A Duality Web in Condensed Matter Systems

We study various dualities in condensed matter systems. The dualities in three dimensions could be derived from a conjecture of a duality between a Dirac fermion theory and an interacting scalar field theory at the Wilson-Fisher fixed point and zero temperature in three dimensions. We show that the dualities are not affected by the non-trivial holonomy, use a mean-field method to study, and discuss the dualities at a finite temperature. Finally, we combine a bulk theory, which is an Abelian $p$-form theory with a theta term in $2p+2$ dimensions, and a boundary theory, which is a $2p+1$ dimensional theory, to discuss constraints and difficulties of a duality web in $2p+1$ dimensions.