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Stability and supersymmetry


Curtright, Thomas Lynn (1977) Stability and supersymmetry. Dissertation (Ph.D.), California Institute of Technology.


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PART I A complete account of a perturbative investigation of ground state instability is presented for a massless theory involving scalar, pseudoscalar, and Majorana spinor fields. The effective potential, dimensional regularization, and renormalization group formalisms are briefly reviewed and then applied in detail to show the semiclassical vacuum of the model is unstable due to radiative corrections when the (pseudo)scalar self-interaction strength, f, is less than the fermion-(pseudo)scalar coupling, [...]. Models with stable ground states are found when [...], and when [...] supersymmetric theory is obtained. The supersymmetric case is thus encountered as a boundary between stable and unstable models. This result is discussed and is conjectured to be a general feature of supersymmetric theories. All perturbative calculations in the analysis are methodically carried out to the level of two-loop Feynman diagrams, and to this level, a variety of renormalization prescriptions are considered. The correlation of the various ultraviolet divergences for the supersymmetric model is explicitly demonstrated and shown not to hold in the general theory.

PART II Renormalization group analysis is used to show the supersymmetric point in the effective coupling constant space is an unstable fixed point for several model gauge theories. The physical significance of this result is discussed in terms of the stability of the semiclassical ground state. In perturbation theory the supersymmetric point appears to be surrounded by regions in the coupling space representing three classes of theories: class one consists of theories for which the effective potential V has no apparent lower bound for large (pseudo) scalar field expectations; class two theories have lower bounds and radiatively induced absolute minima for V with nonzero field expectations; class three theories apparently have an absolute minimum of V at the origin of field space. Thus radiatively induced breaking of gauge invariance occurs for theories in classes one and two, but perturbatively the class one theories appear to have no ground states. Class three theories have ground states in which all gauge invariance remains intact. For the supersymmetric limits of the models examined the origin is known to be neutrally stable in field space, permitting an ambiguous breakdown of gauge invariance but not supersymmetry. This phenomenon is discussed in some detail. Calculations are performed in both Lorentz covariant and noncovariant gauges with a detailed comparison between gauges of the relevant one-loop diagrams. A null-plane limit of the noncovariant gauges is argued not to exist.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Feynman, Richard Phillips
Thesis Committee:
  • Feynman, Richard Phillips (chair)
  • Schwarz, John H.
  • Frautschi, Steven C.
Defense Date:20 January 1977
Record Number:CaltechETD:etd-12092004-161650
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4898
Deposited By: Imported from ETD-db
Deposited On:10 Dec 2004
Last Modified:26 Dec 2012 03:12

Thesis Files

PDF (Curtright_tl_1977.pdf) - Final Version
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