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Two-dimensional dilaton gravity theory and lattice Schwarzian theory

TitleTwo-dimensional dilaton gravity theory and lattice Schwarzian theory
Publication TypeJournal Article
Year of Publication2019
AuthorsS-K. Chu, C-T. Ma, and C-H. Wu
JournalInt. J. Mod. Phys. A
Volume34
Pagination1950176
Date PublishedOCT 20
Type of ArticleArticle
ISSN0217-751X
KeywordsDilaton gravity theory, higher derivative term, isometry, lattice Schwarzian theory
Abstract

We report a holographic study of a two-dimensional 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 two-dimensional 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 R-2, 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 second-order perturbation of boundary cutoff epsilon(2) 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 epsilon of the two-dimensional dilaton gravity theory.

DOI10.1142/S0217751X19501768