N=1 SYM Action and BRST Cohomology

The relation between BRST cohomology and the N=1 supersymmetric Yang-Mills action in 4 dimensions is discussed. In particular, it is shown that both off and on shell N=1 SYM actions are related to a lower dimensional field polynomial by solving the descent equations, which is obtained from the cohomological analysis of linearized Slavnov-Taylor operator \B, in the framework of Algebraic Renormalization. Furthermore we show that off and on shell solutions differ only by a \B- exact term, which is a consequence of the fact that the cohomology of both cases are same.Comment: 14 Pages, LaTex. Revised version. To be published in MPL

N=2 Super Yang Mills Action and BRST Cohomology

The extended BRST cohomology of N=2 super Yang-Mills theory is discussed in the framework of Algebraic Renormalization. In particular, N=2 supersymmetric descent equations are derived from the cohomological analysis of linearized Slavnov-Taylor operator \B. It is then shown that both off- and on-shell N=2 super Yang-Mills actions are related to a lower-dimensional gauge invariant field polynomial Tr\f^2 by solving these descent equations. Moreover, it is found that these off- and on-shell solutions differ only by a \B-exact term, which can be interprated as a consequence of the fact that the cohomology of both cases are the same.Comment: Latex, 1+13 page

Gravitational shock waves and vacuum fluctuations

We show that the vacuum expectation value of the stress-energy tensor of a scalar particle on the background of a spherical gravitational shock wave does not give a finite expression in second order perturbation theory, contrary to the case seen for the impulsive wave. No infrared divergences appear at this order. This result shows that there is a qualitative difference between the shock and impulsive wave solutions which is not exhibited in first order.Comment: Submitted to Class. and Quant. Grav.,7 pages, no figure

On nonsingularity of combinations of three group invertible matrices and three tripotent matrices

Let T=c1T1+c2T2+c3T3- c4(T1T2+T3T1+T2T3), where T1, T2, T3 are three n x n tripotent matrices and c1, c2, c3, c4 are complex numbers with c1, c2, c3 nonzero. In this article, necessary and sufficient conditions for the nonsingularity of such combinations are established and some formulae for the inverses of them are obtained. Some of these results are given in terms of group invertible matrices.We would like to thank the referee for his/her careful reading. The first author was supported by the Vicerrectorado de Investigacion U.P.V. PAID 06-2010-2285.Benítez López, J.; Sarduvan, M.; Ülker, S.; Özdemir, H. (2013). On nonsingularity of combinations of three group invertible matrices and three tripotent matrices. Linear and Multilinear Algebra. 61(4):463-481. https://doi.org/10.1080/03081087.2012.689986S463481614Baksalary, J. K., & Baksalary, O. M. (2004). Nonsingularity of linear combinationsof idempotent matrices. Linear Algebra and its Applications, 388, 25-29. doi:10.1016/j.laa.2004.02.025Baksalary, J. K., Baksalary, O. M., & Özdemir, H. (2004). A note on linear combinations of commuting tripotent matrices. Linear Algebra and its Applications, 388, 45-51. doi:10.1016/j.laa.2004.01.011Benítez, J., Liu, X., & Zhu, T. (2010). Nonsingularity and group invertibility of linear combinations of twok-potent matrices. Linear and Multilinear Algebra, 58(8), 1023-1035. doi:10.1080/03081080903207932Benítez, J., & Thome, N. (2006). {k}-Group Periodic Matrices. SIAM Journal on Matrix Analysis and Applications, 28(1), 9-25. doi:10.1137/s0895479803437384Gross, J., & Trenkler, G. (2000). Nonsingularity of the Difference of Two Oblique Projectors. SIAM Journal on Matrix Analysis and Applications, 21(2), 390-395. doi:10.1137/s0895479897320277Horn, R. A., & Johnson, C. R. (1985). Matrix Analysis. doi:10.1017/cbo9780511810817Koliha, J. J., & Rakočević, V. (2006). The nullity and rank of linear combinations of idempotent matrices. Linear Algebra and its Applications, 418(1), 11-14. doi:10.1016/j.laa.2006.01.011Koliha, J. ., Rakočević, V., & Straškraba, I. (2004). The difference and sum of projectors. Linear Algebra and its Applications, 388, 279-288. doi:10.1016/j.laa.2004.03.008Liu, X., Wu, S., & Benítez, J. (2011). On nonsingularity of combinations of two group invertible matrices and two tripotent matrices. Linear and Multilinear Algebra, 59(12), 1409-1417. doi:10.1080/03081087.2011.558843Meyer, C. (2000). Matrix Analysis and Applied Linear Algebra. doi:10.1137/1.9780898719512Mitra, S. K. (1987). On group inverses and the sharp order. Linear Algebra and its Applications, 92, 17-37. doi:10.1016/0024-3795(87)90248-5Mitra, S. K., & Bhimasankaram, P. (2010). MATRIX PARTIAL ORDERS, SHORTED OPERATORS AND APPLICATIONS. SERIES IN ALGEBRA. doi:10.1142/9789812838452Zhang, F. (1999). Matrix Theory. Universitext. doi:10.1007/978-1-4757-5797-2Zuo, K. (2010). Nonsingularity of the difference and the sum of two idempotent matrices. Linear Algebra and its Applications, 433(2), 476-482. doi:10.1016/j.laa.2010.03.01

