arXiv subjects
Publications and source records attributed to D. M"ulsch.
It is shown that the Spin(7)-invariant super Yang-Mills theory in euight dimensions, which relies on the existence of the Caley invariant, permits the construction of a cohomological extension, which relies on the existence of the eight-dimensional analogue of the Pontryagin invariant arising from a quartic chiral primary operator.
A formulation of the N_T=1, D=8 Euclidean super Yang-Mills theory with generalized self-duality and reduced Spin(7)-invariance is given which avoids the peculiar extra constraints of Nishino and Rajpoot, hep-th/0210132. Its reduction to 7 dimensions leads to the G_2-invariant N_T=2, D=7 super Yang-Mills theory which may be regarded as a higher-dimensional analogue of the N=2, D=3 super-BF theory. When reducing further that G_2-invariant theory to 3 dimensions one gets the N_T=2 super-BF theory coupled to a spinorial hypermultiplet.
The construction of a $N_T=3$ cohomological gauge theory on an hyper-K"ahler eight-fold, whose group theoretical descrition was given by Blau and Thompson, is performed explicitly.
A new type of topological matter interactions involving second-rank antisymmetric tensor matter fields with an underlying $N_T \geq 1$ topological supersymmetry are proposed. The construction of the 4-dimensional, $N_T = 1$ Donaldson-Witten theory, the $N_T = 1$ super-BF model and the $N_T = 2$ topological B-model with tensor matter are explicitly worked out.
It is shown that the dimensional reduction of the N_T=2, D=3 Blau-Thompson model to D=2, i.e., the novel topological twist of N=8, D=2 super Yang-Mills theory, provides an example of a Hodge-type cohomological theory. In that theory the generators of the topological shift, co-shift and gauge symmetry, together with a discrete duality operation, are completely analogous to the de Rham cohomology operators and the Hodge *-operation.
The osp(1,2)-covariant Lagrangian quantization of irreducible gauge theories [hep-th/9712204] is generalized to L-stage reducible theories. The dependence of the generating functional of Green's functions on the choice of gauge in the massive case is dicussed and Ward identities related to osp(1,2) symmetry are given. Massive first stage theories with closed gauge algebra are studied in detail. The generalization of the Chapline-Manton model and topological Yang-Mills theory to the case of massive fields is consedered as examples.
Nonabelian gauge theories with a generic background field A_mu in nonlinear gauges due to Delbourgo and Jarvis are investigated. The A_mu-dependence is completely determined by the help of a linear differential equation which obtaines from the Kluberg-Stern-Zuber and the Lee identity. Its integration leads to a relation between the one-particle irreducible vertex functional in the background field A_mu and the corresponding functional for A_mu = 0. An analogous relation holds for the generating functional of the complete Green functions which, after restriction to physical Green functions, is used to confirm a result obtained by Rouet in the case of linear background gauge.