scholarly journals Gradient flow representation of the four-dimensional $\mathcal{N}=2$ super Yang–Mills supercurrent

2018 ◽  
Vol 2018 (11) ◽  
Author(s):  
Aya Kasai ◽  
Okuto Morikawa ◽  
Hiroshi Suzuki
Keyword(s):  
Gradient Flow ◽  
Yang Mills

scholarly journals Phase structure of N=1 super Yang-Mills theory from the gradient flow

2019 ◽  
Author(s):  
Camilo Lopez ◽  
Georg Bergner ◽  
Stefano Piemonte
Keyword(s):  
Phase Structure ◽  
Gradient Flow ◽  
Yang Mills ◽  
Super Yang Mills Theory

scholarly journals Linear confinement and stress-energy tensor around static quark and anti-quark pair -- Lattice simulation with Yang-Mills gradient flow --

2019 ◽  
Author(s):  
Ryosuke Yanagihara ◽  
Takumi Iritani ◽  
Masakiyo Kitazawa ◽  
Masayuki Asakawa ◽  
Tetsuo Hatsuda ◽  
...  
Keyword(s):  
Gradient Flow ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Lattice Simulation ◽  
Yang Mills ◽  
Stress Energy ◽  
Static Quark

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 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 Space-time symmetries and the Yang-Mills gradient flow

2013 ◽  
Vol 2013 (11) ◽  
Author(s):  
L. Del Debbio ◽  
A. Patella ◽  
A. Rago
Keyword(s):  
Gradient Flow ◽  
Space Time ◽  
Yang Mills

scholarly journals Convergence of the Yang–Mills–Higgs flow on Gauged Holomorphic maps and applications

2018 ◽  
Vol 29 (04) ◽  
pp. 1850024
Author(s):  
Samuel Trautwein
Keyword(s):  
Uniqueness Theorem ◽  
Gradient Flow ◽  
Holomorphic Section ◽  
Holomorphic Maps ◽  
Yang Mills ◽  
Stable Case ◽  
Finite Dimensional ◽  
Closed Riemann Surface ◽  
The Moment ◽  
Negative Gradient

The symplectic vortex equations admit a variational description as global minimum of the Yang–Mills–Higgs functional. We study its negative gradient flow on holomorphic pairs [Formula: see text] where [Formula: see text] is a connection on a principal [Formula: see text]-bundle [Formula: see text] over a closed Riemann surface [Formula: see text] and [Formula: see text] is an equivariant map into a Kähler Hamiltonian [Formula: see text]-manifold. The connection [Formula: see text] induces a holomorphic structure on the Kähler fibration [Formula: see text] and we require that [Formula: see text] descends to a holomorphic section of this fibration. We prove a Łojasiewicz type gradient inequality and show uniform convergence of the negative gradient flow in the [Formula: see text]-topology when [Formula: see text] is equivariantly convex at infinity with proper moment map, [Formula: see text] is holomorphically aspherical and its Kähler metric is analytic. As applications we establish several results inspired by finite dimensional GIT: First, we prove a certain uniqueness property for the critical points of the Yang–Mills–Higgs functional which is the analogue of the Ness uniqueness theorem. Second, we extend Mundet’s Kobayashi–Hitchin correspondence to the polystable and semistable case. The arguments for the polystable case lead to a new proof in the stable case. Third, in proving the semistable correspondence, we establish the moment–weight inequality for the vortex equation and prove the analogue of the Kempf existence and uniqueness theorem.

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