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The c and a-Theorems and the local r...

Shore, Graham.

The c and a-Theorems and the local renormalisation group

Record Type:	Electronic resources : Monograph/item
Title/Author:	The c and a-Theorems and the local renormalisation groupby Graham Shore.
Author:	Shore, Graham.
Published:	Cham :Springer International Publishing :2017.
Description:	vii, 102 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Renormalization group.
Online resource:	http://dx.doi.org/10.1007/978-3-319-54000-9
ISBN:	9783319540009$q(electronic bk.)

The c and a-Theorems and the local renormalisation group
Shore, Graham.

The c and a-Theorems and the local renormalisation group[electronic resource] /by Graham Shore. - Cham :Springer International Publishing :2017. - vii, 102 p. :ill. (some col.), digital ;24 cm. - SpringerBriefs in physics,2191-5423. - SpringerBriefs in physics..

Introduction -- Renormalisation and the Conformal Anomaly -- The Local Renormalisation Group and Weyl Consistency Conditions -- c-Theorem in Two Dimensions -- Local RGE and Weyl Consistency Conditions in Four Dimensions -- c, b and a-Theorems in Four Dimensions -- Global Symmetries and Limit Cycles -- Summary and Outlook.

The Zamolodchikov c-theorem has led to important new insights in the understanding of the Renormalisation Group (RG) and the geometry of the space of QFTs. The present primer introduces and reviews the parallel developments of the search for a higher-dimensional generalisation of the c-theorem and of the Local RG (LRG) The idea of renormalisation with position-dependent couplings, running under local Weyl scaling, is traced from its early realisations to the elegant modern formalism of the LRG. The key role of the associated Weyl consistency conditions in establishing RG flow equations for the coefficients of the trace anomaly in curved spacetime, and their relation to the c-theorem and four-dimensional a-theorem, is explained in detail. A number of different derivations of the c-theorem in two dimensions are presented and subsequently generalised to four dimensions. The obstructions to establishing monotonic C-functions related to the trace anomaly coefficients in four dimensions are explained. The possibility of deriving an a-theorem for the coefficient of the Euler-Gauss-Bonnet density is explored, initially by formulating the QFT on maximally symmetric spaces. Then the formulation of the weak a-theorem using a dispersion relation for four-point functions is presented. Finally, the application of the LRG to the issue of limit cycles in theories with a global symmetry is described, shedding new light on the geometry of the space of couplings in QFT.

ISBN: 9783319540009$q(electronic bk.)

Standard No.: 10.1007/978-3-319-54000-9doiSubjects--Topical Terms:

266976
Renormalization group.

LC Class. No.: QC20.7.R43

Dewey Class. No.: 530.15

The c and a-Theorems and the local renormalisation group
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245 1 4 $a The c and a-Theorems and the local renormalisation group $h [electronic resource] / $c by Graham Shore.
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505 0 $a Introduction -- Renormalisation and the Conformal Anomaly -- The Local Renormalisation Group and Weyl Consistency Conditions -- c-Theorem in Two Dimensions -- Local RGE and Weyl Consistency Conditions in Four Dimensions -- c, b and a-Theorems in Four Dimensions -- Global Symmetries and Limit Cycles -- Summary and Outlook.
520 $a The Zamolodchikov c-theorem has led to important new insights in the understanding of the Renormalisation Group (RG) and the geometry of the space of QFTs. The present primer introduces and reviews the parallel developments of the search for a higher-dimensional generalisation of the c-theorem and of the Local RG (LRG) The idea of renormalisation with position-dependent couplings, running under local Weyl scaling, is traced from its early realisations to the elegant modern formalism of the LRG. The key role of the associated Weyl consistency conditions in establishing RG flow equations for the coefficients of the trace anomaly in curved spacetime, and their relation to the c-theorem and four-dimensional a-theorem, is explained in detail. A number of different derivations of the c-theorem in two dimensions are presented and subsequently generalised to four dimensions. The obstructions to establishing monotonic C-functions related to the trace anomaly coefficients in four dimensions are explained. The possibility of deriving an a-theorem for the coefficient of the Euler-Gauss-Bonnet density is explored, initially by formulating the QFT on maximally symmetric spaces. Then the formulation of the weak a-theorem using a dispersion relation for four-point functions is presented. Finally, the application of the LRG to the issue of limit cycles in theories with a global symmetry is described, shedding new light on the geometry of the space of couplings in QFT.
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