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We propose an approach that allows one to reformulate $n$-dimensional$p$-form mimetic gravity (including usual mimetic gravity as particular case $p= 0$) as nonlinear $(n-p-1)$-form electrodynamics via electric-magneticduality. The resulting dual Lagrangian density is just the square root of theordinary quadratic Lagrangian density of $(n-p-1)$-form electrodynamics. Byapplying field transformation in the action, we show that for the arbitrary $p$this dual theory transforms into the $(p+1)$-brane fluid: the model of thestack of the parallel $(p+1)$-dimensional branes foliating physical spacetime.As the structure of the field transformations depends on $p$, the sets ofsolutions in these models are related differently. We prove, that for $p = 0$and $p = n-2$ dual mimetic models describe usual particle fluid with thepotential flow and to the $(n-1)$-brane fluid respectively. For other values of$p$ not all mimetic solutions behave like that, in general, so we restrictourselves only to the case $n = 4$, $p = 1$. In this case, we show, thatmimetic formulation is dual to the well-known Nielsen-Olesen theory of "dualstrings" and discuss the criterion indicating whether its solutions behave likestring fluid. The cosmological solutions for these models in are alsodiscussed.

Dual models for p-form mimetic gravity and their connection to perfect fluids consisting of (p+1)-branes