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Vanishing DC holographic conductivity from a magnetic monopole condensate

We show how to obtain a vanishing DC conductivity in 3-dimensional strongly coupled QFT's using a massive 2-form field in the bulk that satisfies a special kind of boundary condition. The real and imaginary parts of the AC conductivity are evaluated in this holographic setup and we show that the DC conductivity identically vanishes even for an arbitrarily small (though nonzero) value of the 2-form mass in the bulk. We identify the bulk action of the massive 2-form with an effective theory describing a phase in which magnetic monopoles have condensed in the bulk. Our results indicate that a condensate of magnetic monopoles in a 4-dimensional bulk leads to a vanishing DC holographic conductivity in 3-dimensional strongly coupled QFT's.