Title  TwoDimensional Dilaton Gravity Theory and Lattice Schwarzian Theory 
Publication Type  Journal Article 
Year of Publication  2018 
Authors  Chu, SK, Ma, CT, Wu, CH 
Abstract  We report a holographic study of a twodimensional dilaton gravity theory with the Dirichlet boundary condition for the cases of nonvanishing and vanishing cosmological constants. Our result shows that the boundary theory of the twodimensional dilaton gravity theory with the Dirichlet boundary condition for the case of nonvanishing cosmological constants is the Schwarzian term coupled to a dilaton field, while for the case of vanishing cosmological constant, a theory does not have a kinetic term. We also include the higher derivative term R2, where R is the scalar curvature that is coupled to a dilaton field. We find that the form of the boundary theory is not modified perturbatively. Finally, we show that a lattice holographic picture is realized up to the secondorder perturbation of boundary cutoff ε2 under a constant boundary dilaton field and the nonvanishing cosmological constant by identifying the lattice spacing a of a lattice Schwarzian theory with the boundary cutoff ε of the twodimensional dilaton gravity theory.

URL  https://arxiv.org/abs/1802.04599 