Conformal field theories in a periodic potential: results from holography and field theory

Understand

We study 2+1 dimensional conformal field theories (CFTs) with a globally conserved U(1) charge, placed in a chemical potential which is periodically modulated along the spatial direction $x$ with zero average: $\mu(x) = V \cos(kx)$.

• The dynamics of such theories depends only on the dimensionless ratio $V/k$, and we expect that they flow in the infrared to new CFTs whose universality class changes as a function of $V/k$.
• We compute the frequency-dependent conductivity of strongly-coupled CFTs using holography of the Einstein-Maxwell theory in 4-dimensional anti-de Sitter space.
• We compare the results with the corresponding computation of weakly-coupled CFTs, perturbed away from the CFT of free, massless Dirac fermions (which describes graphene at low energies).