@article{780597,
      recid = {780597},
      author = {Shore, Graham,},
      title = {The c and a-Theorems and the local renormalisation group  /},
      pages = {1 online resource (vii, 102 pages) :},
      abstract = {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 rôle 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.},
      url = {http://library.usi.edu/record/780597},
      doi = {https://doi.org/10.1007/978-3-319-54000-9},
}