In plain language, this means that we compensate the extra minus sign in the supertrace by complexifying the group parameters.
Random Matrix Theory and Chiral Symmetry in QCD
But we will also observe that this condition has an extended gauge symmetry, which we obtain by using J to complexify the real gauge symmetry on the world-volume.
Deformations of calibrated D-branes in flux generalized complex manifolds
As we have explained at the beginning of section 4, the space of generalized complex cycles Chol is preserved by the action of the algebra of complexiﬁed inﬁnitesimal gauge transformations gC , which we obtained by complexifying the world-volume gauge transformations.
Deformations of calibrated D-branes in flux generalized complex manifolds
In the paper it was shown how to drop the requirement that the functions (λi ) and (z i ) are real and how the St¨ackel-Eisenhart theory and the Levi-Civita criterion can be extended to this case, without to complexify the manifold Q.
Complex variables for separation of Hamilton-Jacobi equation on three-dimensional Minkowski space
The proof of Theorem 1.8 We complexify and let VC := V0 ⊗R C.
Pseudo-Riemannian Jacobi-Videv Manifolds
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