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Title: Radial lattice quantization of 3D ϕ 4 field theory

Journal Article · · Physical Review D

The quantum extension of classical finite elements, referred to as quantum finite elements, is applied to the radial quantization of 3d Φ4 theory on a simplicial lattice for the $$\mathbb{R}$$ × $$\mathbb{S}$$2 manifold. Explicit counter terms to cancel the one- and two-loop ultraviolet defects are implemented to reach the quantum continuum theory. Using the Brower-Tamayo cluster Monte Carlo algorithm, numerical results support the QFE ansatz that the critical conformal field theory (CFT) is reached in the continuum with the full isometries of $$\mathbb{R}$$ × $$\mathbb{S}$$2 restored. The Ricci curvature term, while technically irrelevant in the quantum theory, is shown to dramatically improve the convergence opening, the way for high precision Monte Carlo simulation to determine the CFT data: operator dimensions, trilinear OPE couplings and the central charge.

Research Organization:
Boston Univ., MA (United States)
Sponsoring Organization:
USDOE; Swiss National Science Foundation (SNSF)
Grant/Contract Number:
SC0015845; SC0019061; 200021_175761
OSTI ID:
1829176
Alternate ID(s):
OSTI ID: 1833383
Journal Information:
Physical Review D, Journal Name: Physical Review D Vol. 104 Journal Issue: 9; ISSN 2470-0010
Publisher:
American Physical SocietyCopyright Statement
Country of Publication:
United States
Language:
English

References (31)

Random lattice field theory: General formulation journal July 1982
Lattice Dirac fermions on a simplicial Riemannian manifold journal June 2017
Lattice gauge theory for physics beyond the Standard Model journal November 2019
Finite element exterior calculus: from Hodge theory to numerical stability journal January 2010
Two-dimensional simplical quantum gravity journal April 1986
Lattice radial quantization: 3D Ising journal April 2013
Composite Higgs model at a conformal fixed point journal April 2016
A universal result on central charges in the presence of double-trace deformations journal April 2003
Conformal invariance and universality in finite-size scaling journal May 1984
The Large-N Limit of Superconformal Field Theories and Supergravity journal January 1999
Lattice ϕ 4 field theory on Riemann manifolds: Numerical tests for the 2D Ising CFT on S 2 journal July 2018
Hamiltonian truncation study of the φ 4 theory in two dimensions journal April 2015
Dimensional regularisation in the presence of large background fields journal September 1982
Fermion Field on a Random Lattice journal January 1986
The large $N$ limit of superconformal field theories and supergravity journal January 1998
Stealth dark matter: Dark scalar baryons through the Higgs portal journal October 2015
Simplical gravity coupled to scalar matter journal March 1994
Background field calculations in curved spacetime journal April 1984
Embedded dynamics for φ 4 theory journal March 1989
Nearly conformal gauge theories in finite volume journal November 2009
Erratum: Properties and uses of the Wilson flow in lattice QCD journal March 2014
Background field calculations in curved spacetime journal April 1984
Simplicial quantum gravity with higher derivative terms: Formalism and numerical results in four dimensions journal June 1986
A Monte Carlo study of leading order scaling corrections of phi 4 theory on a three-dimensional lattice journal January 1999
Properties and uses of the Wilson flow in lattice QCD journal August 2010
Solving the 3D Ising model with the conformal bootstrap journal July 2012
Bootstrapping mixed correlators in the 3D Ising model journal November 2014
Conformal partial waves and the operator product expansion journal February 2004
Conformal four point functions and the operator product expansion journal April 2001
Universal amplitudes in finite-size scaling: generalisation to arbitrary dimensionality journal September 1985
Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$ c -Minimization and Precise Critical Exponents journal June 2014

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