Finite Size Effects and Conformal Symmetry of $O(N)$ Nonlinear $σ$ Model in Three Dimensions

Details Finite Size Effects and Conformal Symmetry of $O(N)$ Nonlinear $σ$ Model in Three Dimensions Finite Size Effects and Conformal Symmetry of $O(N)$ Nonlinear $σ$ Model in Three Dimensions

1994-05-30

arxiv.org/abs/hep-th/9405189v1

Prog.Theor.Phys.Suppl.118:299-308,1995

Physics

High Energy Physics

High Energy Physics - Theory

12 pages uuencoded compressed PostScript file including 1 figure

Scientific paper

10.1143/PTPS.118.299

We study the $O(N)$ nonlinear $\sigma$ model on a three-dimensional compact space $S^1 \times S^2$ (of radii $L$ and $R$ respectively) by means of large $N$ expansion, focusing on the finite size effects and conformal symmetries of this model at the critical point. We evaluate the correlation length and the Casimir energy of this model and study their dependence on $L$ and $R$. We examine the modular transformation properties of the partition function, and study the dependence of the specific heat on the mass gap in view of possible extension of the $C-$theorem to three dimensions.

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