Abstract
In this paper, we are going to construct the classical field theory on the boundary of the embedding of \mathbb{R} \times S^{1}ℝ×S1 into the manifold MM by the Jacobi sigma model. By applying the poissonization procedure and by generalizing the known method for Poisson sigma models, we express the fields of the model as perturbative expansions in terms of the reduced phase space of the boundary. We calculate these fields up to the second order and illustrate the procedure for contact manifolds.
Highlights
Very recently, the Jacobi sigma models have been realized as embeddings into the Poisson sigma models in a target space of one dimension higher [1, 2] by using a procedure called poissonization [3]
We are going to apply the poissonization technique to obtain the classical field theory on the boundary ∂ Σ of the base space Σ = S1 × [0, L] of a Jacobi sigma model with the target space M. The interest in this type of field theories is on their interpretation as holographic dual fields to the Jacobi sigma models upon quantization
We have constructed the classical boundary field theory associated to the Jacobi sigma model by applying the poissonization procedure which gives a correspondence between the sought for field theory and the boundary field theory of the Poisson sigma model [11]
Summary
The Jacobi sigma models have been realized as embeddings into the Poisson sigma models in a target space of one dimension higher [1, 2] by using a procedure called poissonization [3]. We are going to apply the poissonization technique to obtain the classical field theory on the boundary ∂ Σ of the base space Σ = S1 × [0, L] of a Jacobi sigma model with the target space M. We are going to use this embedding to derive a lower dimensional field theory from the classical field theory of the Poisson sigma model associated to the Jacobi sigma model.
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