Ab-initio Holography

In this talk, I will review our recent work on attempts of first principle construction of holographic duals for field theories relevant to condensed matter systems using renormalization group approaches. In particular, I will show how to implement the procedure for lattice U(N) vector models of complex bosons (in the large N limit) and find the bulk equation of motions with dynamic bi-local fields starting from the field theory. Solving the equations of motions partly analytically and partly numerically (on finite systems), we recover both the in insulating phase and the superfluid phase as well as signatures of the critical point. We interpret these distinct signatures in terms of the distinct geometric features in the bulk.

Reference: P. Lunts, S. Bhattacharjee, J. Miller, E. Schenetter, Y. B. Kim and S.-S. Lee, arXiv:1503.06474; JHEP 107 (2015).