TY - JOUR

T1 - Fluid-electromagnetic helicities and knotted solutions of the fluid-electromagnetic equations

AU - Nastase, Horatiu

AU - Sonnenschein, Jacob

N1 - Publisher Copyright:
© 2022, The Author(s).

PY - 2022/12

Y1 - 2022/12

N2 - In this paper we consider an Euler fluid coupled to external electromagnetism. We prove that the Hopfion fluid-electromagnetic knot, carrying fluid and electromagnetic (EM) helicities, solves the fluid dynamical equations as well as the Abanov Wiegmann (AW) equations for helicities, which are inspired by the axial-current anomaly of a Dirac fermion. We also find a nontrivial knot solution with truly interacting fluid and electromagnetic fields. The key ingredients of these phenomena are the EM and fluid helicities. An EM dual system, with a magnetically charged fluid, is proposed and the analogs of the AW equations are written down. We consider a fluid coupled to a nonlinear generalizations for electromagnetism. The Hopfions are shown to be solutions of the generalized equations. We write down the formalism of fluids in 2+1 dimensions, and we dimensionally reduce the 3+1 dimensional solutions. We determine the EM knotted solutions, from which we derive the fluid knots, by applying special conformal transformations with imaginary parameters on un-knotted null constant EM fields.

AB - In this paper we consider an Euler fluid coupled to external electromagnetism. We prove that the Hopfion fluid-electromagnetic knot, carrying fluid and electromagnetic (EM) helicities, solves the fluid dynamical equations as well as the Abanov Wiegmann (AW) equations for helicities, which are inspired by the axial-current anomaly of a Dirac fermion. We also find a nontrivial knot solution with truly interacting fluid and electromagnetic fields. The key ingredients of these phenomena are the EM and fluid helicities. An EM dual system, with a magnetically charged fluid, is proposed and the analogs of the AW equations are written down. We consider a fluid coupled to a nonlinear generalizations for electromagnetism. The Hopfions are shown to be solutions of the generalized equations. We write down the formalism of fluids in 2+1 dimensions, and we dimensionally reduce the 3+1 dimensional solutions. We determine the EM knotted solutions, from which we derive the fluid knots, by applying special conformal transformations with imaginary parameters on un-knotted null constant EM fields.

KW - Field Theory Hydrodynamics

KW - Solitons Monopoles and Instantons

UR - http://www.scopus.com/inward/record.url?scp=85145171808&partnerID=8YFLogxK

U2 - 10.1007/JHEP12(2022)144

DO - 10.1007/JHEP12(2022)144

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AN - SCOPUS:85145171808

SN - 1126-6708

VL - 2022

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 12

M1 - 144

ER -