scholarly journals Eigenvalue spectrum and scaling dimension of lattice $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Georg Bergner ◽  
David Schaich
Keyword(s):  
Anomalous Dimension ◽  
Finite Lattice ◽  
Continuum Theory ◽  
Lattice Volume ◽  
Yang Mills ◽  
Lattice Regularization ◽  
Perturbative Renormalization ◽  
Zero Values ◽  
Definition Of ◽  
Group Flow

Abstract We investigate the lattice regularization of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory, by stochastically computing the eigenvalue mode number of the fermion operator. This provides important insight into the non-perturbative renormalization group flow of the lattice theory, through the definition of a scale-dependent effective mass anomalous dimension. While this anomalous dimension is expected to vanish in the conformal continuum theory, the finite lattice volume and lattice spacing generically lead to non-zero values, which we use to study the approach to the continuum limit. Our numerical results, comparing multiple lattice volumes, ’t Hooft couplings, and numbers of colors, confirm convergence towards the expected continuum result, while quantifying the increasing significance of lattice artifacts at larger couplings.

scholarly journals Counting Yang-Mills Instantons by Surface Operator Renormalization Group Flow

2021 ◽  
Vol 126 (23) ◽  
Author(s):  
Giulio Bonelli ◽  
Fran Globlek ◽  
Alessandro Tanzini
Keyword(s):  
Renormalization Group ◽  
Renormalization Group Flow ◽  
Yang Mills ◽  
Surface Operator ◽  
Group Flow

scholarly journals Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
L. Borsten ◽  
I. Jubb ◽  
V. Makwana ◽  
S. Nagy
Keyword(s):  
Homogeneous Spaces ◽  
Gauge Fields ◽  
Convolution Product ◽  
Tensor Fields ◽  
Einstein Universe ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Static Einstein Universe ◽  
Definition Of ◽  
Gauge Gravity

Abstract A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of ‘gravity = gauge × gauge’. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the ‘gauge × gauge’ convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

scholarly journals Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance

1994 ◽  
Vol 421 (2) ◽  
pp. 429-455 ◽  
Author(s):  
M. Bonini ◽  
M. D'Attanasio ◽  
G. Marchesini
Keyword(s):  
Renormalization Group ◽  
Gauge Invariance ◽  
Renormalization Group Flow ◽  
Yang Mills ◽  
Group Flow

scholarly journals Renormalon-free definition of the gluon condensate within the large-$\beta_0$ approximation

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
Hiroshi Suzuki ◽  
Hiromasa Takaura
Keyword(s):  
Operator Product Expansion ◽  
Density Operator ◽  
Gradient Flow ◽  
Gluon Condensate ◽  
Operator Product ◽  
Clear Definition ◽  
Lattice Data ◽  
Perturbative Calculation ◽  
Yang Mills ◽  
Definition Of

Abstract We propose a clear definition of the gluon condensate within the large-$\beta_0$ approximation as an attempt toward a systematic argument on the gluon condensate. We define the gluon condensate such that it is free from a renormalon uncertainty, consistent with the renormalization scale independence of each term of the operator product expansion (OPE), and an identical object irrespective of observables. The renormalon uncertainty of $\mathcal{O}(\Lambda^4)$, which renders the gluon condensate ambiguous, is separated from a perturbative calculation by using a recently suggested analytic formulation. The renormalon uncertainty is absorbed into the gluon condensate in the OPE, which makes the gluon condensate free from the renormalon uncertainty. As a result, we can define the OPE in a renormalon-free way. Based on this renormalon-free OPE formula, we discuss numerical extraction of the gluon condensate using the lattice data of the energy density operator defined by the Yang–Mills gradient flow.

scholarly journals Dirac operators with Lorentz scalar shell interactions

2018 ◽  
Vol 30 (05) ◽  
pp. 1850013 ◽  
Author(s):  
Markus Holzmann ◽  
Thomas Ourmières-Bonafos ◽  
Konstantin Pankrashkin
Keyword(s):  
Dirac Operator ◽  
Spectral Properties ◽  
Smooth Surface ◽  
Three Dimensional ◽  
The Self ◽  
Eigenvalue Asymptotics ◽  
Yang Mills ◽  
Lorentz Scalar ◽  
Definition Of ◽  
The Individual

This paper deals with the massive three-dimensional Dirac operator coupled with a Lorentz scalar shell interaction supported on a compact smooth surface. The rigorous definition of the operator involves suitable transmission conditions along the surface. After showing the self-adjointness of the resulting operator, we switch to the investigation of its spectral properties, in particular, to the existence and non-existence of eigenvalues. In the case of an attractive coupling, we study the eigenvalue asymptotics as the mass becomes large and show that the behavior of the individual eigenvalues and their total number are governed by an effective Schrödinger operator on the boundary with an external Yang–Mills potential and a curvature-induced potential.

scholarly journals The full four-loop cusp anomalous dimension in N$$ \mathcal{N} $$ = 4 super Yang-Mills and QCD

2020 ◽  
Vol 2020 (4) ◽  
Author(s):  
Johannes M. Henn ◽  
Gregory P. Korchemsky ◽  
Bernhard Mistlberger
Keyword(s):  
Anomalous Dimension ◽  
Yang Mills ◽  
Cusp Anomalous Dimension

scholarly journals 4D N = 1 SYM supercurrent on the lattice in terms of the gradient flow

