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We discuss the stability of the topological invariant of the stronglyinteracting Weyl semi-metal at finite temperature. We find that if theinteractions and temperature of the system are controlled by the holography,the topology is stable even in the case the Fermi surface become fuzzy. We givean argument to show that although the self energy changes the spectral functionsignificantly to make the Fermi surface fuzzy, it cannot change the singularitystructure of the Berry phase, which leads to the stability of the topology. Wealso find that depending on the mass term structure of the fermion Lagrangian,topological dipoles can be created.

Stability of Topological character of Weyl Semi-metal, and Topological Dipole in Holography