Cluster expansion in terms of knots in gauge theories with finite non‐Abelian gauge groups

Gauge theories establish the standard model of particle physics, and lattice gauge theory (LGT) calculations employing Markov Chain Monte Carlo (MCMC) methods have been pivotal in our understanding of fundamental interactions. The present limitations of MCMC techniques may be overcome by Hamiltonian-based simulations on classical or quantum devices, which further provide the potential to address questions that lay beyond the capabilities of the current approaches. However, for continuous gauge groups, Hamiltonian-based formulations involve infinite-dimensional gauge degrees of freedom that can solely be handled by truncation. Current truncation schemes require dramatically increasing computational resources at small values of the bare couplings, where magnetic field effects become important. Such limitation precludes one from `taking the continuous limit' while working with finite resources. To overcome this limitation, we provide a resource-efficient protocol to simulate LGTs with continuous gauge groups in the Hamiltonian formulation. Our new method allows for calculations at arbitrary values of the bare coupling and lattice spacing. The approach consists of the combination of a Hilbert space truncation with a regularization of the gauge group, which permits an efficient description of the magnetically-dominated regime. We focus here on Abelian gauge theories and use 2+1 dimensional quantum electrodynamics as a benchmark example to demonstrate this efficient framework to achieve the continuum limit in LGTs. This possibility is a key requirement to make quantitative predictions at the field theory level and offers the long-term perspective to utilise quantum simulations to compute physically meaningful quantities in regimes that are precluded to quantum Monte Carlo.

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Non-invertible global symmetries and completeness of the spectrum

Journal of High Energy Physics ◽

10.1007/jhep09(2021)203 ◽

2021 ◽

Vol 2021 (9) ◽

Author(s):

Ben Heidenreich ◽

Jacob McNamara ◽

Miguel Montero ◽

Matthew Reece ◽

Tom Rudelius ◽

...

Keyword(s):

Gauge Theories ◽

Cosmic Strings ◽

Global Symmetry ◽

Complete Spectrum ◽

Abelian Gauge ◽

Analogous Statement ◽

Gauge Groups ◽

Four Dimensions ◽

Chern Simons ◽

General Gauge

Abstract It is widely believed that consistent theories of quantum gravity satisfy two basic kinematic constraints: they are free from any global symmetry, and they contain a complete spectrum of gauge charges. For compact, abelian gauge groups, completeness follows from the absence of a 1-form global symmetry. However, this correspondence breaks down for more general gauge groups, where the breaking of the 1-form symmetry is insufficient to guarantee a complete spectrum. We show that the correspondence may be restored by broadening our notion of symmetry to include non-invertible topological operators, and prove that their absence is sufficient to guarantee a complete spectrum for any compact, possibly disconnected gauge group. In addition, we prove an analogous statement regarding the completeness of twist vortices: codimension-2 objects defined by a discrete holonomy around their worldvolume, such as cosmic strings in four dimensions. We discuss how this correspondence is modified in various, more general contexts, including non-compact gauge groups, Higgsing of gauge theories, and the addition of Chern-Simons terms. Finally, we discuss the implications of our results for the Swampland program, as well as the phenomenological implications of the existence of twist strings.

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JET-GAUGE GROUPS AS BASIC SYMMETRIES OF NON-LINEAR SIGMA AND YANG–MILLS MODELS AND QUANTIZATION

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887812600067 ◽

2012 ◽

Vol 09 (02) ◽

pp. 1260006

Author(s):

VICTOR ALDAYA ◽

MANUEL CALIXTO ◽

JULIO GUERRERO ◽

FRANCISCO F. LOPEZ-RUIZ

Keyword(s):

Sigma Models ◽

Gauge Theories ◽

Canonical Quantization ◽

Group Approach ◽

Abelian Gauge ◽

Gauge Groups ◽

Yang Mills ◽

Non Linear ◽

Non Linear Systems ◽

Linear Sigma Models

The quantum description of non-linear systems finds a deep obstruction in the Canonical Quantization framework and Non-Linear Sigma Models constitute the best representatives. In this paper, we face the quantization of such systems on the grounds of a Group Approach to Quantization, and extend the algorithm to the specific case of massive Non-Abelian gauge theories. The basic geometric structures behind are the so-called "jet-gauge groups".

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TOPOLOGICAL STUDY OF GLOBAL QUANTIZATION IN NON-ABELIAN GAUGE THEORIES AND THE OPEN UNIVERSE

International Journal of Modern Physics A ◽

10.1142/s0217751x94002351 ◽

1994 ◽

Vol 09 (32) ◽

pp. 5729-5741

Author(s):

HUAZHONG ZHANG

Keyword(s):

Homotopy Theory ◽

Gauge Theories ◽

Quantum Effect ◽

Orbit Space ◽

Magnetic Monopoles ◽

Quantization Rule ◽

Abelian Gauge ◽

Gauge Groups ◽

Open Universe ◽

Nonperturbative Solution

We study some topological aspects of non-Abelian gauge theories intimately connected with the Lie algebras of the gauge groups and the homotopy theory in the generalized gauge orbit space. The physics connection with the nonperturbative solution to the strong CP problem by magnetic monopoles and the quantization rule for the effective vacuum angle as originally proposed by the author are also discussed. In addition, some relevant topological formulas are given and discussed. We emphasize that a result7 from their physics application is that the usual gauge orbit space on the compactified space may contain at most a Z2 monopole structure in the SP (2N)(N= rank ) gauge theories; such a Z2 structure may induce spontaneous CP violations in SP (2N) gauge theories, as was noted. Some relevance to the open universe is discussed too. It is expected from our results that the open universe in the case of a nonvanishing θ can also be regarded as a quantum effect of the global quantization in the gauge orbit space. We expect that our results will be useful for other studies of non-Abelian gauge theories in general. Some remarks are also given related to our global quantization and the gauge theories in generalized gauge orbit space.

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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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Seiberg-like dualities for orthogonal and symplectic 3d $$ \mathcal{N} $$ = 2 gauge theories with boundaries

Journal of High Energy Physics ◽

10.1007/jhep07(2021)231 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Tadashi Okazaki ◽

Douglas J. Smith

Keyword(s):

Boundary Conditions ◽

Gauge Theories ◽

Gauge Groups

Abstract We propose dualities of $$ \mathcal{N} $$ N = (0, 2) supersymmetric boundary conditions for 3d $$ \mathcal{N} $$ N = 2 gauge theories with orthogonal and symplectic gauge groups. We show that the boundary ’t Hooft anomalies and half-indices perfectly match for each pair of the proposed dual boundary conditions.

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