Phase transitions in GFT: The Landau perspective

Andreas Georg Aristides Pithis

doi:10.6084/m9.figshare.7033187.v1

Phase transitions in GFT: The Landau perspective

Andreas Georg Aristides Pithis

Physics

Research output: Contribution to journal › Conference paper

Abstract

We investigate the critical behavior of group field theory (GFT) systems in the Gaussian approximation. By applying the Ginzburg criterion to quantify field fluctuations, we find that this approximation is valid for a Lorentzian GFT on SL(2,R), while it breaks down in the case of the GFT model for 3d Euclidean quantum gravity, the so-called Boulatov model. From this we conclude that the Gaussian approximation provides a trustworthy description of a phase transition in the former case. However, it is insufficient for the same purpose in the case of the Boulatov model and suggests that a nonperturbative treatment using the functional renormalization group (FRG) methodology is needed to settle this question. On the other hand, the results in the case of a Lorentzian GFT on SL(2,R) may indicate the necessity of GFT models to be defined on non-compact domains for phase transitions to occur.

Original language	English
Journal	Figshare
DOIs	https://doi.org/10.6084/m9.figshare.7033187.v1
Publication status	Published - 31 Aug 2018

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title = "Phase transitions in GFT: The Landau perspective",

abstract = "We investigate the critical behavior of group field theory (GFT) systems in the Gaussian approximation. By applying the Ginzburg criterion to quantify field fluctuations, we find that this approximation is valid for a Lorentzian GFT on SL(2,R), while it breaks down in the case of the GFT model for 3d Euclidean quantum gravity, the so-called Boulatov model. From this we conclude that the Gaussian approximation provides a trustworthy description of a phase transition in the former case. However, it is insufficient for the same purpose in the case of the Boulatov model and suggests that a nonperturbative treatment using the functional renormalization group (FRG) methodology is needed to settle this question. On the other hand, the results in the case of a Lorentzian GFT on SL(2,R) may indicate the necessity of GFT models to be defined on non-compact domains for phase transitions to occur.",

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AU - Pithis, Andreas Georg Aristides

PY - 2018/8/31

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N2 - We investigate the critical behavior of group field theory (GFT) systems in the Gaussian approximation. By applying the Ginzburg criterion to quantify field fluctuations, we find that this approximation is valid for a Lorentzian GFT on SL(2,R), while it breaks down in the case of the GFT model for 3d Euclidean quantum gravity, the so-called Boulatov model. From this we conclude that the Gaussian approximation provides a trustworthy description of a phase transition in the former case. However, it is insufficient for the same purpose in the case of the Boulatov model and suggests that a nonperturbative treatment using the functional renormalization group (FRG) methodology is needed to settle this question. On the other hand, the results in the case of a Lorentzian GFT on SL(2,R) may indicate the necessity of GFT models to be defined on non-compact domains for phase transitions to occur.

AB - We investigate the critical behavior of group field theory (GFT) systems in the Gaussian approximation. By applying the Ginzburg criterion to quantify field fluctuations, we find that this approximation is valid for a Lorentzian GFT on SL(2,R), while it breaks down in the case of the GFT model for 3d Euclidean quantum gravity, the so-called Boulatov model. From this we conclude that the Gaussian approximation provides a trustworthy description of a phase transition in the former case. However, it is insufficient for the same purpose in the case of the Boulatov model and suggests that a nonperturbative treatment using the functional renormalization group (FRG) methodology is needed to settle this question. On the other hand, the results in the case of a Lorentzian GFT on SL(2,R) may indicate the necessity of GFT models to be defined on non-compact domains for phase transitions to occur.

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DO - 10.6084/m9.figshare.7033187.v1

M3 - Conference paper

JO - Figshare

JF - Figshare

ER -

Phase transitions in GFT: The Landau perspective

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