N=2 SYM Action as a BRST Exact Term, Topological Yang Mills and Instantons

By constructing a nilpotent extended BRST operator \bs that involves the N=2 global supersymmetry transformations of one chirality, we show that the standard N=2 off-shell Super Yang Mills Action can be represented as an exact BRST term \bs \Psi, if the gauge fermion $\Psi$ is allowed to depend on the inverse powers of supersymmetry ghosts. By using this nonanalytical structure of the gauge fermion (via inverse powers of supersymmetry ghosts), we give field redefinitions in terms of composite fields of supersymmetry ghosts and N=2 fields and we show that Witten's topological Yang Mills theory can be obtained from the ordinary Euclidean N=2 Super Yang Mills theory directly by using such field redefinitions. In other words, TYM theory is obtained as a change of variables (without twisting). As a consequence it is found that physical and topological interpretations of N=2 SYM are intertwined together due to the requirement of analyticity of global SUSY ghosts. Moreover, when after an instanton inspired truncation of the model is used, we show that the given field redefinitions yield the Baulieu-Singer formulation of Topological Yang Mills.Comment: Latex, 1+15 pages. Published versio

N=1/2 Supersymmetric gauge theory in noncommutative space

A formulation of (non-anticommutative) N=1/2 supersymmetric U(N) gauge theory in noncommutative space is studied. We show that at one loop UV/IR mixing occurs. A generalization of Seiberg-Witten map to noncommutative and non-anticommutative superspace is employed to obtain an action in terms of commuting fields at first order in the noncommutativity parameter tetha. This leads to abelian and non-abelian gauge theories whose supersymmetry transformations are local and non-local, respectively.Comment: One reference added, published versio

Distinct expression patterns of two Arabidopsis phytocystatin genes, AtCYS1 and AtCYS2, during development and abiotic stresses

The phytocystatins of plants are members of the cystatin superfamily of proteins, which are potent inhibitors of cysteine proteases. The Arabidopsis genome encodes seven phytocystatin isoforms (AtCYSs) in two distantly related AtCYS gene clusters. We selected AtCYS1 and AtCYS2 as representatives for each cluster and then generated transgenic plants expressing the GUS reporter gene under the control of each gene promoter. These plants were used to examine AtCYS expression at various stages of plant development and in response to abiotic stresses. Histochemical analysis of AtCYS1 promoter- and AtCYS2 promoter-GUS transgenic plants revealed that these genes have similar but distinct spatial and temporal expression patterns during normal development. In particular, AtCYS1 was preferentially expressed in the vascular tissue of all organs, whereas AtCYS2 was expressed in trichomes and guard cells in young leaves, caps of roots, and in connecting regions of the immature anthers and filaments and the style and stigma in flowers. In addition, each AtCYS gene has a unique expression profile during abiotic stresses. High temperature and wounding stress enhanced the expression of both AtCYS1 and AtCYS2, but the temporal and spatial patterns of induction differed. From these data, we propose that these two AtCYS genes play important, but distinct, roles in plant development and stress responses

Sense and Antisense Transcripts of Convergent Gene Pairs in Arabidopsis thaliana Can Share a Common Polyadenylation Region

The Arabidopsis genome contains a large number of gene pairs that encode sense and antisense transcripts with overlapping 3′ regions, indicative for a potential role of natural antisense transcription in regulating sense gene expression or transcript processing. When we mapped poly(A) transcripts of three plant gene pairs with long overlapping antisense transcripts, we identified an unusual transcript composition for two of the three gene pairs. Both genes pairs encoded a class of long sense transcripts and a class of short sense transcripts that terminate within the same polyadenylation region as the antisense transcripts encoded by the opposite strand. We find that the presence of the short sense transcript was not dependent on the expression of an antisense transcript. This argues against the assumption that the common termination region for sense and antisense poly(A) transcripts is the result of antisense-specific regulation. We speculate that for some genes evolution may have especially favoured alternative polyadenylation events that shorten transcript length for gene pairs with overlapping sense/antisense transcription, if this reduces the likelihood for dsRNA formation and transcript degradation