Session 11 Of Course 12

Yakawa Couplings include Fujikawa Couplings.  Fujikawa Couplings are examples of Yakawa Couplings in which a one-dimensional superstring becomes a two-dimensional superstring, and, such a coupling in reverse is an example of when a two-dimensional superstring becomes a one-dimensional superstring.  Here is how a one-dimensional superstring becomes a two-dimensional superstring via the Fujikawa Coupling:  A one-dimensional string is ideally a basically straight vibrating strand of discrete energy permittivity.  A one-dimensional string often bears changes in the Laplacian-based mapping of  the concavity of its topology during BRST that works to define the condition of the genus of its topological sway as having the inclusion of an arc-like-shape that acts as  a partial of the said vibrating strand of discrete energy permittivity.  A one-dimensional string often bears changes in the Laplacian-based mapping of the concavity of its topology during BRST that works to define the condition of the genus of its topological sway as having the inclusion of a swivel-like-shape that acts as a partial of the said vibrating strand of discrete energy permittivity.  If the topological format of a given arbitrary one-dimensional superstring bears a genus of being a basically straight vibrating strand during an iteration of BRST, then, or, if the corresponding topological format bears either a mild scalar projection of an arc-like topological sway or a mild scalar projection of a swivel-like topological sway, then, the said given arbitrary superstring may alter to form a two-dimensional string after a relatively small number of iterations of instanton by having the opposite norm-to-holomorphic-based ends of the said superstring bend toward each other until such Poincaire-based loci of the ends of such strings unite via a mathematicaly-based curling operation of which is described as the Green Function.  At this point, the two said opposite ends of the said string unite after the eluded to transient number of instantons via what could be extrapolated in proximity to the two said ends as a fractal of a "Velcro-like" connection that is here local to the cross-sectional surface-area that here exists at the tips of both respective ends of the said string -- in the general field of the directly associated Hilbert-based space that is in the kinematically differentiable neighborhood of the given arbitrary superstring. The process of what I just described happens via the mini-string segments that work to attach both of the said ends via the mentioned fractal of a "Velcro-like" attachment, except that the quantity of the directly related mini-string segments here will cause the affiliated bond that is formed at the two said ends of the prior mentioned one-dimensional string to be fairly rigidly kept -- relatively speaking.  The said Green Function works to cause the said string to bend homeomorphically  and homotopically in a hermitian manner into a vibrating hoop.  The directly related partial of the local-based Hilbert Space that is involved here exists in anywhere from 10 to 32 spatial dimensions plus time, the latter of which involves a Ward-Caucy variation of up to 32pi I degrees of potential freedom -- when in terms of the Poincaire-based field that is directly involved with the differential geometry here.  I will continue with the suspense later!  Sincerely, Sam Roach.