scholarly journals Generalized global symmetries in states with dynamical defects: The case of the transverse sound in field theory and holography

2018 ◽  
Vol 97 (10) ◽  
Author(s):  
Sašo Grozdanov ◽  
Napat Poovuttikul
Keyword(s):  
Field Theory ◽  
Global Symmetries ◽  
Transverse Sound

scholarly journals Anomalous symmetries end at the boundary

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Ryan Thorngren ◽  
Yifan Wang
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Boundary Conditions ◽  
Global Symmetries ◽  
Local Symmetry ◽  
Global Symmetry ◽  
Quantum Field ◽  
Ward Identities ◽  
Diffeomorphism Symmetry ◽  
Gravitational Anomalies

Abstract A global symmetry of a quantum field theory is said to have an ’t Hooft anomaly if it cannot be promoted to a local symmetry of a gauged theory. In this paper, we show that the anomaly is also an obstruction to defining symmetric boundary conditions. This applies to Lorentz symmetries with gravitational anomalies as well. For theories with perturbative anomalies, we demonstrate the obstruction by analyzing the Wess-Zumino consistency conditions and current Ward identities in the presence of a boundary. We then recast the problem in terms of symmetry defects and find the same conclusions for anomalies of discrete and orientation-reversing global symmetries, up to the conjecture that global gravitational anomalies, which may not be associated with any diffeomorphism symmetry, also forbid the existence of boundary conditions. This conjecture holds for known gravitational anomalies in D ≤ 3 which allows us to conclude the obstruction result for D ≤ 4.

scholarly journals Exotic symmetries, duality, and fractons in 2+1-dimensional quantum field theory

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Nathan Seiberg ◽  
Shu-Heng Shao
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Global Symmetries ◽  
Low Energy ◽  
Field Theories ◽  
Continuum Models ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Lattice Systems ◽  
Continuum Field

We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum models represent the low-energy limits of certain known lattice systems. One key aspect of these continuum field theories is the important role played by discontinuous field configurations. In two companion papers, we will present 3+1-dimensional versions of these systems. In particular, we will discuss continuum quantum field theories of some models of fractons.

scholarly journals Global Symmetries of Noncommutative Field Theory

2006 ◽  
Vol 53 ◽  
pp. 865-871 ◽  
Author(s):  
C Gonera ◽  
Pkosiński ◽  
P Maślanka ◽  
S Giller
Keyword(s):  
Field Theory ◽  
Global Symmetries ◽  
Noncommutative Field Theory

scholarly journals Exotic $U(1)$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Nathan Seiberg ◽  
Shu-Heng Shao
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Global Symmetries ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Gauge Symmetries ◽  
Lattice Construction ◽  
Continuum Field

We extend our exploration of nonstandard continuum quantum field theories in 2+12+1 dimensions to 3+13+1 dimensions. These theories exhibit exotic global symmetries, a peculiar spectrum of charged states, unusual gauge symmetries, and surprising dualities. Many of the systems we study have a known lattice construction. In particular, one of them is a known gapless fracton model. The novelty here is in their continuum field theory description. In this paper, we focus on models with a global U(1)U(1) symmetry and in a followup paper we will study models with a global \mathbb{Z}_NℤN symmetry.

Global Symmetries in Quantum Field Theory

1997 ◽  
pp. 23-39
Author(s):  
Antonio Dobado ◽  
Angel Gómez-Nicola ◽  
Antonio L. Maroto ◽  
José R. Peláez
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Global Symmetries ◽  
Quantum Field

scholarly journals Constraints on discrete global symmetries in quantum gravity

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Passant Ali ◽  
Astrid Eichhorn ◽  
Martin Pauly ◽  
Michael M. Scherer
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Global Symmetries ◽  
Effective Field Theory ◽  
Effective Field ◽  
Fine Tuning ◽  
Theory Approach ◽  
Perturbative Regime

