Book Chapter10.1007/978-3-319-54000-9_7
Local RGE and Maximally Symmetric Spaces
Graham M. Shore
- 01 Jan 2017
- pp 61-76
TL;DR: In this paper, it was shown that the two-point Green functions of the energy-momentum tensor in flat spacetime do not yield information about the coefficient β a of the Euler-Gauss-Bonnet density in the trace anomaly and so does not allow the derivation of a conjectured a-theorem in four dimensions.
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Abstract: As we have seen, the two-point Green functions of the energy-momentum tensor in flat spacetime does not yield information about the coefficient β a of the Euler-Gauss-Bonnet density in the trace anomaly and so does not allow the derivation of a conjectured a-theorem in four dimensions. Since two-point Green functions are the most obvious source of the positivity conditions which are necessary to prove monotonicity of the corresponding RG flow, this line of investigation has clearly reached an impasse. A natural way forward, which was pursued in great detail in [17], is to generalise the background to a curved spacetime where the Euler characteristic is non-vanishing.
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References
Is There a c Theorem in Four-Dimensions?
TL;DR: The difficulties of extending Zamolodchikov's c-theorem to dimensions d ≠ 2 are discussed in this paper, where it is shown that the existence of such a c-function, if it satisfies these properties to all orders, is consistent with the expected behavior of QCD in four dimensions.
780
c-theorem and spectral representation
TL;DR: In this paper, the spectral representation of the stress tensor is used to generalize the Zamolodchikov's c-theorem above two space-time dimensions, and a meaningful charge is obtained by defining the theory on curved hyperbolic space.
A Proof of the irreversibility of renormalization group flows in four-dimensions
Stefano Forte,José I. Latorre +1 more
TL;DR: In this article, the irreversibility of renormalization group flows has been shown for unitary, renormalizable theories in four (or generally even) dimensions using Ward identities for scale transformations and spectral representation arguments.
Correlation Functions of the Energy Momentum Tensor on Spaces of Constant Curvature
H. Osborn,Graham M. Shore +1 more
TL;DR: In this article, an analysis of one-and two-point functions of the energy-momentum tensor on homogeneous spaces of constant curvature is undertaken and the possibility of proving a c -theorem in this framework is discussed, in particular in relation to the coefficients c, a, which appear in the energy momentum tensors trace on general curved backgrounds in four dimensions.