Phase and Scaling Properties of Determinants Arising in Topological Field Theories

In topological field theories determinants of maps with negative as well as positive eigenvalues arise. We give a generalisation of the zeta-regularisation technique to derive expressions for the phase and scaling-dependence of these determinants. For theories on odd-dimensional manifolds a simple formula for the scaling dependence is obtained in terms of the dimensions of certain cohomology spaces. This enables a non-perturbative feature of Chern-Simons gauge theory to be reproduced by path-integral methods.Comment: 12 pages, Latex. To appear in Physics Letters

Supergeometry and Arithmetic Geometry

We define a superspace over a ring $R$ as a functor on a subcategory of the category of supercommutative $R$-algebras. As an application the notion of a $p$-adic superspace is introduced and used to give a transparent construction of the Frobenius map on $p$-adic cohomology of a smooth projective variety over the ring of $p$-adic integers.Comment: 14 pages, expanded introduction, more detail

Coupling a Self-Dual Tensor to Gravity in Six Dimensions

A recent result concerning interacting theories of self-dual tensor gauge fields in six dimensions is generalized to include coupling to gravity. The formalism makes five of the six general coordinate invariances manifest, whereas the sixth one requires a non-trivial analysis. The result should be helpful in formulating the world-volume action of the M theory five-brane.Comment: 7 pages, latex, no figure

Symmetry transformations in Batalin-Vilkovisky formalism

This short note is closely related to Sen-Zwiebach paper on gauge transformations in Batalin-Vilkovisky theory (hep-th 9309027). We formulate some conditions of physical equivalence of solutions to the quantum master equation and use these conditions to give a very transparent analysis of symmetry transformations in BV-approach. We prove that in some sense every quantum observable (i.e. every even function $H$ obeying $\Delta_{\rho}(He^S)=0$) determines a symmetry of the theory with the action functional $S$ satisfying quantum master equation $\Delta_{\rho}e^S=0$ \endComment: 3 page

Semiclassical approximation in Batalin-Vilkovisky formalism

The geometry of supermanifolds provided with $Q$-structure (i.e. with odd vector field $Q$ satisfying $\{ Q,Q\} =0$), $P$-structure (odd symplectic structure ) and $S$-structure (volume element) or with various combinations of these structures is studied. The results are applied to the analysis of Batalin-Vilkovisky approach to the quantization of gauge theories. In particular the semiclassical approximation in this approach is expressed in terms of Reidemeister torsion.Comment: 27 page

Focus markers that link topic and comment

This talk deals with the interdependence between the pragmatic categories topic and focus as displayed by certain alleged focus marking particles of some West African languages

What is it about? The topic in some Ghanaian Gur grammars

This talk deals with the pragmatic notion topic and its encoding in Buli and some related Ghanaian Gur languages and reveals that it is responsible for several intricate phenomena in the grammar of these languages

Low tone spreading in Buli

In Buli, tone indicates lexical information as well as grammatical information. The changing of tone patterns regularly observed on lexemes is covered best by an autosegmental approach with autonomous tonal and segmental tiers. It reveals considerable deviations between underlying and surfacing tones at several morpho- yntactic points. Realization of tone is sometimes oppressed or delayed. Cause for such disturbances is in all cases a low tone which spreads to the right and affects following high tones with different results. The aim of this paper is to show how L spreading acts and how it is integrated in the system of tonal contrast

Quantum curves

One says that a pair (P,Q) of ordinary differential operators specify a quantum curve if [P,Q]=const. If a pair of difference operators (K,L) obey the relation KL=const LK we say that they specify a discrete quantum curve. This terminology is prompted by well known results about commuting differential and difference operators, relating pairs of such operators with pairs of meromorphic functions on algebraic curves obeying some conditions. The goal of this paper is to study the moduli spaces of quantum curves. We will show how to quantize a pair of commuting differential or difference operators (i.e. to construct the corresponding quantum curve or discrete quantum curve). The KP-hierarchy acts on the moduli space of quantum curves; we prove that similarly the discrete KP-hierarchy acts on the moduli space of discrete quantum curves.Comment: New results, some correction