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 Exorcising ghosts in quantum gravity

2020 ◽  
Vol 135 (10) ◽  
Author(s):  
Iberê Kuntz
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Gravity ◽  
Boundary Conditions ◽  
Finite Number ◽  
Integration Contour ◽  
Quantum Field ◽  
Curvature Invariants ◽  
Higher Derivative ◽  
Quadratic Gravity

AbstractWe remark that Ostrogradsky ghosts in higher-derivative gravity, with a finite number of derivatives, are fictitious as they result from an unjustified truncation performed in a complete theory containing infinitely many curvature invariants. The apparent ghosts can then be projected out of the quadratic gravity spectrum by redefining the boundary conditions of the theory in terms of an integration contour that does not enclose the ghost poles. This procedure does not alter the renormalizability of the theory. One can thus use quadratic gravity as a quantum field theory of gravity that is both renormalizable and unitary.

scholarly journals QUANTIZATION WITHOUT THE WITTEN ANOMALIES

1996 ◽  
Vol 11 (32n33) ◽  
pp. 2601-2609 ◽  
Author(s):  
T.D. KIEU
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Boundary Conditions ◽  
Path Integral ◽  
Quantum Field ◽  
Quantum Fields ◽  
Berry's Phase ◽  
Berry’S Phase ◽  
Gauge Transformations ◽  
Gauge Anomalies

It is argued that gauge anomalies are only artefacts of the conventional quantization of quantum field theory. When the Berry’s phase is taken into consideration to satisfy certain boundary conditions of the generating path integral, the gauge anomalies associated with homotopically nontrivial gauge transformations are explicitly shown to be eliminated, without any extra quantum fields introduced.

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

THE MODELS OF TWO-DIMENSIONAL CONFORMAL QUANTUM FIELD THEORY WITH Zn SYMMETRY

1988 ◽  
Vol 03 (02) ◽  
pp. 507-520 ◽  
Author(s):  
V.A. FATEEV ◽  
S.L. LYKYANOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Critical Behavior ◽  
Global Symmetry ◽  
Quantum Field ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
Conformally Invariant ◽  
Statistical Systems ◽  
Infinite Set

An infinite set of conformally invariant solutions of the two-dimensional quantum field theory, possessing a global symmetry Zn is constructed. These solutions can describe the critical behavior of Zn symmetric statistical systems.

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