Renormalization of the energy-momentum tensor in three-dimensional scalar SU(N) theories using the Wilson flow

Debbio, Luigi Del; Dobson, Elizabeth; Jüttner, Andreas; Kitching-Morley, Ben; Lee, Joseph K. L.; Nourry, Valentin; Portelli, Antonin; Rocha, Henrique Bergallo; Skenderis, Kostas

doi:10.1103/physrevd.103.114501

Cited by 5 publications

(4 citation statements)

References 58 publications

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“…The simulated masses were in the vicinity of the critical point. It can be seen that the extrapolated value of 𝑐 3 , given by the 𝑦-intercept, gives overlap between the error bands between the position-space method and the Wilson Flow method, as obtained in [10].…”

Section: Emt Renormalisation Resultsmentioning

confidence: 63%

Position-Space Renormalisation of the Energy-Momentum Tensor

Rocha¹,

Debbio²,

Jüttner³

et al. 2023

Proceedings of the 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)

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There is increasing interest in the study of nonperturbative aspects of three-dimensional quantum field theories (QFT). They appear as holographic dual to theories of (strongly coupled) gravity. For instance, in Holographic Cosmology, the two-point function of the Energy-Momentum Tensor (EMT) of a particular class of three-dimensional QFTs can be mapped into the power spectrum of the Cosmic Microwave Background in the gravitational theory. However, the presence of divergent contact terms poses challenges in extracting a renormalised EMT two-point function on the lattice. Using a 𝜙 4 theory of adjoint scalars valued in the su(𝑁) Lie Algebra as a proofof-concept motivated by Holographic Cosmology, we apply a novel method for filtering out such contact terms by making use of infinitely differentiable "bump" functions which enforce a smooth window that excludes contributions at zero spatial separation. The process effectively removes the local contact terms and allows us to extract the continuum limit behaviour of the renormalised EMT two-point function.

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Section: Emt Renormalisation Resultsmentioning

confidence: 63%

Position-Space Renormalisation of the Energy-Momentum Tensor

Rocha¹,

Debbio²,

Jüttner³

et al. 2023

Proceedings of the 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)

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“…Because of the breakdown of translational symmetry in lattice discretisation, one cannot rely on continuum Ward Identities and the issue of renormalising becomes nontrivial. Strides have been made by our collaboration in the pure scalar case by applying the Wilson Flow to renormalisation [22].…”

Section: Pos(lattice2021)270mentioning

confidence: 99%

Critical behaviour and phase structure of 3d Scalar+Gauge Field Theories in the adjoint representation

Rocha¹,

Dobson²,

Juettner³

et al. 2022

Proceedings of the 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021)

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In a class of holographic models for cosmology, the dual theory is given by a massless superrenormalisable QFT in 3 dimensions. In order to obtain cosmological observables, correlators of this QFT may be obtained via lattice field theory. Previous work has focused on scalar 4 matrix theories in the adjoint representation of SU(N). In this work we present preliminary results in the critical behaviour and phase structure of the theory with an SU(N) scalar field coupled to gauge fields by utilising the Heatbath-Overrelaxation (HBOR) algorithm in lattice field theory.

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“…In this holographic approach, cosmological observables, such as the cosmic microwave background (CMB) power spectra, can be described in terms of correlators of the EMT of a dual three-dimensional quantum field theory (QFT) with no gravity. This proceeding summarizes the work in [2]. In this paper, we are interested in renormalizing the EMT of the simplest version of the holographic dual theories, which is the class of 3𝑑 massless scalar QFTs with 𝜙 in the adjoin of 𝑆𝑈 (𝑁) and a 𝜙 4 interaction.…”

Section: Introductionmentioning

confidence: 99%

Renormalization of the $3D$ $SU(N)$ scalar energy-momentum tensor using the Wilson flow

Lee¹,

Debbio²,

Dobson³

et al. 2022

Preprint

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In the holographic approach to cosmology, cosmological observables are described in terms of correlators of a three-dimensional boundary quantum field theory. As a concrete model, we study the 3D massless SU(N) scalar matrix field theory with a 𝜙 4 interaction. On the lattice, the energymomentum tensor (EMT) in this theory can mix with the operator 𝜙 2 . We utilize the Wilson Flow to renormalize the EMT on the lattice, and present numerical results for the mixing coefficient for 𝑁 = 2. Obtaining the renormalized EMT will allow us to make predictions for the CMB power spectra in the regime where the dual QFT is non-perturbative.

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Renormalization of the energy-momentum tensor in three-dimensional scalar SU(N) theories using the Wilson flow

Cited by 5 publications

References 58 publications

Position-Space Renormalisation of the Energy-Momentum Tensor

Position-Space Renormalisation of the Energy-Momentum Tensor

Critical behaviour and phase structure of 3d Scalar+Gauge Field Theories in the adjoint representation

Renormalization of the $3D$ $SU(N)$ scalar energy-momentum tensor using the Wilson flow

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