Related papers: The One-Loop QCD $\beta$-Function as an Index
At the end of 2016, we computed the five-loop (N$^4$LO) contributions to the beta function in perturbative Quantum Chromodynamics (QCD), its generalization to non-Abelian gauge theories with a simple compact Lie group, and for Quantum…
We show how curing an anomaly of the twistor uplift of self-dual Yang-Mills theory implies linear relations among one-loop, $n$-gluon, color-ordered subamplitudes in QCD, when all $n$ gluon helicities are positive, or when exactly one is…
This paper presents, by example, an index theory appropriate to algebras without trace. Whilst we work exclusively with the Cuntz algebras the exposition is designed to indicate how to develop a general theory. Our main result is an index…
We show how the gauge invariant formulation of QCD in terms of loops is free from a hidden $\theta$ parameter and offers an alternative way to solve the $U(1)_A$ puzzle.
We propose a new formula that extracts the quantum Hall conductance from a single (2+1)D gapped wavefunction. The formula applies to general many-body systems that conserve particle number, and is based on the concept of modular flow: i.e.,…
The effective potentials for massless scalar and vector quantum field theories on D dimensional manifolds with p compact noncommutative extra dimensions are evaluated by means of dimensional regularization implemented by zeta function…
The one-loop effective potential in $2D$ dilaton gravity in conformal gauge on the topologically non-trivial plane $\reals \times S^1$ and on the hyperbolic plane $H^2/\Gamma$ is calculated. For arbitrary choice of the tree scalar potential…
A new scheme for the numerical evaluation of the one-loop self-energy correction to all orders in Z \alpha is presented. The scheme proposed inherits the attractive features of the standard potential-expansion method but yields a…
This paper studies the one-loop effective action for Euclidean Maxwell theory about flat four-space bounded by one three-sphere, or two concentric three-spheres. The analysis relies on Faddeev-Popov formalism and $\zeta$-function…
A univalent meromorphic function defined on $\Delta:= \{z \in \mathbb{C}: 1<|z|<\infty \}$ with univalent inverse defined on $\Delta$ is bi-univalent meromorphic in $\Delta$. For certain subclasses of meromorphic bi-univalent functions,…
The one loop vertex in QED is calculated in arbitrary covariant gauges as an analytic function of its momenta. The vertex is decomposed into a longitudinal part, that is fully responsible for ensuring the Ward and Ward-Takahashi identities…
We introduce a method to obtain the analytic solution of the higher-order Baxter equation for twist-two and twist-three operators of planar N=4 SYM. Our result proofs the conjectured formula for the three-loop anomalous dimension of…
Index theory revealed its outstanding role in the study of periodic orbits of Hamiltonian systems and the dynamical consequences of this theory are enormous. Although the index theory in the periodic case is well-established, very few…
In the present work we study the two-point correlation function $R(\epsilon)$ of the quantum mechanical spectrum of a classically chaotic system. Recently this quantity has been computed for chaotic and for disordered systems using periodic…
It is shown how the QED concept of a gauge-, scale- and scheme-independent one-loop effective charge can be extended directly at the diagrammatic level to QCD, thus justifying explicitly the ``naive non-abelianization'' prescription used in…
We study the dependence of beta-function on running coupling constant in holographic models supported by Einstein-dilaton-Maxwell action for light and heavy quarks. Although, in the previous paper [arXiv:2402.14512], we considered different…
We evaluate the one-loop prefactor in the false vacuum decay rate in a theory of a self interacting scalar field in 3+1 dimensions. We use a numerical method, established some time ago, which is based on a well-known theorem on functional…
For $\cal N =$ 1 supersymmetric theories with multiple gauge couplings regularized by higher covariant derivatives, a general expression for three-loop gauge $\beta$-functions is obtained. For this purpose, using general statements about…
We present four-loop results for the gauge beta-function and the fermion mass anomalous dimension for a gauge theory with a general gauge group and a multiplet of fermions transforming according to an arbitrary representation, calculated…
We determine the three-loop $\overline{\text{MS}}$ quartic $ \beta $-function for the most general renormalisable four-dimensional theories. A general parametrization of the $ \beta $-function is compared to known $ \beta $-functions for…