Field Strength Formulation of SU(2) Yang-Mills Theory in the Maximal Abelian Gauge: Perturbation Theory

We present a reformulation of SU(2) Yang-Mills theory in the maximal Abelian gauge, where the non-Abelian gauge field components are exactly integrated out at the expense of a new Abelian tensor field. The latter can be treated in a semiclassical approximation and the corresponding saddle point equation is derived. Besides the non-trivial solutions, which are presumably related to non-perturbative interactions for the Abelian gauge field, the equation of motion for the tensor fields allows for a trivial solution as well. We show that the semiclassical expansion around this trivial solution is equivalent to the standard perturbation theory. In particular, we calculate the one-loop $\beta$-function for the running coupling constant in this approach and reproduce the standard result.Comment: 29 pages LaTeX, 6 postscript figures. Version to be published in Int. J. Mod. Phys.

Sub-mm counterparts to Lyman-break galaxies

We summarize the main results from our SCUBA survey of Lyman-break galaxies (LBGs) at z~3. Analysis of our sample of LBGs reveals a mean flux of S850=0.6$\pm$0.2 mJy, while simple models of emission based on the UV properties predict a mean flux about twice as large. Known populations of LBGs are expected to contribute flux to the weak sub-mm source portion of the far-IR background, but are not likely to comprise the bright source (S850>5 mJy) end of the SCUBA-detected source count. The detection of the LBG, Westphal-MM8, at 1.9 mJy suggests that deeper observations of individual LBGs in our sample could uncover detections at similar levels, consistent with our UV-based predictions. By the same token, many sub-mm selected sources with S850<2 mJy could be LBGs. The data are also consistent with the FarIR/$\beta$ relation holding at z=3.Comment: 6 pages, 1 figure, contributed talk at UMass/INAOE Conference ``Deep Millimeter Surveys'

The Orbifolds of Permutation-Type as Physical String Systems at Multiples of c=26 IV. Orientation Orbifolds Include Orientifolds

In this fourth paper of the series, I clarify the somewhat mysterious relation between the large class of {\it orientation orbifolds} (with twisted open-string CFT's at $\hat c=52$) and {\it orientifolds} (with untwisted open strings at $c=26$), both of which have been associated to division by world-sheet orientation-reversing automorphisms. In particular -- following a spectral clue in the previous paper -- I show that, even as an {\it interacting string system}, a certain half-integer-moded orientation orbifold-string system is in fact equivalent to the archetypal orientifold. The subtitle of this paper, that orientation orbifolds include and generalize standard orientifolds, then follows because there are many other orientation orbifold-string systems -- with higher fractional modeing -- which are not equivalent to untwisted string systems.Comment: 22 pages, typos correcte

Hamiltonian Formulation of Open WZW Strings

Using a Hamiltonian approach, we construct the classical and quantum theory of open WZW strings on a strip. (These are the strings which end on WZW branes.) The development involves non-abelian generalized Dirichlet images in an essential way. At the classical level, we find a new non-commutative geometry in which the equal-time coordinate brackets are non-zero at the world-sheet boundary, and the result is an intrinsically non-abelian effect which vanishes in the abelian limit. Using the classical theory as a guide to the quantum theory, we also find the operator algebra and the analogue of the Knizhnik-Zamolodchikov equations for the the conformal field theory of open WZW strings.Comment: 34 pages. Added an equation in Appendix C; some typos corrected. Footnote b changed. Version to appear on IJMP

Modal Logics with Hard Diamond-free Fragments

We investigate the complexity of modal satisfiability for certain combinations of modal logics. In particular we examine four examples of multimodal logics with dependencies and demonstrate that even if we restrict our inputs to diamond-free formulas (in negation normal form), these logics still have a high complexity. This result illustrates that having D as one or more of the combined logics, as well as the interdependencies among logics can be important sources of complexity even in the absence of diamonds and even when at the same time in our formulas we allow only one propositional variable. We then further investigate and characterize the complexity of the diamond-free, 1-variable fragments of multimodal logics in a general setting.Comment: New version: improvements and corrections according to reviewers' comments. Accepted at LFCS 201

New Spin-Two Gauged Sigma Models and General Conformal Field Theory

Recently, we have studied the general Virasoro construction at one loop in the background of the general non-linear sigma model. Here, we find the action formulation of these new conformal field theories when the background sigma model is itself conformal. In this case, the new conformal field theories are described by a large class of new spin-two gauged sigma models. As examples of the new actions, we discuss the spin-two gauged WZW actions, which describe the conformal field theories of the generic affine-Virasoro construction, and the spin-two gauged g/h coset constructions. We are able to identify the latter as the actions of the local Lie h-invariant conformal field theories, a large class of generically irrational conformal field theories with a local gauge symmetry.Comment: LaTeX, 28 pages, references and clarifying remarks adde

Vertex Operators in 2K Dimensions

A formula is proposed which expresses free fermion fields in 2K dimensions in terms of the Cartan currents of the free fermion current algebra. This leads, in an obvious manner, to a vertex operator construction of nonabelian free fermion current algebras in arbitrary even dimension. It is conjectured that these ideas may generalize to a wide class of conformal field theories.Comment: Minor change in notation. Change in references