On scale versus conformal symmetry in turbulence

Yaron Oz*

*Corresponding author for this work

Research output: Contribution to journalLetterpeer-review


We consider the statistical description of steady state fully developed incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We show that in the absence of condensates turbulence statistics exhibits scale but not conformal symmetry, with the only possible exception being the direct enstrophy cascade in two space dimensions. We argue that the same conclusions hold for compressible non-relativistic turbulence as well as for relativistic turbulence. We discuss the modification of our conclusions in the presence of vacuum expectation values of negative dimension operators (condensates). We consider the issue of non-locality of the stress-energy tensor of inertial range turbulence field theory.

Original languageEnglish
Article number655
JournalEuropean Physical Journal C
Issue number8
StatePublished - 1 Aug 2018


FundersFunder number
I-CORE program of Planning and Budgeting Committee1937/12
ISF Center of Excellence
German-Israeli Foundation for Scientific Research and Development
United States-Israel Binational Science Foundation


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