The bosonic string and superstring models in 26+2 and 10+2 dimensional space--time, and the generalized Chern-Simons action
Abstract
We have covariantized the Lagrangians of the U(1)V * U(1)A models, which have U(1)V * U(1)A gauge symmetry in two dimensions, and studied their symmetric structures. The special property of the U(1)V * U(1)A models is the fact that all these models have an extra time coordinate in the target space-time. The U(1)V * U(1)A models coupled to two-dimensional gravity are string models in 26+2 dimensional target space-time for bosonic string and in 10+2 dimensional target space-time for superstring. Both string models have two time coordinates. In order to construct the covariant Lagrangians of the U(1)V * U(1)A models the generalized Chern-Simons term plays an important role. The supersymmetric generalized Chern-Simons action is also proposed. The Green-Schwarz type of U(1)V * U(1)A superstring model has another fermionic local symmetry as well as -symmetry. The supersymmetry of target space-time is different from the standard one.
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