Correlation functions and renormalization in a scalar field theory on the fuzzy sphere

The fuzzy disk is a discretization of the algebra of functions on the two-dimensional disk using finite matrices which preserves the action of the rotation group. We define a φ4 scalar field theory on it and analyze numerically three different limits for the rank of the matrix going to infinity. The numerical simulations reveal three different phases: uniform and disordered phases already present in the commutative scalar field theory and a nonuniform ordered phase as noncommutative effects. We have computed the transition curves between phases and their scaling. This is in agreement with studies on the fuzzy sphere, although the speed of convergence for the disk seems to be better. We have also performed the limits for the theory in the cases of the theory going to the commutative plane or commutative disk. In this case the theory behaves differently, showing the intimate relationship between the nonuniform phase and noncommutative geometry.

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LARGE-N RENORMALIZATION GROUP ON FUZZY SPHERE

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194513009562 ◽

2013 ◽

Vol 21 ◽

pp. 151-152 ◽

Cited By ~ 1

Author(s):

SHOICHI KAWAMOTO ◽

DAN TOMINO ◽

TSUNEHIDE KUROKI

Keyword(s):

Field Theory ◽

Renormalization Group ◽

Scalar Field ◽

Fixed Points ◽

Renormalization Group Equation ◽

Group Equation ◽

Fuzzy Sphere ◽

Scalar Field Theory ◽

Large N

We study the large-N renormalization group of scalar field theory on a fuzzy sphere. We carry out perturbative analysis and formulate the renormalization group equation. We then search for fixed points and investigate their properties.

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Momentum-space entanglement in scalar field theory on fuzzy spheres

Journal of High Energy Physics ◽

10.1007/jhep12(2021)101 ◽

2021 ◽

Vol 2021 (12) ◽

Author(s):

Shoichi Kawamoto ◽

Tsunehide Kuroki

Keyword(s):

Field Theory ◽

Scalar Field ◽

Momentum Space ◽

Degrees Of Freedom ◽

Entanglement Entropy ◽

Noncommutative Space ◽

Quantum Field ◽

Fuzzy Sphere ◽

Scalar Field Theory ◽

Different Characteristics

Abstract Quantum field theory defined on a noncommutative space is a useful toy model of quantum gravity and is known to have several intriguing properties, such as nonlocality and UV/IR mixing. They suggest novel types of correlation among the degrees of freedom of different energy scales. In this paper, we investigate such correlations by the use of entanglement entropy in the momentum space. We explicitly evaluate the entanglement entropy of scalar field theory on a fuzzy sphere and find that it exhibits different behaviors from that on the usual continuous sphere. We argue that these differences would originate in different characteristics; non-planar contributions and matrix regularizations. It is also found that the mutual information between the low and the high momentum modes shows different scaling behaviors when the effect of a cutoff becomes important.

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Scalar field theory limits of bosonic string amplitudes

Nuclear Physics B ◽

10.1016/s0550-3213(00)00200-5 ◽

2000 ◽

Vol 579 (1-2) ◽

pp. 379-410 ◽

Cited By ~ 16

Author(s):

Alberto Frizzo ◽

Lorenzo Magnea ◽

Rodolfo Russo

Keyword(s):

Field Theory ◽

Scalar Field ◽

Bosonic String ◽

Scalar Field Theory ◽

String Amplitudes

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On causality in polymer scalar field theory

10.1063/1.3647531 ◽

2011 ◽

Cited By ~ 2

Author(s):

Angel A. García-Chung ◽

Hugo A. Morales-Técotl ◽

Luis Arturo Ureña-López ◽

Hugo Aurelio Morales-Técotl ◽

Román Linares-Romero ◽

...

Keyword(s):

Field Theory ◽

Scalar Field ◽

Scalar Field Theory

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ASYMPTOTIC FREEDOM IN A SCALAR FIELD THEORY ON THE LATTICE

Modern Physics Letters A ◽

10.1142/s0217732398002655 ◽

1998 ◽

Vol 13 (31) ◽

pp. 2495-2501 ◽

Cited By ~ 4

Author(s):

KURT LANGFELD ◽

HUGO REINHARDT

Keyword(s):

Field Theory ◽

Scalar Field ◽

Scalar Particle ◽

Higgs Sector ◽

Asymptotic Freedom ◽

Scalar Field Theory ◽

Large N ◽

The Standard Model ◽

Conceptual Problems ◽

The Continuum

A scalar field theory in four space–time dimensions is proposed, which embodies a scalar condensate, but is free of the conceptual problems of standard ϕ4-theory. We propose an N-component, O(N)-symmetric scalar field theory, which is originally defined on the lattice. The scalar lattice model is analytically solved in the large-N limit. The continuum limit is approached via an asymptotically free scaling. The renormalized theory evades triviality, and furthermore gives rise to a dynamically formed mass of the scalar particle. The model might serve as an alternative to the Higgs sector of the standard model, where the quantum level of the standard ϕ4-theory contradicts phenomenology due to triviality.

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