We discuss general theories of N scalar fields with O(N) symmetry. In addition to the standard case of linearly realized symmetry there are also examples that carry nonlinear realizations, with the topology of a cylinder $R\times S^{N-1}$ or a sphere $S^N$. We write flow equations for the theory in the second order of the derivative expansion in the background field and discuss the properties of scaling solutions with vanishing potential.
The gradient flow exact renormalization group (GFERG) is a formulation of the exact renormalization group that keeps exact gauge invariance. GFERG can keep also modified chiral invariance. We will show that this formulation reproduces the correct axial anomaly in four dimensions.
We study renormalization group flow in a non-local version of quantum electrodynamics (QED). We determine the regime in which the theory flows to a local theory in the infrared and study a possible UV completion of four-dimensional QED. In addition, we find that there exist non-local conformal theories with a one-dimensional conformal manifold and non-local deformations of QED in three dimensions that are exactly marginal. Along the way we develop methods for coupling non-local derivatives to external sources and discuss unitarity and conformal vs. scale invariance of these theories.
Field-theoretical calculations performed in an approximation scheme often present a spurious dependence of physical quantities on some unphysical parameters associated with the details of the calculation setup (such as, the renormalization scheme or, in perturbation theory, the resummation procedure). In the present article, we propose to reduce this dependence by invoking conformal invariance. Using as a benchmark the three-dimensional Ising model, we show that, within the derivative expansion at order 4, performed in the nonperturbative renormalization group formalism, the identity associate…
We provide the first step towards renormalization in a nonminimal Lorentz-violating model consisting of normal scalars and modified fermions with mass dimension five operators. We compute the radiative corrections corresponding to the scalar self-energy, and we show that some divergencies are improved and in the scalar sector they are finite. The pole mass of the scalar two-point function is found and shown to lead to modifications of asymptotic states.
We consider a symmetric scalar theory with quartic coupling in 4-dimensions. We show that the 4 loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced at the level of the Lagrangian and is therefore conceptually simpler than a standard 2PI calculation, which requires multiple counterterms. We explain how our method can be used to do the corresponding calculation at the 4PI level, which cannot be done using any known method by introducing counterterms.
At zero temperature, the Lorentz invariance is strictly preserved in three-dimensional quantum electrodynamics. This property ensures that the velocity of massless fermions is not renormalized by the gauge interaction. At finite temperature, however, the Lorentz invariance is explicitly broken by the thermal fluctuation. The longitudinal component of gauge interaction becomes short-ranged due to thermal screening, whereas the transverse component remains long-ranged because of local gauge invariance. The transverse gauge interaction leads to singular corrections to the fermion self-energy and …
We present five-loop results for the renormalization of various models with a cubic interaction (in ${d = 6 - 2 \varepsilon}$ dimensions). For the scalar model and its ${O(n)}$-symmetric extension we provide renormalization constants, anomalous dimensions and critical exponents. We discuss in detail the method of calculation, and provide all counterterms up to five loops. This allows one to consider generalizations of the ${φ^3}$ theory to other symmetries.
We argue that conformal invariance is a common thread linking several scalar effective field theories that appear in the double copy and scattering equations. For a derivatively coupled scalar with a quartic ${\cal O}(p^4)$ vertex, classical conformal invariance dictates an infinite tower of additional interactions that coincide exactly with Dirac-Born-Infeld theory analytically continued to spacetime dimension $D=0$. For the case of a quartic ${\cal O}(p^6)$ vertex, classical conformal invariance constrains the theory to be the special Galileon in $D=-2$ dimensions. We also verify the conform…
This paper presents divergent contributions of the radiative corrections for a Lorentz-violating extension of the scalar electrodynamics. We initially discuss some features of the model and extract the Feynman rules. Then we compute the one-loop radiative corrections using Feynman parametrization and dimensional regularization in order to evaluate the integrals. We also discuss Furry's theorem validity and renormalization in the present context.
With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions. That is because conformal field theories form a large class of massless no-scale renormalizable quantum field theories. It is generally believed, however, that renormalization breaks conformal invariance and with the absence of a reported success to find a conformally invariant renormalization scheme, an alternative approach is followed in this thesis. We beg…
We renormalize various scalar field theories with a $ϕ^n$ self interaction such as $n$ $=$ $5$, $7$ and $9$ in their respective critical dimensions which are non-integer. The renormalization group functions for the $O(N)$ symmetric extensions are also computed.
