scholarly journals FUNCTIONAL RENORMALIZATION OF NONCOMMUTATIVE SCALAR FIELD THEORY

2011 ◽  
Vol 26 (23) ◽  
pp. 4009-4051 ◽  
Author(s):  
ALESSANDRO SFONDRINI ◽  
TIM A. KOSLOWSKI
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
High Energy ◽  
Flow Equation ◽  
Renormalization Group Equation ◽  
Dual Model ◽  
Group Equation ◽  
Scalar Field Theory ◽  
Covariant Model ◽  
The Matrix

In this paper we apply the Functional Renormalization Group Equation (FRGE) to the noncommutative scalar field theory proposed by Grosse and Wulkenhaar. We derive the flow equation in the matrix representation and discuss the theory space for the self-dual model. The features introduced by the external dimensionful scale provided by the noncommutativity parameter, originally pointed out in R. Gurau and O. J. Rosten, J. High Energy Phys.0907, 064 (2009), are discussed in the FRGE context. Using a technical assumption, but without resorting to any truncation, it is then shown that the theory is asymptotically safe for suitably small values of the ϕ4coupling, recovering the result of M. Disertori et al., Phys. Lett. B649, 95 (2007). Finally, we show how the FRGE can be easily used to compute the one-loop beta-functions of the duality covariant model.

scholarly journals LARGE-N RENORMALIZATION GROUP ON FUZZY SPHERE

2013 ◽  
Vol 21 ◽  
pp. 151-152 ◽  
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.

scholarly journals CONVERGENCE OF DERIVATIVE EXPANSIONS IN SCALAR FIELD THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 2095-2100 ◽  
Author(s):  
TIM R. MORRIS ◽  
JOHN F. TIGHE
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Flow Equation ◽  
Renormalisation Group ◽  
Massless Scalar ◽  
Derivative Expansion ◽  
Scalar Field Theory ◽  
Β Function

The convergence of the derivative expansion of the exact renormalisation group is investigated via the computation of the β function of massless scalar λφ4 theory. The derivative expansion of the Polchinski flow equation converges at one loop for certain fast falling smooth cutoffs. Convergence of the derivative expansion of the Legendre flow equation is trivial at one loop, but also can occur at two loops and in particular converges for an exponential cutoff.

scholarly journals Commutative–non-commutative dualities

2020 ◽  
Vol 98 (2) ◽  
pp. 158-166
Author(s):  
F.G. Scholtz ◽  
P.H. Williams ◽  
J.N. Kriel
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Scalar Field ◽  
Lorentz Symmetry ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Dual Theory ◽  
Constructive Approach ◽  
Non Local ◽  
Exact Renormalization Group

We show that it is in principle possible to construct dualities between commutative and non-commutative theories in a systematic way. This construction exploits a generalization of the exact renormalization group equation (ERG). We apply this to the simple case of the Landau problem and then generalize it to the free and interacting non-canonical scalar field theory. This constructive approach offers the advantage of tracking the implementation of the Lorentz symmetry in the non-commutative dual theory. In principle, it allows for the construction of completely consistent non-commutative and non-local theories where the Lorentz symmetry and unitarity are still respected, but may be implemented in a highly non-trivial and non-local manner.

scholarly journals NONCOMMUTATIVE FIELD THEORY: NUMERICAL ANALYSIS WITH THE FUZZY DISK

2012 ◽  
Vol 27 (24) ◽  
pp. 1250137 ◽  
Author(s):  
FEDELE LIZZI ◽  
BERNARDINO SPISSO
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Rotation Group ◽  
Intimate Relationship ◽  
Noncommutative Field Theory ◽  
Fuzzy Sphere ◽  
Scalar Field Theory ◽  
Algebra Of Functions ◽  
The Matrix ◽  
Transition Curves

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.

scholarly journals Scalar field theory limits of bosonic string amplitudes

2000 ◽  
Vol 579 (1-2) ◽  
pp. 379-410 ◽  
Author(s):  
Alberto Frizzo ◽  
Lorenzo Magnea ◽  
Rodolfo Russo
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Bosonic String ◽  
Scalar Field Theory ◽  
String Amplitudes

On causality in polymer scalar field theory

2011 ◽  
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

scholarly journals ASYMPTOTIC FREEDOM IN A SCALAR FIELD THEORY ON THE LATTICE

1998 ◽  
Vol 13 (31) ◽  
pp. 2495-2501 ◽  
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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