Abstract
The technique for constructing conformally invariant theories within the coset space construction is developed. It reproduces all consequences of the conformal invariance and Lagrangians of widely-known conformal field theories. The method of induced representations, which plays the key role in the construction, allows to reveal a special role of the "Nambu-Goldstone fields" for special conformal transformations. Namely, their dependence on the coordinates turns out to be fixed by the symmetries. This results in the appearance of the constraints on possible forms of Lagrangians, which ensure that discrete symmetries are indeed symmetries of the theory.
Highlights
Kharuk*The technique for constructing conformally invariant theories within the coset space construction is developed
AND SUMMARYThe coset space technique (CST) is a very powerful tool for obtaining Lagrangians with nonlinear1 realization of symmetries
The problems with applying the CST to the conformal group were stemming from the fact that the coset space ConfðdÞ=eiPμxμ is not homogeneously reductive
Summary
The technique for constructing conformally invariant theories within the coset space construction is developed. It reproduces all consequences of the conformal invariance and Lagrangians of widely known conformal field theories. The method of induced representations, which plays the key role in the construction, allows us to reveal a special role of the Nambu-Goldstone fields for special conformal transformations. Their dependence on the coordinates turns out to be fixed by the symmetries. This results in the appearance of the constraints on possible forms of Lagrangians, which ensure that discrete symmetries are symmetries of the theory
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