Intertwined orders and Fermionic Spectral Functions in Holography

Spatially modulated black holes are constructed, which allow a U(1) symmetry and translational invariance to be broken spontaneously at the same time. Our construction provides an example of a system where various orders are intertwined with each other and have a common origin. In particular, there is a dual description for the pair density wave, in which the superconducting order parameter is spatially modulated but has a zero average. The fermionic spectral function is then investigated in uni-directional striped phases, where the breaking of translational invariance can be generated either spontaneously or explicitly. Spectral weight suppression and fermi arc-like features with strong holographic lattices have been uncovered.