相关论文: The geometry of RG flows in theory space
The space of couplings of a given theory is the arena of interest in this article. Equipped with a metric ansatz akin to the Fisher information matrix in the space of parameters in statistics (similar metrics in physics are the…
The renormalization group flow in two-dimensional field theories that are coupled to gravity has unusual features: First, the flow equations are second order in derivatives. Second, in the presence of handles the flow has quantum mechanical…
In this paper, I compare the generators of the renormalization group flow, or the geometric $\beta$-functions for dimensional regularization and operator regularization. I then extend the analysis to show that the geometric $\beta$-function…
A natural geometry, arising from the embedding into a Hilbert space of the parametrised probability measure for a given lattice model, is used to study the symmetry properties of real-space renormalisation group (RG) flow. In the projective…
In this talk methods for a rigorous control of the renormalization group (RG) flow of field theories are discussed. The RG equations involve the flow of an infinite number of local partition functions. By the method of exact beta-function…
It is shown that the renormalisation group (RG) equation can be viewed as an equation for Lie transport of physical amplitudes along the integral curves generated by the $\beta$-functions of a quantum field theory. The anomalous dimensions…
We show that if the beta functions of a field theory are given by the gradient of a certain potential on the space of couplings, a gravitational background in one more dimension can express the renormalization group (RG) flow of the theory.…
The renormalization group flow in two--dimensional field theories is modified if they are coupled to gravity. Beta function coefficients are changed, the $c$--theorem is no longer strictly valid, and flows from fixed points with central…
We calculate numerically the renormalization group (RG) flow of lattice QCD in two-coupling space, $(\beta_{1\times 1},\beta_{1\times 2})$. This is the first explicit calculation of the RG flow of SU(3) gauge theory. From the RG flow,a…
The $\beta$-functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings that respect the symmetry and locality are generated under the renormalization group flow, and the exact…
It is shown that the renormalisation group flow in coupling constant space can be interpreted in terms of a dynamical equation for the couplings analogous to viscous fluid flow under the action of a potential. For free scalar field theory…
We obtain the exact renormalization group (RG) flow equation for a self interacting real scalar field in an expanding cosmological background. The beta functional for the potential in the local potential approximation is determined in terms…
A recently proposed renormalization group technique, based on the hierarchical structures present in theories with fluctuating geometry, is implemented in the model of branched polymers. The renormalization group equations can be solved…
We investigate the properties of the renormalisation group (RG) flow of two-dimensional sigma models with a generic metric coupling by utilising known results for the Ricci flow. We point out that on many occasions the RG flow develops…
The gradient property of the renormalisation group (RG) flow of multiscalar theories is examined perturbatively in $d=4$ and $d=4-\varepsilon$ dimensions. Such theories undergo RG flows in the space of quartic couplings $\lambda^I$.…
We study two-dimensional spherical defects in d-dimensional Conformal Field Theories. We argue that the Renormalization Group (RG) flows on such defects admit the existence of a decreasing entropy function. At the fixed points of the flow,…
We investigate the renormalization group (RG) structure of the gradient flow. Instead of using the original bare action to generate the flow, we propose to use the effective action at each flow time. We write down the basic equation for…
We investigate the renormalization group (RG) flow of SU(3) lattice gauge theory in a two coupling space with couplings $\beta_{11}$ and $\beta_{12}$ corresponding to $1\times 1$ and $1\times 2$ loops respectively. Extensive numerical…
We study the renormalization group equations of the fully anisotropic $\lambda$-deformed CFTs involving the direct product of two current algebras at different levels $k_{1,2}$ for general semi-simple groups. The exact, in the deformation…
The renormalisation group (RG) flow on the space of couplings of a simple model with two couplings is examined. The model considered is that of a single component scalar field with $\phi^4$ self interaction coupled, via Yukawa coupling, to…