Kähler gauge dependence of generalized non-linear σ-model with local complex supersymmetry in 1 + 1 dimensions
✍ Scribed by Kengo Yamagishi
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 758 KB
- Volume
- 150
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
The 1 + 1 dimensional analogue of the quantizaton procedure of the gravitational constant by Witten and Bagger in a generalized non-linear u-model is studied. By making use of the tensor calculus in 1 t I dimensions, the model is constructed and found to be manifestly independent of the Klhler gauge transformation. Therefore, the topological properties are not produced in the 1 + 1 dimensional models.
I. INTRODUCTION
Recently, it was shown [ 1 ] on geometrical grounds that the gravitational constant is quantized in a generalized non-linear u-model coupled to supergravity in 3 + 1 space-time dimensions. The theory is consistent only if the ratio of the gravitation and the u-model coupling constant is an integer. In order to produce such a topological property, it is important for the model to permit a Kahler gauge dependence which is compensated by succeeding local chiral transformations. This kind of mechanism would be independent of the space-time dimensions. The purpose of the present work is to investigate whether such a gauge dependent supersymmetric model can be possible in 1 + 1 space-time dimensions without any additional internal symmetries.
The non-linear o-models [2] in 1 + 1 dimensions have been studied in detail because of their similarities with four-dimensional gauge theories. In particular, the models in which the scalar fields take values on a Kahler manifold [3] are known to be important in investigating topological properties of quantum field theories [ 4 1. The simplest example is CPT-' model, and its structure has been thoroughly studied [ 51. The general formulation of the global supersymmetric extension was first made by Zumino [6] several years ago. It bears O(2) extended supersymmetry. The Lagrangian takes very simple form in the language of superspace: S = . d=x d4f?K(Qi, sj). J 439