Nonperturbative quantization ‘a la Heisenberg for non-Abelian gauge theories: two-equation approximation. Applications: a flux tube solution and a scalar model of glueball

Geometry and Quantum Dynamics

10.1093/oso/9780198788393.003.0014 ◽

2017 ◽

Author(s):

Laurent Baulieu ◽

John Iliopoulos ◽

Roland Sénéor

Keyword(s):

General Relativity ◽

Quantum Dynamics ◽

Gauge Theories ◽

Brst Symmetry ◽

Abelian Gauge ◽

Yang Mills ◽

History Of ◽

Brst Invariance

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.

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Cwebs beyond three loops in multiparton amplitudes

Journal of High Energy Physics ◽

10.1007/jhep03(2021)188 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Neelima Agarwal ◽

Lorenzo Magnea ◽

Sourav Pal ◽

Anurag Tripathi

Keyword(s):

Gauge Theories ◽

Anomalous Dimension ◽

Wilson Line ◽

Building Blocks ◽

Feynman Diagrams ◽

Loop Order ◽

Abelian Gauge ◽

Sum Rule ◽

Combinatorial Properties ◽

Low Dimensional

Abstract Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, and we computed the mixing matrices for all Cwebs connecting four or five Wilson lines at four loops. Here we complete the evaluation of four-loop mixing matrices, presenting the results for all Cwebs connecting two and three Wilson lines. We observe that the conjuctured column sum rule is obeyed by all the mixing matrices that appear at four-loops. We also show how low-dimensional mixing matrices can be uniquely determined from their known combinatorial properties, and provide some all-order results for selected classes of mixing matrices. Our results complete the required colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.

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Covariant phase space and soft factorization in non-Abelian gauge theories

Journal of High Energy Physics ◽

10.1007/jhep03(2021)015 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Temple He ◽

Prahar Mitra

Keyword(s):

Phase Space ◽

Ward Identity ◽

Gauge Theories ◽

Minkowski Spacetime ◽

Soft Gluon ◽

Careful Study ◽

Abelian Gauge ◽

Gauge Sector ◽

Vacuum States ◽

The One

Abstract We perform a careful study of the infrared sector of massless non-abelian gauge theories in four-dimensional Minkowski spacetime using the covariant phase space formalism, taking into account the boundary contributions arising from the gauge sector of the theory. Upon quantization, we show that the boundary contributions lead to an infinite degeneracy of the vacua. The Hilbert space of the vacuum sector is not only shown to be remarkably simple, but also universal. We derive a Ward identity that relates the n-point amplitude between two generic in- and out-vacuum states to the one computed in standard QFT. In addition, we demonstrate that the familiar single soft gluon theorem and multiple consecutive soft gluon theorem are consequences of the Ward identity.

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Effective String Description of the Confining Flux Tube at Finite Temperature

Universe ◽

10.3390/universe7060170 ◽

2021 ◽

Vol 7 (6) ◽

pp. 170

Author(s):

Michele Caselle

Keyword(s):

Flux Tube ◽

Dimensional Reduction ◽

Conformal Invariance ◽

Finite Temperature ◽

Gauge Theories ◽

Linear Increase ◽

General Introduction ◽

Interquark Potential ◽

Effective String Theory ◽

Good Agreement

In this review, after a general introduction to the effective string theory (EST) description of confinement in pure gauge theories, we discuss the behaviour of EST as the temperature is increased. We show that, as the deconfinement point is approached from below, several universal features of confining gauge theories, like the ratio Tc/σ0, the linear increase of the squared width of the flux tube with the interquark distance, or the temperature dependence of the interquark potential, can be accurately predicted by the effective string. Moreover, in the vicinity of the deconfinement point the EST behaviour turns out to be in good agreement with what was predicted by conformal invariance or by dimensional reduction, thus further supporting the validity of an EST approach to confinement.

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