Topological Susceptibility under Gradient Flow

Mejía-Díaz, Héctor; Cichy, Krzysztof; Dromard, Arthur; Gerber, Urs; Sandoval, Ilya Orson; Bietenholz, Wolfgang; Forcrand, Philippe de

doi:10.1051/epjconf/201817511024

Cited by 3 publications

(3 citation statements)

References 27 publications

(38 reference statements)

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“…Spin diffusion along the t-channel 23 can be viewed as being mediated by reggeon exchange (corresponding to the η 0 ) in the isosinglet sector. At large x B , g 1 can be computed using lattice QCD methods [24][25][26][27][28][29]68]. However at small x B , particularly in Regge asymptotics, lattice computations are challenging due to the difficulties posed by i) computing higher moments of local operators, ii) boosting the proton to high energies on the lattice [69].…”

Section: Axion-like Action At Small Xb: Gluon Saturation and Sphalero...mentioning

confidence: 99%

“…In the Bjorken limit, as we will discuss briefly, the formalism of Shore and Veneziano goes through for g 1 (x B , Q 2 ), precisely as for its first moment Σ(Q 2 ). The corresponding matrix element can be computed on the lattice similarly to prior lattice computations [24][25][26][27]. For discussions of how to extract Σ(Q 2 ) directly from the slope (with t) of the topological susceptibility, see [28]; a recent review of lattice extractions of the topological susceptibility can be found in [29].…”

Section: Introductionmentioning

confidence: 99%

“…The color sources ρ are static on the relevant time scales 25. The evolution equation for W Y [ρ] satisfies the Kossakowski-Lindblad form of the density matrix for open quantum systems[86] 26. One must understand E ≡ E(ρ) and B ≡ B(ρ) in the Hamiltonian employed in that derivation.…”

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confidence: 99%

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The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics

Tarasov,

Venugopalan

2021

Preprint

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In [1], we demonstrated that structure function g1(xB, Q 2 ) measured in polarized deeply inelastic scattering (DIS) is dominated by the triangle anomaly in both Bjorken (Q 2 → 0) and Regge (xB → 0) asymptotics. In the worldline formulation of quantum field theory, the triangle anomaly arises from the imaginary part of the worldline effective action. We show explicitly how a Wess-Zumino-Witten term coupling the topological charge density to a primordial isosinglet η arises in this framework. We demonstrate the fundamental role played by this contribution both in topological mass generation of the η and in the cancellation of the off-forward pole arising from the triangle anomaly in the proton's helicity Σ(Q 2 ). We recover the striking result by Shore and Veneziano that Σ ∝ χ (0), where χ is the slope of the QCD topological susceptibility in the forward limit. We construct an axion-like effective action for g1 at small xB that describes the interplay between gluon saturation and the topology of the QCD vacuum. In particular, we outline the role of "over-thebarrier" sphaleron-like transitions in spin diffusion at small xB. Such topological transitions can be measured in polarized DIS at a future Electron-Ion Collider., with the ≈ sign denoting that a term needs to be added on the l.h.s corresponding to a linear combination of the isotriplet and isooctet axial vector charges of the proton. These contributions are weakly dependent on Q 2 and we will ignore them henceforth to focus on isosinglet contributions to g 1 (x B , Q 2 ).

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Section: Axion-like Action At Small Xb: Gluon Saturation and Sphalero...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics

Tarasov,

Venugopalan

2021

Preprint

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Role of the chiral anomaly in polarized deeply inelastic scattering. II. Topological screening and transitions from emergent axionlike dynamics

Tarasov

Venugopalan

2022

Phys. Rev. D

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Topological susceptibility of the 2D O(3) model under gradient flow

et al. 2018

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The 2d O(3) model is widely used as a toy model for ferromagnetism and for Quantum Chromodynamics. With the latter it shares -among other basic aspects -the property that the continuum functional integral splits into topological sectors. Topology can also be defined in its lattice regularised version, but semi-classical arguments suggest that the topological susceptibility χ t does not scale towards a finite continuum limit. Previous numerical studies confirmed that the quantity χ t ξ 2 diverges at large correlation length ξ. Here we investigate the question whether or not this divergence persists when the configurations are smoothened by the Gradient Flow (GF). The GF destroys part of the topological windings; on fine lattices this strongly reduces χ t . However, even when the flow time is so long that the GF impact range -or smoothing radius -attains ξ/2, we still do not observe evidence of continuum scaling.

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Topological Susceptibility under Gradient Flow

Cited by 3 publications

References 27 publications

The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics

The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics

Role of the chiral anomaly in polarized deeply inelastic scattering. II. Topological screening and transitions from emergent axionlike dynamics

Topological susceptibility of the 2D O(3) model under gradient flow

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