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We investigate the discrete $\beta$ function of the 2-flavor SU(3) sextet model using the finite volume gradient flow scheme. Our results, using clover improved nHYP smeared Wilson fermions, follow the (non-universal) 4-loop…
We investigate the phase structure of non-commutative scalar field theories and find evidence for ordered phases which break translation invariance. A self-consistent one-loop analysis indicates that the transition into these ordered phases…
It is shown that the renormalization group turns to be a symmetry group in a theory initially formulated in a space of scale-dependent functions, i.e, those depending on both the position $x$ and the resolution $a$. Such theory, earlier…
Renormalisation Group (RG) flows in theory space (the space of couplings) are generated by a vector field -- the $\beta$ function. Using a specific metric ansatz in theory space and certain methods employed largely in the context of General…
We present a detailed version of our recent work on the renormalization group approach to multicritical scalar theories with higher derivative kinetic term of the form $\phi(-\Box)^k\phi$ and upper critical dimension $d_c = 2nk/(n-1)$.…
We consider a possibility to unify the methods of regularization, such as the renormalization group method, stochastic quantization etc., by the extension of the standard field theory of the square-integrable functions $\phi(b)\in…
We argue that in general renormalizable field theories the topological angles may develop an additive beta function starting no earlier than 2-loop order. The leading expression is uniquely determined by a single model-independent…
The nontrivial fixed point discovered for $\phi^4$-marginal couplings in tensorial group field theories have been showed to be incompatible with Ward-Takahashi identities. In this previous analysis we have stated that the case of models…
We consider the model of a massless charged scalar field, in (2+1) dimensions, with a self interaction of the form $lambda (\phi^* \phi)^3$ and interacting with a Chern Simons field. We calculate the renormalization group $\beta$ functions…
Renormalization group equations play a central role in effective field theories, both maintaining perturbative control and allowing one to determine the correct low-energy phenomenology. In this work, we complete the one-loop…
Differential regularization is applied to a field theory of a non-relativistic charged boson field $\phi$ with $\lambda (\phi {}^{*} \phi)^2$ self-interaction and coupling to a statistics-changing $U(1)$ Chern-Simons gauge field.…
We study the renormalization group flow of the O(N) non-linear sigma model in arbitrary dimensions. The effective action of the model is truncated to fourth order in the derivative expansion and the flow is obtained by combining the…
This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…
The most general version of a renormalizable $d=4$ theory corresponding to a dimensionless higher-derivative scalar field model in curved spacetime is explored. The classical action of the theory contains $12$ independent functions, which…
We reexamine the functional renormalization-group theory of wetting transitions. As a starting point of the analysis we apply an exact equation describing renormalization group flow of the generating functional for irreducible vertex…
We present a new method for renormalisation group improvement of the effective potential of a quantum field theory with an arbitrary number of scalar fields. The method amounts to solving the renormalisation group equation for the effective…
To resum large logarithms in multi-scale problems a generalization of $\MS$ is introduced allowing for as many renormalization scales as there are generic scales in the problem. In the new \lq\lq minimal multi-scale subtraction scheme''…
We calculate the critical exponent $\eta$ of the $D$-dimensional Ising model from a simple truncation of the functional renormalization group flow equations for a scalar field theory with long-range interaction. Our approach relies on the…
In previous studies, we proposed a scaling ansatz for electron-electron interactions under renormalization group transformation. With the inclusion of phonon-mediated interactions, we show that the scaling ansatz, characterized by 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…