Hyperbolic lattice for scalar field theory in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>AdS</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>
Richard C. Brower, Cameron V. Cogburn, E B Owen
Abstract
We construct a tessellation of ${\mathrm{AdS}}_{3}$, by extending the equilateral triangulation of ${\mathrm{AdS}}_{2}$ on the Poincar\'e disk based on the (2,3,7) triangle group, suitable for studying strongly coupled phenomena and the $\mathrm{AdS}/\mathrm{CFT}$ correspondence. A Hamiltonian form conducive to the study of dynamics and quantum computation is presented. We show agreement between lattice calculations and analytic results for the free scalar theory and find evidence of a second-order critical transition for ${\ensuremath{\phi}}^{4}$ theory using Monte Carlo simulations. Applications of this anti--de Sitter Hamiltonian formulation to real time evolution and quantum computing are discussed.