2018 ◽  
Vol 175 ◽  
pp. 11014
Author(s):  
Kenji Hieda ◽  
Aya Kasai ◽  
Hiroki Makino ◽  
Hiroshi Suzuki
Keyword(s):  
Gradient Flow ◽  
Independent Manner ◽  
Yang Mills ◽  
Loop Level ◽  
Lattice Regularization ◽  
The One ◽  
Noether Current ◽  
Super Yang Mills Theory

The gradient flow [1–5] gives rise to a versatile method to construct renor-malized composite operators in a regularization-independent manner. By adopting this method, the authors of Refs. [6–9] obtained the expression of Noether currents on the lattice in the cases where the associated symmetries are broken by lattice regularization. We apply the same method to the Noether current associated with supersymmetry, i.e., the supercurrent. We consider the 4D N = 1 super Yang–Mills theory and calculate the renormalized supercurrent in the one-loop level in the Wess–Zumino gauge. We then re-express this supercurrent in terms of the flowed gauge and flowed gaugino fields [10].

scholarly journals Classical phase space and Hadamard states in the BRST formalism for gauge field theories on curved spacetime

2017 ◽  
Vol 29 (04) ◽  
pp. 1750014 ◽  
Author(s):  
Michał Wrochna ◽  
Jochen Zahn
Keyword(s):  
Phase Space ◽  
Cauchy Surface ◽  
Gauge Field Theories ◽  
Subsidiary Condition ◽  
Yang Mills ◽  
Special Cases ◽  
Hadamard States ◽  
Hyperbolic Spacetimes ◽  
Definition Of ◽  
Classical Phase Space

We investigate linearized gauge theories on globally hyperbolic spacetimes in the BRST formalism. A consistent definition of the classical phase space and of its Cauchy surface analogue is proposed. We prove that it is isomorphic to the phase space in the ‘subsidiary condition’ approach of Hack and Schenkel in the case of Maxwell, Yang–Mills, and Rarita–Schwinger fields. Defining Hadamard states in the BRST formalism in a standard way, their existence in the Maxwell and Yang–Mills case is concluded from known results in the subsidiary condition (or Gupta–Bleuler) formalism. Within our framework, we also formulate criteria for non-degeneracy of the phase space in terms of BRST cohomology and discuss special cases. These include an example in the Yang–Mills case, where degeneracy is not related to a non-trivial topology of the Cauchy surface.

On finite lattices of degrees of constructibility of reals

1976 ◽  
Vol 41 (2) ◽  
pp. 313-322 ◽  
Author(s):  
Zofia Adamowicz
Keyword(s):  
Standard Model ◽  
Finite Lattice ◽  
Partial Ordering ◽  
Turing Degrees ◽  
Upper Semilattice ◽  
Finite Lattices ◽  
Definition Of ◽  
The Universe

Theorem. Assume that there exists a standard model of ZFC + V = L. Then there is a model of ZFC in which the partial ordering of the degrees of constructibility of reals is isomorphic with a given finite lattice.The proof of the theorem uses forcing. The definition of the forcing conditions and the proofs of some of the lemmas are connected with Lerman's paper on initial segments of the upper semilattice of the Turing degrees [2]. As an auxiliary notion we shall introduce the notion of a sequential representation of a lattice, which slightly differs from Lerman's representation.Let K be a given finite lattice. Assume that the universe of K is an integer l. Let ≤K be the ordering in K. A sequential representation of K is a sequence Ui ⊆ Ui+1 of finite subsets of ωi such that the following holds:(1) For any s, s′ Є Ui, i Є ω, k, m Є l, k ≤Km & s(m) = s′(m) → s(k) = s′(k).(2) For any s Є Ui, i Є ω, s(0) = 0 where 0 is the least element of K.(3) For any s, s′ Є i Є ω, k,j Є l, if k y Kj = m and s(k) = s′(k) & s(j) = s′(j) → s(m) = s′(m), where vK denotes the join in K.

scholarly journals SUPERSYMMETRIC YANG–MILLS THEORIES WITH EXACT SUPERSYMMETRY ON THE LATTICE

2011 ◽  
Vol 26 (30n31) ◽  
pp. 5057-5132 ◽  
Author(s):  
ANOSH JOSEPH
Keyword(s):  
Field Theory ◽  
Euclidean Space ◽  
Topological Field Theory ◽  
Strongly Coupled ◽  
Dimensional Lattice ◽  
Yang Mills ◽  
Gravitational Theories ◽  
Topological Field ◽  
Perturbative Renormalization ◽  
The One

Inspired by the ideas from topological field theory it is possible to rewrite the supersymmetric charges of certain classes of extended supersymmetric Yang–Mills (SYM) theories in such a way that they are compatible with the discretization on a Euclidean space–time lattice. Such theories are known as maximally twisted SYM theories. In this review we discuss the construction and some applications of such classes of theories. The one-loop perturbative renormalization of the four-dimensional lattice [Formula: see text] SYM is discussed in particular. The lattice theories constructed using twisted approach play an important role in investigating the thermal phases of strongly coupled SYM theories and also the thermodynamic properties of their dual gravitational theories.

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