Search results for "Euclidean"

RG flows of Quantum Einstein Gravity in the linear-geometric approximation

2014

We construct a novel Wetterich-type functional renormalization group equation for gravity which encodes the gravitational degrees of freedom in terms of gauge-invariant fluctuation fields. Applying a linear-geometric approximation the structure of the new flow equation is considerably simpler than the standard Quantum Einstein Gravity construction since only transverse-traceless and trace part of the metric fluctuations propagate in loops. The geometric flow reproduces the phase-diagram of the Einstein-Hilbert truncation including the non-Gaussian fixed point essential for Asymptotic Safety. Extending the analysis to the polynomial $f(R)$-approximation establishes that this fixed point come…

Measure dependence of 2D simplicial quantum gravity

1995

We study pure 2D Euclidean quantum gravity with $R^2$ interaction on spherical lattices, employing Regge's formulation. We attempt to measure the string susceptibility exponent $\gamma_{\rm str}$ by using a finite-size scaling Ansatz in the expectation value of $R^2$. To check on effects of the path integral measure we investigate two scale invariant measures, the "computer" measure $dl/l$ and the Misner measure $dl/\sqrt A$.

Non-perturbative renormalization of lattice operators in coordinate space

2004

We present the first numerical implementation of a non-perturbative renormalization method for lattice operators, based on the study of correlation functions in coordinate space at short Euclidean distance. The method is applied to compute the renormalization constants of bilinear quark operators for the non-perturbative O(a)-improved Wilson action in the quenched approximation. The matching with perturbative schemes, such as MS-bar, is computed at the next-to-leading order in continuum perturbation theory. A feasibility study of this technique with Neuberger fermions is also presented.

Electromagnetic Corrections for Pions and Kaons : Masses and Polarizabilities

1996

The unknown constants in Chiral Perturbation Theory needed for an all orders analysis of the polarizabilities and electromagnetic corrections to the masses of the pseudo-Goldstone bosons are estimated at leading order in $1/N_c$. We organize the calculation in an $1/N_c$-expansion and separate long- and short-distance physics contributions by introducing an Euclidean cut-off. The long-distance part is evaluated using the ENJL model and the short-distance part using perturbative QCD and factorization. We obtain very good matching between both. We then include these estimates in a full Chiral Perturbation Theory calculation to order $e^2$ $p^2$ for the masses and $p^6$ for the polarizabilitie…

A field theoretic realization of a universal bundle for gravity

1992

Abstract Based upon a local vector supersymmetry algebra, we discuss the general structure of the quantum action for topological gravity theories in arbitrary dimensions. The precise form of the action depends on the particular dimension, and also on the moduli space of interest. We describe the general features by examining a theory of topological gravity in two dimensions, with a moduli space specified by vanishing curvature two-form. It is shown that these topological gravity models together with their observables provide a field theoretic realization of a universal bundle for gravity.

An estimate for the thermal photon rate from lattice QCD

2017

We estimate the production rate of photons by the quark-gluon plasma in lattice QCD. We propose a new correlation function which provides better control over the systematic uncertainty in estimating the photon production rate at photon momenta in the range {\pi}T/2 to 2{\pi}T. The relevant Euclidean vector current correlation functions are computed with $N_{\mathrm f}$ = 2 Wilson clover fermions in the chirally-symmetric phase. In order to estimate the photon rate, an ill-posed problem for the vector-channel spectral function must be regularized. We use both a direct model for the spectral function and a model-independent estimate from the Backus-Gilbert method to give an estimate for the p…

The Non-Abelian Vector Gauge Particle ρ

2020

So far we have shown how pion self-interaction and pion-mass generation are tied together. This phenomenon, a result of the three-dimensional non-linear realization of the triplet isotopic pion field, is a consequence of a dimensional reduction from four-dimensional Euclidean space to a three-dimensional curved isotopic space with positive curvature, i.e., by way of chiral-symmetry breaking and subsequent pionic mass generation in a curved isotopic spin background with K = λ2, λ = 2f0∕mπ, which is taken from low-energy π − N interaction.

Quantum Einstein Gravity: Towards an Asymptotically Safe Field Theory of Gravity

2007

Real and Complex Singularities

2016

In this paper a Minkowski analogue of the Euclidean medial axis of a closed and smooth plane curve is introduced. Its generic local configurations are studied and the types of shocks that occur on these are also determined.

Analytic Continuation of the Kite Family

2019

We consider results for the master integrals of the kite family, given in terms of ELi-functions which are power series in the nome q of an elliptic curve. The analytic continuation of these results beyond the Euclidean region is reduced to the analytic continuation of the two period integrals which define q. We discuss the solution to the latter problem from the perspective of the Picard–Lefschetz formula.