Related papers: Perturbative and non-pertrubative trace anomalies

We study certain aspects of the recently proposed notion of nonrelativistic diffeomorphism invariance. In particular, we consider specific examples of invariant actions, extended gauge symmetry as well as an application to the theory of…

Let $H, V$ be self-adjoint operators such that $V$ belongs to the weak trace class ideal. We prove higher order perturbation formula $$\tau\big(f(H+V)-\sum_{j=0}^{n-1}\frac{1}{j!}\frac{d^j}{dt^j} f(H+tV)\big|_{t=0}\big)=\int_{\mathbb{R}}…

Perturbative calculations involving fermion loops in quantum field theories require tracing over Dirac matrices. A simple way to regulate the divergences that generically appear in these calculations is dimensional regularisation, which has…

We review the parity anomaly of the massless Dirac fermion in $2+1$ dimensions from the Hamiltonian, as opposed to the path integral, point of view. We have two main goals for this note. First, we hope to make the parity anomaly more…

Conformal defects -- extended objects in conformal field theories -- carry localised excitations inherited from symmetry currents, known as the displacements and tilts. They capture the linear response of the defect to deformations of its…

Diffractive systems are quantum-mechanical models with point-like singularities where usual semiclassical approximation breaks down. An overview of recent investigations of such systems is presented. The following examples are considered in…

A recent construction of the electroweak theory, based on perturbative quantum gauge invariance alone, is extended to the case of more generations of fermions with arbitrary mixing. The conditions implied by second order gauge invariance…

We consider the transport of passive admixture in locally homogeneous isotropic reflectionally noninvariant turbulence of incompressible fluid. It is shown that anomalous convective flow appears which direction does not coincide with that…

Integrating over a continuum Majorana fermion formally yields a functional pfaffian. We show that the phase of this pfaffian is ambiguous, as it depends on the choice of basis. This ambiguity is naturally resolved within a non-perturbative…

We evaluate the axial anomaly for the general Ginsparg-Wilson fermion operator $D = D_c (\Id + R D_c)^{-1}$ with $R = r \Id$. For any chirally symmetric $D_c$ which in the free fermion limit, is free of species doubling and behaves like $i…

We derive explicit anomaly-index formulas for four-dimensional Weyl fermions charged under the finite symmetries $\mathrm{Spin}\times\mathbb Z_n$ and $\mathrm{Spin}\times_{\mathbb Z_2^{\mathrm F}}\mathbb Z_{2m}^{\mathrm F}$. The strategy is…

We study a series of the Wess-Zumino actions obtained by repeatedly integrating conformal anomalies with respect to the conformal-factor field that appear at higher loops. We show that they arise as physical quantities required to make…

Torsion can be realized as dislocation in the crystal lattice of material. It is particularly interesting if the material has fermions in the spectrum, such as graphene, topological insulators, Dirac and Weyl semimetals, as it's transport…

We consider theories with gauged chiral fermions in which there are abelian anomalies, and no nonabelian anomalies (but there may be nonabelian gauge fields present). We construct an associated theory that is gauge invariant,…

Networks (graphs) in psychology are often restricted to settings without interventions. Here we consider a framework borrowed from biology that involves multiple interventions from different contexts (observations and experiments) in a…

For a four dimensional, unitary, diffeomorphism- and scale invariant quantum field theory without higher derivatives and a well defined scale current we argue that scale invariance implies conformal invariance. The proof relies on the…

Using trace anomalies, we determine the vacuum stress tensors of arbitrary even dimensional conformal field theories in Weyl flat backgrounds. We demonstrate a simple relation between the Casimir energy on the real line times a sphere and…

Anomalous diffusion processes pose a unique challenge in classification and characterization. Previously (Mangalam et al., 2023, Physical Review Research 5, 023144), we established a framework for understanding anomalous diffusion using…

The consideration of quantum fields defined on a spacetime lattice provides computational techniques which are invaluable for studying gauge theories nonperturbatively from first principles. Perturbation theory is an essential aspect of…

We review briefly some well known facts about trace anomaly and then concentrate on its 'infrared' manifestation. Among other things we show by means of dispersion relations that dilatations and translations are conflicting symmetries. We…