M5-brane geometries, T-duality and fluxes

We describe a duality relation between configurations of M5-branes in M-theory and type IIB theory on Taub-NUT geometries with NSNS and RR 3-form field strength fluxes. The flux parameters are controlled by the angles between the M5-brane and the (T)duality directions. For one M5-brane, the duality leads to a family of supersymmetric flux configurations which interpolates between imaginary self-dual fluxes and fluxes similar to the Polchinski-Strassler kind. For multiple M5-branes, the IIB configurations are related to fluxes for twisted sector fields in orbifolds. The dual M5-brane picture also provides a geometric interpretation for several properties of flux configurations (like the supersymmetry conditions, their contribution to tadpoles, etc), and for many non-trivial effects in the IIB side. Among the latter, the dielectric effect for probe D3-branes is dual to the recombination of probe M5-branes with background ones; also, a picture of a decay channel for non-supersymmetric fluxes is suggested.Comment: 30 pages, 3 figure

Casimir effect due to a single boundary as a manifestation of the Weyl problem

The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases the divergences can be eliminated by methods such as zeta-function regularization or through physical arguments (ultraviolet transparency of the boundary would provide a cutoff). Using the example of a massless scalar field theory with a single Dirichlet boundary we explore the relationship between such approaches, with the goal of better understanding the origin of the divergences. We are guided by the insight due to Dowker and Kennedy (1978) and Deutsch and Candelas (1979), that the divergences represent measurable effects that can be interpreted with the aid of the theory of the asymptotic distribution of eigenvalues of the Laplacian discussed by Weyl. In many cases the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having geometrical origin, and an "intrinsic" term that is independent of the cutoff. The Weyl terms make a measurable contribution to the physical situation even when regularization methods succeed in isolating the intrinsic part. Regularization methods fail when the Weyl terms and intrinsic parts of the Casimir effect cannot be clearly separated. Specifically, we demonstrate that the Casimir self-energy of a smooth boundary in two dimensions is a sum of two Weyl terms (exhibiting quadratic and logarithmic cutoff dependence), a geometrical term that is independent of cutoff, and a non-geometrical intrinsic term. As by-products we resolve the puzzle of the divergent Casimir force on a ring and correct the sign of the coefficient of linear tension of the Dirichlet line predicted in earlier treatments.Comment: 13 pages, 1 figure, minor changes to the text, extra references added, version to be published in J. Phys.