Renormalisation of nondifferentiable potentials
Abstract
Nondifferentiable potentials, such as the Vshaped (linear) potential, appear in various areas of physics. For example, the effective action for branons in the framework of the brane world scenario contains a Liouvilletype interaction, i.e., an exponential of the Vshaped function. Another example is coming from particle physics when the standard model Higgs potential is replaced by a periodic selfinteraction of an Ncomponent scalar field which depends on the length, thus it is O(N) symmetric. We first compare classical and quantum dynamics near nonanalytic points and discuss in this context the role of quantum fluctuations. We then study the renormalisation of such potentials, focusing on the Exact Wilsonian Renormalisation approach, and we discuss how quantum fluctuations smoothen the bare singularity of the potential. Applications of these results to the nondifferentiable effective branon potential and to the O(N) models when the spatial dimension is varied and to the O(N) extension of the sineGordon model in (1+1) dimensions are presented.
 Publication:

Journal of High Energy Physics
 Pub Date:
 July 2022
 DOI:
 10.1007/JHEP07(2022)012
 arXiv:
 arXiv:2112.14696
 Bibcode:
 2022JHEP...07..012A
 Keywords:

 Renormalization and Regularization;
 Renormalization Group;
 Field Theories in Higher Dimensions;
 Large Extra Dimensions;
 High Energy Physics  Theory
 EPrint:
 v3: final version published in JHEP, 12 pages, 5 figures