Abstract The question whether global symmetries can be realized in quantum-gravity-matter-systems has far-reaching phenomenological consequences. Here, we collect evidence that within an asymptotically safe context, discrete global symmetries of the form ℤn, n > 4, cannot be realized in a near-perturbative regime. In contrast, an effective-field-theory approach to quantum gravity might feature such symmetries, providing a mechanism to generate mass hierarchies in the infrared without the need for additional fine-tuning.

scholarly journals Chern-Weil global symmetries and how quantum gravity avoids them

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Ben Heidenreich ◽  
Jacob McNamara ◽  
Miguel Montero ◽  
Matthew Reece ◽  
Tom Rudelius ◽  
...  
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Global Symmetries ◽  
Effective Field Theory ◽  
Degrees Of Freedom ◽  
Effective Field ◽  
Global Symmetry ◽  
Unified Framework ◽  
Particle Phenomenology

Abstract We draw attention to a class of generalized global symmetries, which we call “Chern-Weil global symmetries,” that arise ubiquitously in gauge theories. The Noether currents of these Chern-Weil global symmetries are given by wedge products of gauge field strengths, such as F2 ∧ H3 and tr($$ {F}_2^2 $$ F 2 2 ), and their conservation follows from Bianchi identities. As a result, they are not easy to break. However, it is widely believed that exact global symmetries are not allowed in a consistent theory of quantum gravity. As a result, any Chern-Weil global symmetry in a low-energy effective field theory must be either broken or gauged when the theory is coupled to gravity. In this paper, we explore the processes by which Chern-Weil symmetries may be broken or gauged in effective field theory and string theory. We will see that many familiar phenomena in string theory, such as axions, Chern-Simons terms, worldvolume degrees of freedom, and branes ending on or dissolving in other branes, can be interpreted as consequences of the absence of Chern-Weil symmetries in quantum gravity, suggesting that they might be general features of quantum gravity. We further discuss implications of breaking and gauging Chern-Weil symmetries for particle phenomenology and for boundary CFTs of AdS bulk theories. Chern-Weil global symmetries thus offer a unified framework for understanding many familiar aspects of quantum field theory and quantum gravity.

A First Glance at Renormalisation and Symmetry

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Global Symmetries ◽  
Scale Invariance ◽  
Quantum Field ◽  
Classical Symmetries

The fate of the classical symmetries in a quantum field theory after renormalisation. Global symmetries versus gaugec symmetries. The Adler–Bell–Jackiw anomaly. The breaking of scale invariance and the Callan–Symanzik equation. The example of a non-perturbative anomaly.

scholarly journals Generalized global symmetries and holography

2018 ◽  
Vol 4 (1) ◽  
Author(s):  
Diego Hofman ◽  
Nabil Iqbal
Keyword(s):  
Field Theory ◽  
Global Symmetries ◽  
Gauge Theories ◽  
Gauge Fields ◽  
Goldstone Mode ◽  
Hydrodynamic Behavior ◽  
Conformal Field ◽  
Anisotropic Scaling ◽  
Holographic Duals ◽  
Chern Simons

We study the holographic duals of four-dimensional field theories with 1-form global symmetries, both discrete and continuous. Such higher-form global symmetries are associated with antisymmetric tensor gauge fields in the bulk. Various different realizations are possible: we demonstrate that a Maxwell action for the bulk antisymmetric gauge field results in a non-conformal field theory with a marginally running double-trace coupling. We explore its hydrodynamic behavior at finite temperature and make contact with recent symmetry-based formulations of magnetohydrodynamics. We also argue that discrete global symmetries on the boundary are dual to discrete gauge theories in the bulk. Such gauge theories have a bulk Chern-Simons description: we clarify the conventional 0-form case and work out the 1-form case. Depending on boundary conditions, such discrete symmetries may be embedded in continuous higher-form symmetries that are spontaneously broken. We study the resulting boundary Goldstone mode, which in the 1-form case may be thought of as a boundary photon. Our results clarify how the global form of the field theory gauge group is encoded in holography. Finally, we study the interplay of Maxwell and Chern-Simons terms put together. We work out the operator content and demonstrate the existence of new backreacted anisotropic scaling solutions that carry higher-form charge.

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