Absence Of Higher Order Corrections Research Articles

Impact of theoretical uncertainties on model parameter reconstruction from GW signals sourced by cosmological phase transitions

Different computational techniques for cosmological phase transition parameters can impact the gravitational wave (GW) spectra predicted in a given particle physics model. To scrutinize the importance of this effect, we perform large-scale parameter scans of the dynamical real-singlet extended Standard Model using three perturbative approximations for the effective potential; the MS¯ and on shell schemes at leading order, and three-dimensional thermal effective theory (3D EFT) at next-to-leading order. While predictions of GW amplitudes are typically unreliable in the absence of higher-order corrections, we show that the reconstructed model parameter spaces are robust up to a few percent in uncertainty. While 3D EFT is accurate from one-loop order, theoretical uncertainties of reconstructed model parameters, using four-dimensional standard techniques, remain dominant over the experimental ones even for signals merely strong enough to claim a detection by LISA. Published by the American Physical Society 2024

Unruh effect universality: emergent conical geometry from density operator

The Unruh effect has been investigated from the point of view of the quantum statistical Zubarev density operator in space with the Minkowski metric. Quantum corrections of the fourth order in acceleration to the energy-momentum tensor of real and complex scalar fields, and Dirac field are calculated. Both massless and massive fields are considered. The method for regularization of discovered infrared divergences for scalar fields is proposed. The calculated corrections make it possible to substantiate the Unruh effect from the point of view of the statistical approach, and to explicitly show its universality for various quantum field theories of massless and massive fields. The obtained results exactly coincide with the ones obtained earlier by calculation of the vacuum aver- age of energy-momentum tensor in a space with a conical singularity. Thus, the duality of two methods for describing an accelerated medium is substantiated. One may also speak about the emergence of geometry with conical singularity from thermodynamics. In particular, the polynomiality of the energy-momentum tensor and the absence of higher-order corrections in acceleration can be explicitly demonstrated.

Absence of higher order corrections to noncommutative Chern-Simons coupling

We analyze the structure of noncommutative pure Chern-Simons theory systematically in the axial gauge. We show that there is no IR/UV mixing in this theory in this gauge. In fact, we show, using the usual BRST identities as well as the identities following from vector supersymmetry, that this is a free theory. As a result, the tree level Chern-Simons coefficient is not renormalized. It also holds that the Chern-Simons coefficient is not modified at finite temperature. As a byproduct of our analysis, we prove that the ghosts completely decouple in the axial gauge in a noncommutative gauge theory.

Absence of higher order corrections to the non-Abelian topological mass term

We study the Yang-Mills-Chern-Simons theory systematically in an effort to generalize the Coleman-Hill result to the non-Abelian case. We show that, while the Chern-Simons coefficient is in general gauge dependent in a non-Abelian theory, it takes on a physical meaning in the axial gauge. Using the non-Abelian Ward identities as well as the analyticity of the amplitudes in the momentum variables, we show that, in the axial gauge, the Chern-Simons coefficient does not receive any quantum correction beyond one loop. This allows us to deduce that the ratio ${4\pi m\over g^{2}}$ is unrenormalized, in a non-Abelian theory, beyond one loop in any infrared safe gauge. This is the appropriate generalization of the Coleman-Hill result to non-Abelian theories. Various other interesting properties of the theory are also discussed.

Absence of higher order corrections to the non-Abelian Chern–Simons coefficient

We extend the Coleman–Hill analysis to non-Abelian Chern–Simons theories containing a tree level topological mass term. We show, in the case of a pure Yang–Mills–Chern–Simons theory, that there are no corrections to the coefficient of the Chern–Simons term beyond one loop in the axial gauge. Our arguments use constraints coming only from small gauge Ward identities as well as the analyticity of the amplitudes, much like the proof in the Abelian case. Some implications of this result are also discussed.

A simple proof of the non-renormalization of the Chern–Simons coupling

We give a very simple proof that the renormalization of the Chern–Simons coupling in the Wilsonian effective action is exhausted at one-loop. Our proof can apply to arbitrary 2+1-dimensional abelian as well as nonabelian gauge theories without a bare Chern–Simons coupling, including any non-renormalizable interactions and non-minimal couplings. Our proof reveals that small (but not large) gauge invariance is enough to ensure the absence of higher order corrections.

Absence of Higher-Order Corrections in the Anomalous Axial-Vector Divergence Equation

We consider two simple field-theoretic models, (a) spinor electrodynamics and (b) the $\ensuremath{\sigma}$ model with the Polkinghorne axial-vector current, and show in each case that the axial-vector current satisfies a simple anomalous divergence equation exactly to all orders of perturbation theory. We check our general argument by an explicit calculation to second order in radiative corrections. The general argument is made tractable by introducing a cutoff, but to check the validity of this artifice, the second-order calculation is carried out entirely in terms of renormalized vertex and propagator functions, in which no cutoff appears.