TY - JOUR

T1 - Spontaneous symmetry breaking, conformal anomaly and incompressible fluid turbulence

AU - Oz, Yaron

N1 - Publisher Copyright:
© 2017, The Author(s).

PY - 2017/11/1

Y1 - 2017/11/1

N2 - We propose an effective conformal field theory (CFT) description of steady state incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We derive a KPZ-type equation for the anomalous scaling of the longitudinal velocity structure functions and relate the intermittency parameter to the boundary Euler (A-type) conformal anomaly coefficient. The proposed theory consists of a mean field CFT that exhibits Kolmogorov linear scaling (K41 theory) coupled to a dilaton. The dilaton is a Nambu-Goldstone gapless mode that arises from a spontaneous breaking due to the energy flux of the separate scale and time symmetries of the inviscid Navier-Stokes equations to a K41 scaling with a dynamical exponent z=23. The dilaton acts as a random measure that dresses the K41 theory and introduces intermittency. We discuss the two, three and large number of space dimensions cases and how entanglement entropy can be used to characterize the intermittency strength.

AB - We propose an effective conformal field theory (CFT) description of steady state incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We derive a KPZ-type equation for the anomalous scaling of the longitudinal velocity structure functions and relate the intermittency parameter to the boundary Euler (A-type) conformal anomaly coefficient. The proposed theory consists of a mean field CFT that exhibits Kolmogorov linear scaling (K41 theory) coupled to a dilaton. The dilaton is a Nambu-Goldstone gapless mode that arises from a spontaneous breaking due to the energy flux of the separate scale and time symmetries of the inviscid Navier-Stokes equations to a K41 scaling with a dynamical exponent z=23. The dilaton acts as a random measure that dresses the K41 theory and introduces intermittency. We discuss the two, three and large number of space dimensions cases and how entanglement entropy can be used to characterize the intermittency strength.

KW - Anomalies in Field and String Theories

KW - Boundary Quantum Field Theory

KW - Conformal Field Theory

KW - Random Systems

UR - http://www.scopus.com/inward/record.url?scp=85033798663&partnerID=8YFLogxK

U2 - 10.1007/JHEP11(2017)040

DO - 10.1007/JHEP11(2017)040

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AN - SCOPUS:85033798663

SN - 1126-6708

VL - 2017

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 11

M1 - 40

ER -