From confinement to adjoint zero-modes

Pérez, Margarita Garcı́a; González-Arroyo, Antonio; Sastre, Alfonso

doi:10.48550/arxiv.1003.5022

Cited by 2 publications

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“…[68]. In this context, the semiclassical picture based on the less standard case of fractional instantons follows the ideas put forward by González-Arroyo and collaborators in a series of works [69,70,71,72,73], see also [74,75,76].…”

Section: Semiclassical Picturementioning

confidence: 97%

Memory efficient finite volume schemes with twisted boundary conditions

et al. 2021

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In this paper we explore a finite volume renormalization scheme that combines three main ingredients: a coupling based on the gradient flow, the use of twisted boundary conditions and a particular asymmetric geometry, that for SU(N) gauge theories consists on a hypercubic box of size $$l^2 \times (Nl)^2$$ l 2 × ( N l ) 2 , a choice motivated by the study of volume independence in large N gauge theories. We argue that this scheme has several advantages that make it particularly suited for precision determinations of the strong coupling, among them translational invariance, an analytic expansion in the coupling and a reduced memory footprint with respect to standard simulations on symmetric lattices, allowing for a more efficient use of current GPU clusters. We test this scheme numerically with a determination of the $$\Lambda $$ Λ parameter in the SU(3) pure gauge theory. We show that the use of an asymmetric geometry has no significant impact in the size of scaling violations, obtaining a value $$\Lambda _{\overline{\mathrm{MS}}}\sqrt{8 t_0} =0.603(17)$$ Λ MS ¯ 8 t 0 = 0.603 ( 17 ) in good agreement with the existing literature. The role of topology freezing, that is relevant for the determination of the coupling in this particular scheme and for large N applications, is discussed in detail.

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Section: Semiclassical Picturementioning

confidence: 97%

Memory efficient finite volume schemes with twisted boundary conditions

et al. 2021

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“…This program had some appealing features, and a number of difficulties, see Ref. [29] for an assessment. Despite that, it is clear that these works carry merit, and are underappreciated.…”

Section: Introductionmentioning

confidence: 99%

Strongly coupled QFT dynamics via TQFT coupling

Ünsal

2020

Preprint

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We consider a class of quantum field theories and quantum mechanics, which we couple to Z N topological QFTs, in order to classify non-perturbative effects in the original theory. The Z N TQFT structure arises naturally from turning on a classical background field for a Z N 0-or 1-form global symmetry. In SU (N ) Yang-Mills theory coupled to Z N TQFT, the non-perturbative expansion parameter is exp[−S I /N ] = exp[−8π 2 /g 2 N ] both in the semiclassical weak coupling domain and strong coupling domain, corresponding to a fractional topological charge configurations. To classify the non-perturbative effects in original SU (N ) theory, we must use P SU (N ) bundle and lift configurations (critical points at infinity) for which there is no obstruction back to SU (N ). These provide a refinement of instanton sums: integer topological charge, but crucially fractional action configurations contribute, providing a TQFT protected generalization of resurgent semi-classical expansion to strong coupling. Monopole-instantons (or fractional instantons) on T 3 × S 1 L can be interpreted as tunneling events in the 't Hooft flux background in the P SU (N ) bundle. The construction provides a new perspective to the strong coupling regime of QFTs and resolves a number of old standing issues, especially, fixes the conflicts between the large-N and instanton analysis. We derive the mass gap at θ = 0 and gaplessness at θ = π in CP 1 model, and mass gap for arbitrary θ in CP N −1 , N ≥ 3 on R 2 .

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From confinement to adjoint zero-modes

Cited by 2 publications

References 0 publications

Memory efficient finite volume schemes with twisted boundary conditions

Memory efficient finite volume schemes with twisted boundary conditions

Strongly coupled QFT dynamics via TQFT coupling

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