Renormalization group flow as optimal transport

Cotler, Jordan; Rezchikov, Semon

doi:10.1103/physrevd.108.025003

Cited by 13 publications

(6 citation statements)

References 64 publications

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“…Equation (5.6) is known as Polchinski's exact renormalization group [95], which provides a general and non-perturbative description for the running of JHEP04(2024)004 couplings in the low-energy effective theory. See [96][97][98][99][100] for recent reviews and discussions. It is worth mentioning that, Polchinski's equation (5.6) is not the only option to satisfy the condition in (5.4).…”

Section: Diffusion As the Rg Flow On The Boundarymentioning

confidence: 99%

On the IR divergences in de Sitter space: loops, resummation and the semi-classical wavefunction

Céspedes,

Davis,

Wang

2024

J. High Energ. Phys.

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In this paper, we revisit the infrared (IR) divergences in de Sitter (dS) space using the wavefunction method, and explicitly explore how the resummation of higher-order loops leads to the stochastic formalism. In light of recent developments of the cosmological bootstrap, we track the behaviour of these nontrivial IR effects from perturbation theory to the non-perturbative regime. Specifically, we first examine the perturbative computation of wavefunction coefficients, and show that there is a clear distinction between classical components from tree-level diagrams and quantum ones from loop processes. Cosmological correlators at loop level receive contributions from tree-level wavefunction coefficients, which we dub classical loops. This distinction significantly simplifies the analysis of loop-level IR divergences, as we find the leading contributions always come from these classical loops. Then we compare with correlators from the perturbative stochastic computation, and find the results there are essentially the ones from classical loops, while quantum loops are only present as subleading corrections. This demonstrates that the leading IR effects are contained in the semi-classical wavefunction which is a resummation of all the tree-level diagrams. With this insight, we go beyond perturbation theory and present a new derivation of the stochastic formalism using the saddle-point approximation. We show that the Fokker-Planck equation follows as a consequence of two effects: the drift from the Schrödinger equation that describes the bulk time evolution, and the diffusion from the Polchinski’s equation which corresponds to the exact renormalization group flow of the coarse-grained theory on the boundary. Our analysis highlights the precise and simple link between the stochastic formalism and the semi-classical wavefunction.

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Section: Diffusion As the Rg Flow On The Boundarymentioning

confidence: 99%

On the IR divergences in de Sitter space: loops, resummation and the semi-classical wavefunction

Céspedes,

Davis,

Wang

2024

J. High Energ. Phys.

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“…)η is the traceless part of the Hessian of η. In the second step we have used the definition (10), and again the identity (40). Recalling that for us N = 2− D < 0, the second and third terms in the parenthesis in (80b) are positive.…”

Section: I)mentioning

confidence: 99%

Gravity from thermodynamics: Optimal transport and negative effective dimensions

et al. 2023

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We prove an equivalence between the classical equations of motion governing vacuum gravity compactifications (and more general warped-product spacetimes) and a concavity property of entropy under time evolution. This is obtained by linking the theory of optimal transport to the Raychaudhuri equation in the internal space, where the warp factor introduces effective notions of curvature and (negative) internal dimension. When the Reduced Energy Condition is satisfied, concavity can be characterized in terms of the cosmological constant \LambdaΛ; as a consequence, the masses of the spin-two Kaluza-Klein fields obey bounds in terms of \LambdaΛ alone. We show that some Cheeger bounds on the KK spectrum hold even without assuming synthetic Ricci lower bounds, in the large class of infinitesimally Hilbertian metric measure spaces, which includes D-brane and O-plane singularities. As an application, we show how some approximate string theory solutions in the literature achieve scale separation, and we construct a new explicit parametrically scale-separated AdS solution of M-theory supported by Casimir energy.

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“…In particular this led to functional optimisation as set up in [13,23] as well as the recent development of essential RG flows [27,34,35]. This idea has also been picked up for Machine Learning applications to functional renormalisation in [36].…”

Section: Rg-adapted Flowsmentioning

confidence: 99%

“…With the choice (36) we have S dyn,k [0] = 0. Moreover, the RG-adapted field expansion entails that S…”

Section: Rg-adapted Expansionmentioning

confidence: 99%

Functional flows for complex effective actions

Ihssen,

Pawlowski

2023

SciPost Phys.

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In the present work we set up a general functional renormalisation group framework for the computation of complex effective actions. For explicit computations we consider both flows of the Wilsonian effective action and the one-particle irreducible (1PI) effective action. The latter is based on an appropriate definition of a Legendre transform for complex actions, and we show its validity by comparison to exact results in zero dimensions, as well as a comparison to results for the Wilsonian effective action. In the present implementations of the general approaches, the flow of the Wilsonian effective action has a wider range of applicability and we obtain results for the effective potential of complex fields in \phi^4ϕ4-theories from zero up to four dimensions. These results are also compared with results from the 1PI effective action within its range of applicability. The complex effective action also allows us to determine the location of the Lee-Yang zeros for general parameter values. We also discuss the extension of the present results to general theories including QCD.

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Renormalization group flow as optimal transport

Cited by 13 publications

References 64 publications

On the IR divergences in de Sitter space: loops, resummation and the semi-classical wavefunction

On the IR divergences in de Sitter space: loops, resummation and the semi-classical wavefunction

Gravity from thermodynamics: Optimal transport and negative effective dimensions

Functional flows for complex effective actions

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