scholarly journals 3d large $N$ vector models at the boundary

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Lorenzo Di Pietro ◽  
Edoardo Lauria ◽  
Pierluigi Niro
Keyword(s):  
Fixed Point ◽  
Weak Coupling ◽  
Vector Model ◽  
Boundary Theory ◽  
Weak Duality ◽  
Renormalization Group Flow ◽  
Boundary Interaction ◽  
Large N ◽  
Group Flow ◽  
N Vector

We consider a 4d scalar field coupled to large NN free or critical O(N)O(N) vector models, either bosonic or fermionic, on a 3d boundary. We compute the \betaβ function of the classically marginal bulk/boundary interaction at the first non-trivial order in the large NN expansion and exactly in the coupling. Starting with the free (critical) vector model at weak coupling, we find a fixed point at infinite coupling in which the boundary theory is the critical (free) vector model and the bulk decouples. We show that a strong/weak duality relates one description of the renormalization group flow to another one in which the free and the critical vector models are exchanged. We then consider the theory with an additional Maxwell field in the bulk, which also gives decoupling limits with gauged vector models on the boundary.

scholarly journals The cubic fixed point at large N

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Damon J. Binder
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Ising Model ◽  
Ising Models ◽  
Three Dimensions ◽  
Renormalization Group Flow ◽  
Conformal Bootstrap ◽  
Large N ◽  
Group Flow ◽  
3D Ising Model

Abstract By considering the renormalization group flow between N coupled Ising models in the UV and the cubic fixed point in the IR, we study the large N behavior of the cubic fixed points in three dimensions. We derive a diagrammatic expansion for the 1/N corrections to correlation functions. Leading large N corrections to conformal dimensions at the cubic fixed point are then evaluated using numeric conformal bootstrap data for the 3d Ising model.

scholarly journals RENORMALIZATION GROUP FLOW EQUATIONS FOR THE SCALAR O(N) THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 2119-2124 ◽  
Author(s):  
B.-J. SCHAEFER ◽  
O. BOHR ◽  
J. WAMBACH
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Three Dimensions ◽  
Leading Order ◽  
Renormalization Group Flow ◽  
Derivative Expansion ◽  
Scalar Theory ◽  
Flow Equations ◽  
Self Consistent ◽  
Group Flow

Self-consistent new renormalization group flow equations for an O(N)-symmetric scalar theory are approximated in next-to-leading order of the derivative expansion. The Wilson-Fisher fixed point in three dimensions is analyzed in detail and various critical exponents are calculated.

scholarly journals ASYMPTOTIC SAFETY IN HIGHER-DERIVATIVE GRAVITY

2009 ◽  
Vol 24 (28) ◽  
pp. 2233-2241 ◽  
Author(s):  
DARIO BENEDETTI ◽  
PEDRO F. MACHADO ◽  
FRANK SAUERESSIG
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Renormalization Group Flow ◽  
Functional Renormalization Group ◽  
Asymptotic Safety ◽  
Higher Derivative ◽  
Gravity Theories ◽  
Group Flow ◽  
Nonperturbative Renormalization

We study the nonperturbative renormalization group flow of higher-derivative gravity employing functional renormalization group techniques. The nonperturbative contributions to the β-functions shift the known perturbative ultraviolet fixed point into a nontrivial fixed point with three UV-attractive and one UV-repulsive eigendirections, consistent with the asymptotic safety conjecture of gravity. The implication of this transition on the unitarity problem, typically haunting higher-derivative gravity theories, is discussed.

Evolution of the Robertson–Walker metric under 2-loop renormalization group flow

2017 ◽  
Vol 26 (03) ◽  
pp. 1750021
Author(s):  
F. Hesamifard ◽  
M. M. Rezaii
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Ricci Flow ◽  
Necessary Condition ◽  
Renormalization Group Flow ◽  
Twisted Product ◽  
Walker Metric ◽  
Group Flow

Here, we study the evolution of a Robertson–Walker (RW) metric under the Ricci flow and 2-loop renormalization group flow (RG-2 flow). We show that a RW metric is a fixed point of the Ricci flow and it is not a solution of the RG-2 flow. RG-2 flow is considered on a doubly twisted product metric with further assumptions and also we introduce a necessary condition for existence of the solution of RG-2 flow.

scholarly journals IMPROVED ACTION FUNCTIONALS IN NON-PERTURBATIVE QUANTUM GRAVITY

2005 ◽  
Vol 20 (11) ◽  
pp. 2358-2363 ◽  
Author(s):  
A. BONANNO ◽  
G. ESPOSITO ◽  
C. RUBANO
Keyword(s):  
Fixed Point ◽  
Lagrangian Description ◽  
Action Functional ◽  
Renormalization Group Flow ◽  
Variable G And Λ ◽  
Einstein Theory ◽  
Pure Gravity ◽  
Perturbative Quantum ◽  
Models Of Gravity ◽  
Group Flow

Models of gravity with variable G and Λ have acquired greater relevance after the recent evidence in favour of the Einstein theory being non-perturbatively renormalizable in the Weinberg sense. The present paper builds a modified Arnowitt–Deser–Misner (ADM) action functional for such models which leads to a power-law growth of the scale factor for pure gravity and for a massless ϕ4 theory in a Universe with Robertson–Walker symmetry, in agreement with the recently developed fixed-point cosmology. Interestingly, the renormalization-group flow at the fixed point is found to be compatible with a Lagrangian description of the running quantities G and Λ.

scholarly journals RENORMALIZATION GROUP FLOW EQUATIONS AND THE PHASE TRANSITION IN O(N)-MODELS

2001 ◽  
Vol 16 (23) ◽  
pp. 3823-3852 ◽  
Author(s):  
O. BOHR ◽  
B.-J. SCHAEFER ◽  
J. WAMBACH
Keyword(s):  
Phase Transition ◽  
Fixed Point ◽  
Three Dimensions ◽  
Leading Order ◽  
Renormalization Group Flow ◽  
Derivative Expansion ◽  
Flow Equations ◽  
Novel Approach ◽  
Self Consistent ◽  
Group Flow

We derive and solve numerically self-consistent flow equations for a general O(N)-symmetric effective potential without any polynomial truncation. The flow equations combined with a sort of a heat-kernel regularization are approximated in next-to-leading order of the derivative expansion. We investigate the method at finite temperature and study the nature of the phase transition in detail. Several beta functions, the Wilson–Fisher fixed point in three dimensions for various N are analyzed and various critical exponents β, ν, δ and η are independently calculated in order to emphasize the reliability of this novel approach.

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