Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 43, Issue 21, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/43/21/215401
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Funding
- Rutgers New High Energy Theory Center
- Edinburgh Mathematical Society
- STFC [ST/G000514/1, ST/G000522/1] Funding Source: UKRI
- Science and Technology Facilities Council [ST/G000522/1, ST/G000514/1] Funding Source: researchfish
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We give a non-perturbative proof of a gradient formula for beta functions of two-dimensional quantum field theories. The gradient formula has the form. partial derivative(i)c = -(g(ij) + Delta g(ij) + b(ij))beta(j) where beta(j) are the beta functions, c and g(ij) are the Zamolodchikov c-function and metric respectively, b(ij) is an antisymmetric tensor introduced by Osborn and Delta g(ij) is a certain metric correction. The formula is derived under the assumption of stress-energy conservation and certain conditions on the infrared behavior the most significant of which is the condition that the large-distance limit of the field theory does not exhibit spontaneously broken global conformal symmetry. Being specialized to nonlinear sigma models this formula implies a one-to-one correspondence between renormalization group fixed points and critical points of c.
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