TY - JOUR

T1 - Scalar fields on fluctuating hyperbolic geometries

AU - Asaduzzaman, Muhammad

AU - Catterall, Simon

N1 - Funding Information:
This work is supported in part by the U.S. Department of Energy (DOE), Office of Science, Office of High Energy Physics, under Award Number DE-SC0009998 and DE-SC0019139. Numerical computations were performed at Syracuse University HTC Campus Grid: NSF award ACI-1341006.
Publisher Copyright:
© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0)

PY - 2022/7/8

Y1 - 2022/7/8

N2 - We present results on the behavior of the boundary-boundary correlation function of scalar fields propagating on discrete two-dimensional random triangulations representing manifolds with the topology of a disk. We use a gravitational action that includes a curvature squared operator, which favors a regular tessellation of hyperbolic space for large values of its coupling. We probe the resultant geometry by analyzing the propagator of a massive scalar field and show that the conformal behavior seen in the uniform hyperbolic space survives as the coupling approaches zero. The analysis of the boundary correlator suggests that holographic predictions survive, at least, weak quantum gravity corrections. We then show how such an R2 operator might be induced as a result of integrating out massive lattice fermions and show preliminary result for boundary correlation functions that include the effects of this fermionic backreaction on the geometry.

AB - We present results on the behavior of the boundary-boundary correlation function of scalar fields propagating on discrete two-dimensional random triangulations representing manifolds with the topology of a disk. We use a gravitational action that includes a curvature squared operator, which favors a regular tessellation of hyperbolic space for large values of its coupling. We probe the resultant geometry by analyzing the propagator of a massive scalar field and show that the conformal behavior seen in the uniform hyperbolic space survives as the coupling approaches zero. The analysis of the boundary correlator suggests that holographic predictions survive, at least, weak quantum gravity corrections. We then show how such an R2 operator might be induced as a result of integrating out massive lattice fermions and show preliminary result for boundary correlation functions that include the effects of this fermionic backreaction on the geometry.

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M3 - Conference Article

AN - SCOPUS:85134434743

SN - 1824-8039

VL - 396

JO - Proceedings of Science

JF - Proceedings of Science

M1 - 430

T2 - 38th International Symposium on Lattice Field Theory, LATTICE 2021

Y2 - 26 July 2021 through 30 July 2021

ER -