scholarly journals On the infrared behaviour of QCD Green functions in the Maximally Abelian gauge

2012 ◽  
Author(s):  
Reinhard Alkofer ◽  
Markus Huber ◽  
Valentin Mader ◽  
Andreas Windisch
Keyword(s):  
Green Functions ◽  
Abelian Gauge ◽  
Infrared Behaviour

scholarly journals The Infrared Behaviour of the Pure Yang–Mills Green Functions

2012 ◽  
Vol 53 (3-4) ◽  
pp. 387-436 ◽  
Author(s):  
Ph. Boucaud ◽  
J. P. Leroy ◽  
A. Le Yaouanc ◽  
J. Micheli ◽  
O. Pène ◽  
...  
Keyword(s):  
Green Functions ◽  
Yang Mills ◽  
Infrared Behaviour

LOCALIZATION OF NONLOCAL LAGRANGIANS AND MASS GENERATION FOR NON-ABELIAN GAUGE FIELDS

2008 ◽  
Vol 23 (26) ◽  
pp. 4289-4313
Author(s):  
ALEXEY SEVOSTYANOV
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Gauge Fields ◽  
Green Functions ◽  
Coupling Constant ◽  
Mass Generation ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Three Dimensional Space

We introduce and study the four-dimensional analogue of a mass generation mechanism for non-Abelian gauge fields suggested in the paper, Phys. Lett. B403, 297 (1997), in the case of three-dimensional space–time. The construction of the corresponding quantized theory is based on the fact that some nonlocal actions may generate local expressions for Green functions. An example of such a theory is the ordinary Yang–Mills field where the contribution of the Faddeev–Popov determinant to the Green functions can be made local by introducing additional ghost fields. We show that the quantized Hamiltonian for our theory unitarily acts in a Hilbert space of states and prove that the theory is renormalizable to all orders of perturbation theory. One-loop coupling constant and mass renormalizations are also calculated.

SLAVNOV–TAYLOR IDENTITIES

2010 ◽  
Vol 25 (05) ◽  
pp. 903-907
Author(s):  
ANDREI A. SLAVNOV
Keyword(s):  
Quantum Theory ◽  
Gauge Invariance ◽  
Gauge Fields ◽  
Green Functions ◽  
Abelian Gauge ◽  
Slavnov Taylor Identities

Slavnov–Taylor identities: relations between Green functions, which provide the gauge invariance of the quantum theory including non-Abelian gauge fields.

Geometry and Quantum Dynamics

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.

scholarly journals Non-Abelian generalizations of the Hofstadter model: spin–orbit-coupled butterfly pairs

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Yi Yang ◽  
Bo Zhen ◽  
John D. Joannopoulos ◽  
Marin Soljačić
Keyword(s):  
Quantum Hall ◽  
Building Blocks ◽  
Real Space ◽  
Gauge Fields ◽  
Spin Orbit ◽  
Abelian Gauge ◽  
Experimental Realization ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum ◽  
Necessary And Sufficient

Abstract The Hofstadter model, well known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum Hall effect. Inspired by the real-space building blocks of non-Abelian gauge fields from a recent experiment, we introduce and theoretically study two non-Abelian generalizations of the Hofstadter model. Each model describes two pairs of Hofstadter butterflies that are spin–orbit coupled. In contrast to the original Hofstadter model that can be equivalently studied in the Landau and symmetric gauges, the corresponding non-Abelian generalizations exhibit distinct spectra due to the non-commutativity of the gauge fields. We derive the genuine (necessary and sufficient) non-Abelian condition for the two models from the commutativity of their arbitrary loop operators. At zero energy, the models are gapless and host Weyl and Dirac points protected by internal and crystalline symmetries. Double (8-fold), triple (12-fold), and quadrupole (16-fold) Dirac points also emerge, especially under equal hopping phases of the non-Abelian potentials. At other fillings, the gapped phases of the models give rise to topological insulators. We conclude by discussing possible schemes for experimental realization of the models on photonic platforms.

scholarly journals Cwebs beyond three loops in multiparton amplitudes

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.

scholarly journals Bulk-Boundary Correspondence for Non-Hermitian Hamiltonians via Green Functions

2021 ◽  
Vol 126 (21) ◽  
Author(s):  
Heinrich-Gregor Zirnstein ◽  
Gil Refael ◽  
Bernd Rosenow
Keyword(s):  
Green Functions ◽  
Boundary Correspondence

scholarly journals Exploring the landscape of CHL strings on Td

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Anamaría Font ◽  
Bernardo Fraiman ◽  
Mariana Graña ◽  
Carmen A. Núñez ◽  
Héctor Parra De Freitas
Keyword(s):  
Gauge Group ◽  
Moduli Space ◽  
Dynkin Diagram ◽  
Fundamental Groups ◽  
Computer Algorithms ◽  
Abelian Gauge ◽  
Reduced Rank ◽  
Systematic Exploration ◽  
String Models ◽  
Simply Connected

Abstract Compactifications of the heterotic string on special Td/ℤ2 orbifolds realize a landscape of string models with 16 supercharges and a gauge group on the left-moving sector of reduced rank d + 8. The momenta of untwisted and twisted states span a lattice known as the Mikhailov lattice II(d), which is not self-dual for d > 1. By using computer algorithms which exploit the properties of lattice embeddings, we perform a systematic exploration of the moduli space for d ≤ 2, and give a list of maximally enhanced points where the U(1)d+8 enhances to a rank d + 8 non-Abelian gauge group. For d = 1, these groups are simply-laced and simply-connected, and in fact can be obtained from the Dynkin diagram of E10. For d = 2 there are also symplectic and doubly-connected groups. For the latter we find the precise form of their fundamental groups from embeddings of lattices into the dual of II(2). Our results easily generalize to d > 2.

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

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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