Citation
Marcus, Neil (1984) Finiteness in Supersymmetric Theories. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4t2ft947. https://resolver.caltech.edu/CaltechTHESIS:11262018165108335
Abstract
A two loop calculation in the N = 4 supersymmetric Yang Mills theory is performed in various dimensions. The theory is found to be twoloop finite in six dimensions or less, but infinite in seven and nine dimensions. The sixdimensional result can be explained by a formulation of the theory in terms of N = 2 superfields. The divergence in seven dimensions is naively compatible with both N=2 and N=4 superfield power counting rules, but is of a form that cannot be written as an onshell N=4 superfield integral. The hypothesized N=4 extended superfield formalism therefore either does not exist, or at least has weaker consequences than would have been expected. By analogy, fourdimensional supergravity theories are expected to be infinite at three loops.
Some general issues about the meaning of finiteness in nonrenormalizable theories are discussed. In particular, the use of field redefinitions, the generalization of wavefunction renormalizations to nonrenormalizable theories, and whether counterterms should be used in calculations in "finite" theories are studied. It is shown that theories finite to n loops can have at most simplepole divergences at n + 1 loops.
A method for simplifying the calculation of infinite parts of Feynman diagrams is developed. Based on the observation that counterterms are local functions, all integrals are reduced to logarithmically divergent ones with no dependence on masses or external momenta. The method is of general use, and is particularly effective for manypoint Green functions at more than one loop.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Physics 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Physics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  23 May 1984 
Record Number:  CaltechTHESIS:11262018165108335 
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:11262018165108335 
DOI:  10.7907/4t2ft947 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  11284 
Collection:  CaltechTHESIS 
Deposited By:  Mel Ray 
Deposited On:  27 Nov 2018 21:10 
Last Modified:  16 Apr 2021 23:29 
Thesis Files

PDF
 Final Version
See Usage Policy. 25MB 
Repository Staff Only: item control page