Renormalisation of non-differentiable potentials

Year: 2022

Authors: Alexandre J., Defenu N., Grigolia G., Màriàn IG., Mdinaradze D., Trombettoni A., Turovtsi-Shiutev Y., Nandori I.

Autors Affiliation: Kings Coll London, Dept Phys, London WC2R 2LS, England; Heidelberg Univ, Inst Theoret Phys, D-69120 Heidelberg, Germany; Univ Debrecen, POB 105, H-4010 Debrecen, Hungary; Univ Trento, Dept Phys, Via Sommar 14, I-38123 Povo, Trento, Italy; Atomki, POB 51, H-4001 Debrecen, Hungary; MTA DE Particle Phys Res Grp, POB 51, H-4001 Debrecen, Hungary; Univ Trieste, Dept Phys, Str Costiera 11, I-34151 Trieste, Italy; CNR IOM DEMOCRITOS Simulat Ctr, Via Bonomea 265, I-34136 Trieste, Italy; Uzhgorod Natl Univ, 14 Univ Str, UA-88000 Uzhgorod, Ukraine.

Abstract: Non-differentiable potentials, such as the V-shaped (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 Liouville-type interaction, i.e., an exponential of the V-shaped function. Another example is coming from particle physics when the standard model Higgs potential is replaced by a periodic self-interaction of an N-component scalar field which depends on the length, thus it is O(N) symmetric. We first compare classical and quantum dynamics near non-analytic 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 non-differentiable effective branon potential and to the O(N) models when the spatial dimension is varied and to the O(N) extension of the sine-Gordon model in (1+1) dimensions are presented.

Journal/Review: JOURNAL OF HIGH ENERGY PHYSICS

Volume: (7)      Pages from: 12-1  to: 12-24

More Information: Useful discussions with G. Somogyi are gratefully acknowledged. Support for the CNR/MTA Italy-Hungary 2019-2021 Joint Project Strongly interacting systems in confined geometries and funding from the Visegrad grant are gratefully acknowledged. The work of Jean Alexandre is supported by the STFC, UK, grant ST/P000258/1.
KeyWords: Renormalization and Regularization; Renormalization Group; Field Theories in Higher Dimensions; Large Extra Dimensions
DOI: 10.1007/JHEP07(2022)012

ImpactFactor: 5.400