Abstract
We discuss the stability of the topological invariant of the strongly interacting Weyl semi-metal at finite temperature. We find that if the interactions and temperature of the system are controlled by the holography, the topology is stable even in the case the Fermi surface become fuzzy. We give an argument to show that although the self energy changes the spectral function significantly to make the Fermi surface fuzzy, it cannot change the singularity structure of the Berry phase, which leads to the stability of the topology. We also find that depending on the mass term structure of the fermion Lagrangian, topological dipoles can be created.
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