scholarly journals Triangle anomalies and nonrelativistic Nambu-Goldstone modes of generalized global symmetries

2019 ◽  
Vol 99 (12) ◽  
Author(s):  
Noriyuki Sogabe ◽  
Naoki Yamamoto
Keyword(s):  
Global Symmetries ◽  
Goldstone Modes

scholarly journals Counting Nambu-Goldstone Modes of Higher-Form Global Symmetries

2021 ◽  
Vol 126 (7) ◽  
Author(s):  
Yoshimasa Hidaka ◽  
Yuji Hirono ◽  
Ryo Yokokura
Keyword(s):  
Global Symmetries ◽  
Goldstone Modes

scholarly journals Goldstone modes and photonization for higher form symmetries

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Diego Hofman ◽  
Nabil Iqbal
Keyword(s):  
Global Symmetries ◽  
Central Extension ◽  
Complex Analysis ◽  
Global Symmetry ◽  
Moody Algebra ◽  
Four Dimensions ◽  
Conformal Theory ◽  
Maxwell Electrodynamics ◽  
Defect Operator ◽  
Goldstone Modes

We discuss generalized global symmetries and their breaking. We extend Goldstone’s theorem to higher form symmetries by showing that a perimeter law for an extended pp-dimensional defect operator charged under a continuous pp-form generalized global symmetry necessarily results in a gapless mode in the spectrum. We also show that a pp-form symmetry in a conformal theory in 2(p+1)2(p+1) dimensions has a free realization. In four dimensions this means any 1-form symmetry in a CFT_4CFT4 can be realized by free Maxwell electrodynamics, i.e. the current can be photonized. The theory has infinitely many conserved 0-form charges that are constructed by integrating the symmetry currents against suitable 1-forms. We study these charges by developing a twistor-based formalism that is a 4d analogue of the usual holomorphic complex analysis familiar in CFT_2CFT2. The charges are shown to obey an algebra with central extension, which is an analogue of the 2d Abelian Kac-Moody algebra for higher form symmetries.

Global symmetries and Noether’s theorem

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Global Symmetries ◽  
Symmetry Transformation ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Quantum Field ◽  
Expectation Value ◽  
Minkowski Space Time ◽  
Integral Measure ◽  
Colour Charge ◽  
Internal Symmetries

Noethers theorem shows that continuous global symmetries lead classically to conservation laws. Such symmetries can be divided into spacetime and internal symmetries. The invariance of Minkowski space-time under global Poincaré transformations leads to the conservation of the four-momentum and the total angular momentum. Examples for conserved charges due to internal symmetries are electric and colour charge. The vacuum expectation value of a Noether current is shown to beconserved in a quantum field theory if the symmetry transformation keeps the path-integral measure invariant.

scholarly journals Effective Lagrangian for Nambu-Goldstone modes in nonequilibrium open systems

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Masaru Hongo ◽  
Suro Kim ◽  
Toshifumi Noumi ◽  
Atsuhisa Ota
Keyword(s):  
Open Systems ◽  
Effective Lagrangian ◽  
Goldstone Modes

scholarly journals Asymptotic symmetries and celestial CFT

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Laura Donnay ◽  
Sabrina Pasterski ◽  
Andrea Puhm
Keyword(s):  
Principal Series ◽  
Finite Energy ◽  
Continuous Series ◽  
Asymptotic Symmetry ◽  
Null Infinity ◽  
Conformal Dimension ◽  
Contour Integrals ◽  
Celestial Sphere ◽  
Goldstone Modes ◽  
Asymptotic Symmetries

Abstract We provide a unified treatment of conformally soft Goldstone modes which arise when spin-one or spin-two conformal primary wavefunctions become pure gauge for certain integer values of the conformal dimension ∆. This effort lands us at the crossroads of two ongoing debates about what the appropriate conformal basis for celestial CFT is and what the asymptotic symmetry group of Einstein gravity at null infinity should be. Finite energy wavefunctions are captured by the principal continuous series ∆ ∈ 1 + iℝ and form a complete basis. We show that conformal primaries with analytically continued conformal dimension can be understood as certain contour integrals on the principal series. This clarifies how conformally soft Goldstone modes fit in but do not augment this basis. Conformally soft gravitons of dimension two and zero which are related by a shadow transform are shown to generate superrotations and non-meromorphic diffeomorphisms of the celestial sphere which we refer to as shadow superrotations. This dovetails the Virasoro and Diff(S2) asymptotic symmetry proposals and puts on equal footing the discussion of their associated soft charges, which correspond to the stress tensor and its shadow in the two-dimensional celestial CFT.

scholarly journals Symmetries and anomalies of (1+1)d theories: 2-groups and symmetry fractionalization

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Matthew Yu
Keyword(s):  
Spectral Sequence ◽  
Global Symmetries ◽  
Group Symmetry ◽  
Low Dimension ◽  
The One ◽  
Group Symmetries

Abstract We investigate the interactions of discrete zero-form and one-form global symmetries in (1+1)d theories. Focus is put on the interactions that the symmetries can have on each other, which in this low dimension result in 2-group symmetries or symmetry fractionalization. A large part of the discussion will be to understand a major feature in (1+1)d: the multiple sectors into which a theory decomposes. We perform gauging of the one-form symmetry, and remark on the effects this has on our theories, especially in the case when there is a global 2-group symmetry. We also implement the spectral sequence to calculate anomalies for the 2-group theories and symmetry fractionalized theory in the bosonic and fermionic cases. Lastly, we discuss topological manipulations on the operators which implement the symmetries, and draw insights on the (1+1)d effects of such manipulations by coupling to a bulk (2+1)d theory.

Global symmetries in four and higher dimensions

1986 ◽  
Vol 271 (1) ◽  
pp. 21-52 ◽  
Author(s):  
Mark W. Goodman ◽  
Edward Witten
Keyword(s):  
Global Symmetries ◽  
Higher Dimensions

scholarly journals Global symmetry, Euclidean gravity, and the black hole information problem

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Daniel Harlow ◽  
Edgar Shaghoulian
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Global Symmetries ◽  
Close Connection ◽  
Usual Sense ◽  
Global Symmetry ◽  
Recent Argument ◽  
Black Hole Information ◽  
Information Problem ◽  
Low Dimensional

Abstract In this paper we argue for a close connection between the non-existence of global symmetries in quantum gravity and a unitary resolution of the black hole information problem. In particular we show how the essential ingredients of recent calculations of the Page curve of an evaporating black hole can be used to generalize a recent argument against global symmetries beyond the AdS/CFT correspondence to more realistic theories of quantum gravity. We also give several low-dimensional examples of quantum gravity theories which do not have a unitary resolution of the black hole information problem in the usual sense, and which therefore can and do have global symmetries. Motivated by this discussion, we conjecture that in a certain sense Euclidean quantum gravity is equivalent to holography.

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