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Title: The curious case of large-N expansions on a (pseudo)sphere

Journal Article · · Nuclear Physics. B
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We elucidate the large-N dynamics of one-dimensional sigma models with spherical and hyperbolic target spaces and find a duality between the Lagrange multiplier and the angular momentum. In the hyperbolic model we propose a new class of operators based on the irreducible representations of hyperbolic space. We also uncover unexpected zero modes which lead to the double scaling of the 1/N expansion and explore these modes using Gelfand-Dikiy equations.

Research Organization:
Univ. of Pennsylvania, Philadelphia, PA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
DOE-EY-76-02-3071; AC02-76ER03071
OSTI ID:
1228136
Alternate ID(s):
OSTI ID: 1184850
Journal Information:
Nuclear Physics. B, Journal Name: Nuclear Physics. B Vol. 893 Journal Issue: C; ISSN 0550-3213
Publisher:
ElsevierCopyright Statement
Country of Publication:
Netherlands
Language:
English
Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

References (11)

The quantum mechanical supersymmetric O(3) and O(2,1) σ- models journal May 1983
The path integral on the pseudosphere journal February 1988
Non-linear sigma models with anti-de Sitter target spaces journal August 2006
Non-trivial saddle points and band structure of bound states of the two-dimensional O(N) vector model journal January 1995
Spontaneous breakdown of continuous symmetries near two dimensions journal October 1976
De Sitter space and eternity journal July 2008
Quantum theory of compact and non-compact σ models journal February 1984
Symmetry breaking in the non-compact sigma model journal October 1983
Kinks and bound states in the Gross-Neveu model journal April 1995
Non-Amenability and Spontaneous Symmetry Breaking – The Hyperbolic Spin-Chain – journal November 2005
The large N expansion in hyperbolic sigma models journal July 2008

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Related Subjects

97 MATHEMATICS AND COMPUTING