest rates and a real appreciation to generate the sum of excess domestic saving and foreign borrowing to finance it. The argument is a straightforward extension of the idea of "crowding out" at full employment to an open economy.The current situation is not sustainable, however. Eventually international investors will begin to resist further absorption of dollars into their portfolios, so U.S. interest rates will have to rise further, as the markets seem to expect, and the dollar will have to depreciate. This will continue until the current account is back in approximate balance, and the entire load of deficit financing is shifted to excess U.S. saving. In his comments on Branson's paper, Jacob A. Frenkel discusses additional factors that have contributed to the evolution of the dollar since 1980. He concludes that in addition to U.S. fiscal policies, monetary policy in the United States and the fiscal position of the U.K., West Germany and Japan have also contributed to the dollar's strength.

Higher Spin Gravitational Couplings and the Yang--Mills Detour Complex

Gravitational interactions of higher spin fields are generically plagued by inconsistencies. We present a simple framework that couples higher spins to a broad class of gravitational backgrounds (including Ricci flat and Einstein) consistently at the classical level. The model is the simplest example of a Yang--Mills detour complex, which recently has been applied in the mathematical setting of conformal geometry. An analysis of asymptotic scattering states about the trivial field theory vacuum in the simplest version of the theory yields a rich spectrum marred by negative norm excitations. The result is a theory of a physical massless graviton, scalar field, and massive vector along with a degenerate pair of zero norm photon excitations. Coherent states of the unstable sector of the model do have positive norms, but their evolution is no longer unitary and their amplitudes grow with time. The model is of considerable interest for braneworld scenarios and ghost condensation models, and invariant theory.Comment: 19 pages LaTe

The conformal Killing equation on forms -- prolongations and applications

We construct a conformally invariant vector bundle connection such that its equation of parallel transport is a first order system that gives a prolongation of the conformal Killing equation on differential forms. Parallel sections of this connection are related bijectively to solutions of the conformal Killing equation. We construct other conformally invariant connections, also giving prolongations of the conformal Killing equation, that bijectively relate solutions of the conformal Killing equation on $k$-forms to a twisting of the conformal Killing equation on (k - l)-forms for various integers l. These tools are used to develop a helicity raising and lowering construction in the general setting and on conformally Einstein manifolds.Comment: 37 page

Arthurian Elements in \u3ci\u3eThe Hideous Strength\u3c/i\u3e

“A look at the specifically Arthurian inspirations behind parts of [That Hideous Strength] [...] how Lewis diverged from the traditional sources in crafting his tale, and what he did with them.

Quantum Effective Action in Spacetimes with Branes and Boundaries

We construct quantum effective action in spacetime with branes/boundaries. This construction is based on the reduction of the underlying Neumann type boundary value problem for the propagator of the theory to that of the much more manageable Dirichlet problem. In its turn, this reduction follows from the recently suggested Neumann-Dirichlet duality which we extend beyond the tree level approximation. In the one-loop approximation this duality suggests that the functional determinant of the differential operator subject to Neumann boundary conditions in the bulk factorizes into the product of its Dirichlet counterpart and the functional determinant of a special operator on the brane -- the inverse of the brane-to-brane propagator. As a byproduct of this relation we suggest a new method for surface terms of the heat kernel expansion. This method allows one to circumvent well-known difficulties in heat kernel theory on manifolds with boundaries for a wide class of generalized Neumann boundary conditions. In particular, we easily recover several lowest order surface terms in the case of Robin and oblique boundary conditions. We briefly discuss multi-loop applications of the suggested Dirichlet reduction and the prospects of constructing the universal background field method for systems with branes/boundaries, analogous to the Schwinger-DeWitt technique.Comment: LaTeX, 25 pages, final version, to appear in Phys. Rev.