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MODIFICATION TO EINSTEIN'S FIELD EQUATIONS IMPOSED BY STRING THEORY AND CONSEQUENCES FOR THE CLASSICAL TESTS OF GENERAL RELATIVITY
Title
MODIFICATION TO EINSTEIN'S FIELD EQUATIONS IMPOSED BY STRING THEORY AND CONSEQUENCES FOR THE CLASSICAL TESTS OF GENERAL RELATIVITY.
Creator
Frye, Christopher, Efthimiou, Costas, University of Central Florida
Abstract / Description
String theory imposes slight modifications to Einstein's equations of general relativity. In Green, Schwarz, and Witten's classic text, the authors claim that the gravitational field equations in empty space should contain, in addition to the Ricci tensor, an extra term which is first order in the string constant alpha-prime and proportional to the Riemann curvature tensor squared. They do admit, however, that this simple modification is just schematic. We show that these modified equations...
Show moreString theory imposes slight modifications to Einstein's equations of general relativity. In Green, Schwarz, and Witten's classic text, the authors claim that the gravitational field equations in empty space should contain, in addition to the Ricci tensor, an extra term which is first order in the string constant alpha-prime and proportional to the Riemann curvature tensor squared. They do admit, however, that this simple modification is just schematic. We show that these modified equations do not admit an isotropic solution. We then investigate the consequences of the modified gravitational equations when they are coupled to the dilaton field. Callan, Myers, and Perry have found a static isotropic solution to these equations. We calculate the additional perihelion precession of Mercury, the added deflection of photons by the sun, and the extra gravitational redshift which should be present if these equations hold. We determine that additional effects due to string theory in each of these cases are quite minuscule.
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Date Issued
2013
Identifier
CFH0004411, ucf:45087
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFH0004411
Field Theoretic Lagrangian Stencils from Off-Shell Supermultiplet Gauge Quotients
Title
Field Theoretic Lagrangian Stencils from Off-Shell Supermultiplet Gauge Quotients.
Creator
Katona, Gregory, Klemm, Richard, Hubsch, Tristan, Peale, Robert, Shivamoggi, Bhimsen, University of Central Florida
Abstract / Description
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.
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Date Issued
2013
Identifier
CFE0005011, ucf:50004
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0005011