Double scaling limit in O(N) vector models

Di Vecchia, P.; Kato, M.; Ohta, N.

doi:10.1016/0550-3213(91)90478-G

Double scaling limit in O(N) vector models

Nov 12, 1990

26 pages

Published in:

Nucl.Phys.B 357 (1991) 495-520

Published: 1991

DOI:

10.1016/0550-3213(91)90478-G

Report number:

NORDITA-90-59-P,
OS-GE-13-90

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Abstract: (Elsevier)

Using the standard 1/ N expansion, we study O( N ) vector models with an arbitrary potential in zero dimensions and we show that a double scaling limit exists as in the case of matrix models. We find in general a hierarchy of critical theories labelled by an integer k . The universal partition function of the k th theory obtained in the double scaling limit is constructed both from the effective action in the double scaling limit and as a solution of a k th order differential equation that follows from the Schwinger-Dyson equations of the theory in the same limit. We also show that the theory possesses the Virasoro symmetry acting on the partition function.

model: vector
symmetry: O(N)
expansion 1/N
scaling
dimension: 0
partition function
effective action
Dyson-Schwinger equation
symmetry: Virasoro
potential

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