Higher-form symmetries and $d-wave$ superconductors from doped Mott insulators

One path to high-temperature cuprate superconductors is doping a Mott insulator. In this paper, we study this system from the view point of higher-form symmetries. On the introduction of slave bosons, the $t-J$ model at a finite hole doping can be written in the form of $U(1)$ gauge theories. After a duality transformation, they can be written as a generalized $BF$ theory, in which the higher-form symmetries are more manifest. We identify the emergent continuous and discrete higher-form symmetries in both $s-wave$ and $d-wave$ superconducting phases, expected to be realized from a doped Mott insulator. The existence of a topological order is tested by examining if there is a spontaneously broken discrete one-form symmetry. We claim that a spontaneous breaking of discrete one-form symmetry may extend to a phase that has massless Dirac fermions in the limit of large number of flavors. We discuss the possibility of a topological phase transition inside the superconducting dome of high $T_{c}$ cuprates.