Jet coordinates for local BRST cohomology

The construction of appropriate jet space coordinates for calculating local BRST cohomology groups is discussed. The relation to tensor calculus is briefly reviewed too.Comment: 11 pages, correction in eq. (29), to appear in Lett.Math.Phy

Local BRST cohomology and covariance

The paper provides a framework for a systematic analysis of the local BRST cohomology in a large class of gauge theories. The approach is based on the cohomology of s+d in the jet space of fields and antifields, s and d being the BRST operator and exterior derivative respectively. It relates the BRST cohomology to an underlying gauge covariant algebra and reduces its computation to a compactly formulated problem involving only suitably defined generalized connections and tensor fields. The latter are shown to provide the building blocks of physically relevant quantities such as gauge invariant actions, Noether currents and gauge anomalies, as well as of the equations of motion.Comment: 33 pages, latex 2.09, no figures, introduction extended + minor modifications; final version, to appear in Commun. Math. Phy

Supersymmetry algebra cohomology II: Primitive elements in 2 and 3 dimensions

The primitive elements of the supersymmetry algebra cohomology as defined in a companion paper are computed exhaustively for standard supersymmetry algebras in dimensions D=2 and D=3, for all signatures (t,D-t) and all numbers N of sets of supersymmetries.Comment: 19 pages; v3: matches published version; presentation of D=3 analysis streamlined; presentation of lemmas 2.3 and 2.5 improved; minor correction of misprints; minor change of titl

B\"acklund Transformations an Zero-Curvature Representations of Systems of Partial Differential Equations

It is shown that B\"acklund transformations (BTs) and zero-curvature representations (ZCRs) of systems of partial differential equations (PDEs) are closely related. The connection is established by nonlinear representations of the symmetry group underlying the ZCR which induce gauge transformations relating different BTs. This connection is used to construct BTs from ZCRs (and vice versa). Furthermore a procedure is outlined which allows a systematic search for ZCRs of a given system of PDEs.Comment: 25 page

Lectures on supergravity

The text is an essentially self-contained introduction to four-dimensional N=1 supergravity, including its couplings to super Yang-Mills and chiral matter multiplets, for readers with basic knowledge of standard gauge theories and general relativity. Emphasis is put on showing how supergravity fits in the general framework of gauge theories and how it can be derived from a tensor calculus for gauge theories of a standard form. Contents: 1. Introduction, 2. Gauge symmetries in the jet space approach, 3. D=4, N=1 pure supergravity, 4. Tensor calculus for standard gauge theories, 5. Off-shell formulations of D=4, N=1 supergravity with matter, A. Lorentz algebra, spinors, Grassmann parity, B. Explicit verification of local supersymmetry.Comment: 48 pages, lectures given at Mitteldeutsche Physik-Combo 2001/2002; v2: added terms in eq. (4.28); v3: typos corrected; v4: very minor improvements in sections 1 and A.2 (reference to Minkowski metric included in sec. 1, "pseudo Majorana" removed, sign factors included in last 3 eqs. in sec. A.2

On the determination of anomalies in supersymmetric theories

We develop an efficient technique to compute anomalies in supersymmetric theories by combining the so-called nonlocal regularization method and superspace techniques. To illustrate the method we apply it to a four dimensional toy model with potentially anomalous N=1 supersymmetry and prove explicitly that in this model all the candidate supersymmetry anomalies have vanishing coefficients at the one-loop level.Comment: 16 pages, no figures, revtex; no major changes, contents reorganized, version to appear in Phys. Rev.