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Field Theoretic Lagrangian Stencils from OffShell Supermultiplet Gauge Quotients
 Date Issued:
 2013
 Abstract/Description:
 Recent efforts to classify offshell 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 nodepair 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 finitedimensional unitary representations in Lie algebras, sets off chains of algebraic paradigms in discretegraph and continuousfield 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, SalamStrathdee superfields: YI fermionic and X bosonic. The system, bilinear in the component fields exhibits a total of thirteen free parameters, seven of which specify Zeemanlike 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 ChiralChiral and ChiraltwistedChiral multiplet, while a subset admits two inequivalent such extensions. In a natural progression, a continuum of observably and usefully inequivalent, finitedimensional offshellrepresentations 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 34parameter 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 Xphase sensitive, offshell path integrals with promising correlationsto group product decompositions and to deriving source emergences of higherorder background fluxforms on 2dimensional manifolds, the stacks of which comprise spacetime volumes. Application to nonlinear sigma models would naturally follow, having potential use in M and F string theories.
Title:  Field Theoretic Lagrangian Stencils from OffShell Supermultiplet Gauge Quotients. 
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Name(s): 
Katona, Gregory, Author Klemm, Richard, Committee Chair Hubsch, Tristan, Committee CoChair Peale, Robert, Committee Member Shivamoggi, Bhimsen, Committee Member , Committee Member University of Central Florida, Degree Grantor 

Type of Resource:  text  
Date Issued:  2013  
Publisher:  University of Central Florida  
Language(s):  English  
Abstract/Description:  Recent efforts to classify offshell 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 nodepair 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 finitedimensional unitary representations in Lie algebras, sets off chains of algebraic paradigms in discretegraph and continuousfield 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, SalamStrathdee superfields: YI fermionic and X bosonic. The system, bilinear in the component fields exhibits a total of thirteen free parameters, seven of which specify Zeemanlike 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 ChiralChiral and ChiraltwistedChiral multiplet, while a subset admits two inequivalent such extensions. In a natural progression, a continuum of observably and usefully inequivalent, finitedimensional offshellrepresentations 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 34parameter 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 Xphase sensitive, offshell path integrals with promising correlationsto group product decompositions and to deriving source emergences of higherorder background fluxforms on 2dimensional manifolds, the stacks of which comprise spacetime volumes. Application to nonlinear sigma models would naturally follow, having potential use in M and F string theories.  
Identifier:  CFE0005011 (IID), ucf:50004 (fedora)  
Note(s): 
20131201 Ph.D. Sciences, Physics Doctoral This record was generated from author submitted information. 

Subject(s):  Supersymmetry  Superspace  Supermultiplet  Adinkra  Automata  Adiankraic Tensor Product Decomposition  GroupTheoretic  Lorentz Group  SU(2)  SO(3)  Gauge Quotient  Isomorphism  Surjective  Bijective  Image Mapping  Indefinite Adiankraic Network Sequence  Super Poincare Group  HaagLopuszanskiSohnius theorem  String Theory  MTheory  FTheory  Nonlinear Sigma Model  (Numerical) Algebraic Geometry  Algebraic Paradigms  Worldsheet  Worldsheet Stacks  Supersymmetric Lagrangians  Ansatz Templates  Super Potentials  Quantum Mechanics  Field Theory  Fermionic  Bosonic  (Super) Zeeman  Background Flux Fields  Supergravity  Superfields  Young Tableaux  SUSY Tableaux  Controlled Chaos  Supercharge Continuum  Chiral  ChiralTwistedChiral  
Persistent Link to This Record:  http://purl.flvc.org/ucf/fd/CFE0005011  
Restrictions on Access:  public 20131215  
Host Institution:  UCF 