### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 237-303 |

Number of pages | 67 |

Journal | Annals of Physics |

Volume | 112 |

Issue number | 2 |

DOIs | |

State | Published - 1978 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*112*(2), 237-303. https://doi.org/10.1016/S0003-4916(78)80001-3

**Stability and supersymmetry : Models with local gauge symmetry.** / Curtright, Thomas; Ghandour, Ghassan.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 112, no. 2, pp. 237-303. https://doi.org/10.1016/S0003-4916(78)80001-3

}

TY - JOUR

T1 - Stability and supersymmetry

T2 - Models with local gauge symmetry

AU - Curtright, Thomas

AU - Ghandour, Ghassan

PY - 1978

Y1 - 1978

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0039034603&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039034603&partnerID=8YFLogxK

U2 - 10.1016/S0003-4916(78)80001-3

DO - 10.1016/S0003-4916(78)80001-3

M3 - Article

AN - SCOPUS:0039034603

VL - 112

SP - 237

EP - 303

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 2

ER -