ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The O(N) nonlinear sigma model in a D-dimensional space of the form RD−M×TM, RD−M×SM, or TM×SP is studied, where RM, TM, and SM correspond to flat space, a torus, and a sphere, respectively. Using zeta-regularization and the 1/N expansion, the corresponding partition functions—for deriving the free energy—and the gap equations are obtained. In particular, the free energy at the critical point on R2q+1×S2p+2 vanishes in accordance with the conformal equivalence to the flat space RD. Numerical solutions of the gap equations at the critical coupling constants are given for several values of D. The properties of the partition function and its asymptotic behavior for large D are discussed. In a similar way, a higher-derivative nonlinear sigma model is investigated, too. The physical relevance of our results is discussed. © 1996 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.531437
Permalink
