Pedagogical comments about nonperturbative Ward-constrained melonic renormalization group flow

Lahoche, Vincent; Samary, Dine Ousmane

doi:10.1103/physrevd.101.024001

Cited by 15 publications

(18 citation statements)

References 38 publications

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“…This hard inference problem is simplified within the LPA, because the expression for the effective kinetic action differs only by the mass parameter u 2 (k). The derivation of the flow equations follows the general strategy [65]. Taking the second derivative of the Equation ( 18) with respect to M µ , we get:…”

Section: Rg From Theory To Numerical Investigationsmentioning

confidence: 99%

Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra I: Matricial Data

Lahoche

Samary

Tamaazousti

2021

Entropy

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Renormalization group techniques are widely used in modern physics to describe the relevant low energy aspects of systems involving a large number of degrees of freedom. Those techniques are thus expected to be a powerful tool to address open issues in data analysis when datasets are highly correlated. Signal detection and recognition for a covariance matrix having a nearly continuous spectra is currently one of these opened issues. First, investigations in this direction have been proposed in recent investigations from an analogy between coarse-graining and principal component analysis (PCA), regarding separation of sampling noise modes as a UV cut-off for small eigenvalues of the covariance matrix. The field theoretical framework proposed in this paper is a synthesis of these complementary point of views, aiming to be a general and operational framework, both for theoretical investigations and for experimental detection. Our investigations focus on signal detection. They exhibit numerical investigations in favor of a connection between symmetry breaking and the existence of an intrinsic detection threshold.

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Section: Rg From Theory To Numerical Investigationsmentioning

confidence: 99%

Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra I: Matricial Data

Lahoche

Samary

Tamaazousti

2021

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“…Note that this factorization is not inoffensive, and may introduce disagreements with the required boundary conditions [53,[60][61][62][63]. We distinguish two levels of approximation, the standard LPA where we enforce Z(k) = 1, and the improved version LPA , taking into account the RG flow of the running field strength Z(k).…”

Section: Local Potential Approximationmentioning

confidence: 99%

“…To take into account the non-vanishing flow for Z , it is suitable to factorize a global Z factor in front of the definition of

. We choose to work with the optimized Litim regulator, which has been proved to have nice properties in regards to optimization, stability and integrability [ 59 ]:

Note that this factorization is not inoffensive, and may introduce disagreements with the required boundary conditions [ 53 , 60 , 61 , 62 , 63 ]. We distinguish two levels of approximation, the standard LPA where we enforce

, and the improved version LPA

, taking into account the RG flow of the running field strength

.…”

Section: Preliminariesmentioning

confidence: 99%

Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra II: Tensorial Data

Lahoche

Samary²,

Tamaazousti

2021

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The tensorial principal component analysis is a generalization of ordinary principal component analysis focusing on data which are suitably described by tensors rather than matrices. This paper aims at giving the nonperturbative renormalization group formalism, based on a slight generalization of the covariance matrix, to investigate signal detection for the difficult issue of nearly continuous spectra. Renormalization group allows constructing an effective description keeping only relevant features in the low “energy” (i.e., large eigenvalues) limit and thus providing universal descriptions allowing to associate the presence of the signal with objectives and computable quantities. Among them, in this paper, we focus on the vacuum expectation value. We exhibit experimental evidence in favor of a connection between symmetry breaking and the existence of an intrinsic detection threshold, in agreement with our conclusions for matrices, providing a new step in the direction of a universal statement.

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“…This aspect of the complex field in TGFT seems to have been overlooked so far in the literature [27][28][29][30][50][51][52][53][54][55][56][57][58][59][60][61]. Under some mild conditions it is straightforward to obtain the 2×2 trace of the inverse of the operator…”

Section: Frg Equation In Tgftmentioning

confidence: 99%

Phase transitions in TGFT: functional renormalization group in the cyclic-melonic potential approximation and equivalence to O(N) models

Pithis

Thürigen

2020

J. High Energ. Phys.

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In the group field theory approach to quantum gravity, continuous spacetime geometry is expected to emerge via phase transition. However, understanding the phase diagram and finding fixed points under the renormalization group flow remains a major challenge. In this work we tackle the issue for a tensorial group field theory using the functional renormalization group method. We derive the flow equation for the effective potential at any order restricting to a subclass of tensorial interactions called cyclic melonic and projecting to a constant field in group space. For a tensor field of rank r on U(1) we explicitly calculate beta functions and find equivalence with those of O(N) models but with an effective dimension flowing from r − 1 to zero. In the r − 1 dimensional regime, the equivalence to O(N) models is modified by a tensor specific flow of the anomalous dimension with the consequence that the Wilson-Fisher type fixed point solution has two branches. However, due to the flow to dimension zero, fixed points describing a transition between a broken and unbroken phase do not persist and we find universal symmetry restoration. To overcome this limitation, it is necessary to go beyond compact configuration space.

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Pedagogical comments about nonperturbative Ward-constrained melonic renormalization group flow

Cited by 15 publications

References 38 publications

Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra I: Matricial Data

Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra I: Matricial Data

Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra II: Tensorial Data

Phase transitions in TGFT: functional renormalization group in the cyclic-melonic potential approximation and equivalence to O(N) models

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