Higher Spin BRS Cohomology of Supersymmetric Chiral Matter in D=4

We examine the BRS cohomology of chiral matter in $N=1$, $D=4$ supersymmetry to determine a general form of composite superfield operators which can suffer from supersymmetry anomalies. Composite superfield operators \Y_{(a,b)} are products of the elementary chiral superfields $S$ and \ov S and the derivative operators D_\a, \ov D_{\dot \b} and \pa_{\a \dot \b}. Such superfields \Y_{(a,b)} can be chosen to have `$a$' symmetrized undotted indices \a_i and `$b$' symmetrized dotted indices \dot \b_j. The result derived here is that each composite superfield \Y_{(a,b)} is subject to potential supersymmetry anomalies if $a-b$ is an odd number, which means that \Y_{(a,b)} is a fermionic superfield.Comment: 15 pages, CPT-TAMU-20/9

Fuzzy Surfaces of Genus Zero

A fuzzy version of the ordinary round 2-sphere has been constructed with an invariant curvature. We here consider linear connections on arbitrary fuzzy surfaces of genus zero. We shall find as before that they are more or less rigidly dependent on the differential calculus used but that a large number of the latter can be constructed which are not covariant under the action of the rotation group. For technical reasons we have been forced to limit our considerations to fuzzy surfaces which are small perturbations of the fuzzy sphere.Comment: 11 pages, Late

Noncommutative spacetime symmetries: Twist versus covariance

We prove that the Moyal product is covariant under linear affine spacetime transformations. From the covariance law, by introducing an $(x,\Theta)$-space where the spacetime coordinates and the noncommutativity matrix components are on the same footing, we obtain a noncommutative representation of the affine algebra, its generators being differential operators in $(x,\Theta)$-space. As a particular case, the Weyl Lie algebra is studied and known results for Weyl invariant noncommutative field theories are rederived in a nutshell. We also show that this covariance cannot be extended to spacetime transformations generated by differential operators whose coefficients are polynomials of order larger than one. We compare our approach with the twist-deformed enveloping algebra description of spacetime transformations.Comment: 19 pages in revtex, references adde

Algebraic characterization of the Wess-Zumino consistency conditions in gauge theories

A new way of solving the descent equations corresponding to the Wess-Zumino consistency conditions is presented. The method relies on the introduction of an operator $\delta$ which allows to decompose the exterior space-time derivative $d$ as a $BRS$ commutator. The case of the Yang-Mills theories is treated in detail.Comment: 16 pages, UGVA-DPT 1992/08-781 to appear in Comm. Math. Phy

Seiberg-Witten maps and anomalies in noncommutative Yang-Mills theories

A BRST-cohomological analysis of Seiberg-Witten maps and results on gauge anomalies in noncommutative Yang-Mills theories with general gauge groups are reviewed.Comment: 9 pages, talk at 9th Adriatic Meeting, Dubrovnik, Croatia, 4-14 Sept. 200

Yang-Mills gauge anomalies in the presence of gravity with torsion

The BRST transformations for the Yang-Mills gauge fields in the presence of gravity with torsion are discussed by using the so-called Maurer-Cartan horizontality conditions. With the help of an operator \d which allows to decompose the exterior spacetime derivative as a BRST commutator we solve the Wess-Zumino consistency condition corresponding to invariant Chern-Simons terms and gauge anomalies.Comment: 24 pages, report REF. TUW 94-1

Renormalization of the asymptotically expanded Yang-Mills spectral action

We study renormalizability aspects of the spectral action for the Yang-Mills system on a flat 4-dimensional background manifold, focusing on its asymptotic expansion. Interpreting the latter as a higher-derivative gauge theory, a power-counting argument shows that it is superrenormalizable. We determine the counterterms at one-loop using zeta function regularization in a background field gauge and establish their gauge invariance. Consequently, the corresponding field theory can be renormalized by a simple shift of the spectral function appearing in the spectral action. This manuscript provides more details than the shorter companion paper, where we have used a (formal) quantum action principle to arrive at gauge invariance of the counterterms. Here, we give in addition an explicit expression for the gauge propagator and compare to recent results in the literature.Comment: 28 pages; revised version. To appear in CMP. arXiv admin note: substantial text overlap with arXiv:1101.480

Dual theories for mixed symmetry fields. Spin-two case: (1,1) versus (2,1) Young symmetry type fields

We show that the parent Lagrangian method gives a natural generalization of the dual theories concept for non p-form fields. Using this generalization we construct here a three-parameter family of Lagrangians that are dual to the Fierz-Pauli description of a free massive spin-two system. The dual field is a three-index tensor T, which dinamically belongs to the (2,1) representation of the Lorentz group. As expected, the massless limit of our Lagrangian, which is parameter independent, has two propagating degrees of freedom per space point.Comment: 10 pages, no figure

Protection of outbred mice against a vaginal challenge by a Chlamydia trachomatis serovar E recombinant major outer membrane protein vaccine is dependent on phosphate substitution in the adjuvant.

Chlamydia trachomatis is the most common bacterial sexually-transmitted pathogen for which there is no vaccine. We previously demonstrated that the degree of phosphate substitution in an aluminum hydroxide adjuvant in a TLR-4-based C. trachomatis serovar E (Ser E) recombinant major outer membrane protein (rMOMP) formulation had an impact on the induced antibody titers and IFN-γ levels. Here, we have extended these observations using outbreed CD-1 mice immunized with C. trachomatis Ser E rMOMP formulations to evaluate the impact on bacterial challenge. The results confirmed that the rMOMP vaccine containing the adjuvant with the highest phosphate substitution induced the highest neutralizing antibody titers while the formulation with the lowest phosphate substitution induced the highest IFN-γ production. The most robust protection was observed in mice vaccinated with the formulation containing the adjuvant with the lowest phosphate substitution, as shown by the number of mice with positive vaginal cultures, number of positive cultures and number of C. trachomatis inclusion forming units recovered. This is the first report showing that vaccination of an outbred strain of mice with rMOMP induces protection against a vaginal challenge with C. trachomatis

Classical and Quantum Mechanics from the universal Poisson-Rinehart algebra of a manifold

The Lie and module (Rinehart) algebraic structure of vector fields of compact support over C infinity functions on a (connected) manifold M define a unique universal non-commutative Poisson * algebra. For a compact manifold, a (antihermitian) variable Z, central with respect to both the product and the Lie product, relates commutators and Poisson brackets; in the non-compact case, sequences of locally central variables allow for the addition of an element with the same role. Quotients with respect to the (positive) values taken by Z* Z define classical Poisson algebras and quantum observable algebras, with the Planck constant given by -iZ. Under standard regularity conditions, the corresponding states and Hilbert space representations uniquely give rise to classical and quantum mechanics on M.Comment: Talk given by the first author at the 40th Symposium on Mathematical Physics, Torun, June 25-28, 200