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Yang-Mills Theory in Six-Dimensional Superspace


Koller, Jeffrey George (1984) Yang-Mills Theory in Six-Dimensional Superspace. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/RP3T-S865.


The superspace approach provides a manifestly supersymmetric formulation of supersymmetric theories. For N= 1 supersymmetry one can use either constrained or unconstrained superfields for such a formulation. Only the unconstrained formulation is suitable for quantum calculations. Until now, all interacting N>1 theories have been written using constrained superfields. No solutions of the nonlinear constraint equations were known.

In this work, we first review the superspace approach and its relation to conventional component methods. The difference between constrained and unconstrained formulations is explained, and the origin of the nonlinear constraints in supersymmetric gauge theories is discussed. It is then shown that these nonlinear constraint equations can be solved by transforming them into linear equations. The method is shown to work for N=1 Yang-Mills theory in four dimensions.

N=2 Yang-Mills theory is formulated in constrained form in six-dimensional superspace, which can be dimensionally reduced to four-dimensional N=2 extended superspace. We construct a superfield calculus for six-dimensional superspace, and show that known matter multiplets can be described very simply. Our method for solving constraints is then applied to the constrained N=2 Yang-Mills theory, and we obtain an explicit solution in terms of an unconstrained superfield. The solution of the constraints can easily be expanded in powers of the unconstrained superfield, and a similar expansion of the action is also given. A background-field expansion is provided for any gauge theory in which the constraints can be solved by our methods. Some implications of this for superspace gauge theories are briefly discussed.

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):
  • Frautschi, Steven C.
Thesis Committee:
  • Frautschi, Steven C. (chair)
  • Schwarz, John H.
  • Porter, Frank C.
  • Blandford, Roger D.
Defense Date:22 May 1984
Non-Caltech Author Email:jkoller (AT)
Record Number:CaltechTHESIS:06042014-113206988
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8477
Deposited On:05 Jun 2014 15:30
Last Modified:21 Dec 2019 02:12

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