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- Title
- Field Theoretic Lagrangian Stencils from Off-Shell Supermultiplet Gauge Quotients.
- Creator
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Katona, Gregory, Klemm, Richard, Hubsch, Tristan, Peale, Robert, Shivamoggi, Bhimsen, University of Central Florida
- Abstract / Description
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Recent efforts to classify off-shell representations of supersymmetry without a central charge have focused upon directed, supermultiplet graphs of hypercubic topology known as Adinkras. These encodings of Super Poincare algebras, depict every generator of a chosen supersymmetry as a node-pair transformtion between fermionic / bosonic componentfields. This research thesis is a culmination of investigating novel diagrammatic sums of gauge quotients by supersymmetric images of other Adinkras,...
Show moreRecent efforts to classify off-shell representations of supersymmetry without a central charge have focused upon directed, supermultiplet graphs of hypercubic topology known as Adinkras. These encodings of Super Poincare algebras, depict every generator of a chosen supersymmetry as a node-pair transformtion between fermionic / bosonic componentfields. This research thesis is a culmination of investigating novel diagrammatic sums of gauge quotients by supersymmetric images of other Adinkras, and the correlated building of field theoretic worldline Lagrangians to accommodate both classical and quantum venues. We find Ref [40], that such gauge quotients do not yield other stand alone or (")proper(") Adinkras as afore sighted, nor can they be decomposed into supermultiplet sums, but are rather a connected (")Adinkraic network("). Their iteration, analogous to Weyl's construction for producing all finite-dimensional unitary representations in Lie algebras, sets off chains of algebraic paradigms in discrete-graph and continuous-field variables, the links of which feature distinct, supersymmetric Lagrangian templates. Collectively, these Adiankraic series air new symbolic genera for equation to phase moments in Feynman path integrals. Guided in this light, we proceed by constructing Lagrangians actions for the N = 3 supermultiplet YI /(iDI X) for I = 1, 2, 3, where YI and X are standard, Salam-Strathdee superfields: YI fermionic and X bosonic. The system, bilinear in the component fields exhibits a total of thirteen free parameters, seven of which specify Zeeman-like coupling to external background (magnetic) fluxes. All but special subsets of this parameter space describe aperiodic oscillatory responses, some of which are found to be surprisingly controlled by the golden ratio, ? ? 1.61803, Ref [52]. It is further determined that these Lagrangians allow an N = 3 ? 4 supersymmetric extension to the Chiral-Chiral and Chiral-twisted-Chiral multiplet, while a subset admits two inequivalent such extensions. In a natural progression, a continuum of observably and usefully inequivalent, finite-dimensional off-shellrepresentations of worldline N = 4 extended supersymmetry are explored, that are variatefrom one another but in the value of a tuning parameter, Ref [53]. Their dynamics turnsout to be nontrivial already when restricting to just bilinear Lagrangians. In particular, wefind a 34-parameter family of bilinear Lagrangians that couple two differently tuned supermultiplets to each other and to external magnetic fluxes, where the explicit parameter dependence is unremovable by any field redefinition and is therefore observable. This offers the evaluation of X-phase sensitive, off-shell path integrals with promising correlationsto group product decompositions and to deriving source emergences of higher-order background flux-forms on 2-dimensional manifolds, the stacks of which comprise space-time volumes. Application to nonlinear sigma models would naturally follow, having potential use in M- and F- string theories.
Show less - Date Issued
- 2013
- Identifier
- CFE0005011, ucf:50004
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0005011
