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Title: Symmetry realization via a dynamical inverse Higgs mechanism

Abstract

The Ward identities associated with spontaneously broken symmetries can be saturated by Goldstone bosons. However, when space-time symmetries are broken, the number of Goldstone bosons necessary to non-linearly realize the symmetry can be less than the number of broken generators. The loss of Goldstones may be due to a redundancy or the generation of a gap. In either case the associated Goldstone may be removed from the spectrum. This phenomena is called an Inverse Higgs Mechanism (IHM) and its appearance has a well defined mathematical condition. However, there are cases when a Goldstone boson associated with a broken generator does not appear in the low energy theory despite the lack of the existence of an associated IHM. In this paper we will show that in such cases the relevant broken symmetry can be realized, without the aid of an associated Goldstone, if there exists a proper set of operator constraints, which we call a Dynamical Inverse Higgs Mechanism (DIHM). We consider the spontaneous breaking of boosts, rotations and conformal transformations in the context of Fermi liquids, finding three possible paths to symmetry realization: pure Goldstones, no Goldstones and DIHM, or some mixture thereof. We show that in the two dimensionalmore » degenerate electron system the DIHM route is the only consistent way to realize spontaneously broken boosts and dilatations, while in three dimensions these symmetries could just as well be realized via the inclusion of non-derivatively coupled Goldstone bosons. We present the action, including the leading order non-linearities, for the rotational Goldstone (angulon), and discuss the constraint associated with the possible DIHM that would need to be imposed to remove it from the spectrum. Finally we discuss the conditions under which Goldstone bosons are non-derivatively coupled, a necessary condition for the existence of a Dynamical Inverse Higgs Constraint (DIHC), generalizing the results for Vishwanath and Wantanabe.« less

Authors:
 [1]; ORCiD logo [1]
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  1. Carnegie Mellon Univ., Pittsburgh, PA (United States)
Publication Date:
Research Org.:
Univ. of Arizona, Tucson, AZ (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1507707
Grant/Contract Number:  
FG02-04ER41338; FG02-06ER41449
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 5; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective Field Theories; Space-Time Symmetries; Spontaneous Symmetry Breaking

Citation Formats

Rothstein, Ira Z., and Shrivastava, Prashant. Symmetry realization via a dynamical inverse Higgs mechanism. United States: N. p., 2018. Web. doi:10.1007/jhep05(2018)014.
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Rothstein, Ira Z., & Shrivastava, Prashant. Symmetry realization via a dynamical inverse Higgs mechanism. United States. https://doi.org/10.1007/jhep05(2018)014
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Rothstein, Ira Z., and Shrivastava, Prashant. Thu . "Symmetry realization via a dynamical inverse Higgs mechanism". United States. https://doi.org/10.1007/jhep05(2018)014. https://www.osti.gov/servlets/purl/1507707.
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@article{osti_1507707,
title = {Symmetry realization via a dynamical inverse Higgs mechanism},
author = {Rothstein, Ira Z. and Shrivastava, Prashant},
abstractNote = {The Ward identities associated with spontaneously broken symmetries can be saturated by Goldstone bosons. However, when space-time symmetries are broken, the number of Goldstone bosons necessary to non-linearly realize the symmetry can be less than the number of broken generators. The loss of Goldstones may be due to a redundancy or the generation of a gap. In either case the associated Goldstone may be removed from the spectrum. This phenomena is called an Inverse Higgs Mechanism (IHM) and its appearance has a well defined mathematical condition. However, there are cases when a Goldstone boson associated with a broken generator does not appear in the low energy theory despite the lack of the existence of an associated IHM. In this paper we will show that in such cases the relevant broken symmetry can be realized, without the aid of an associated Goldstone, if there exists a proper set of operator constraints, which we call a Dynamical Inverse Higgs Mechanism (DIHM). We consider the spontaneous breaking of boosts, rotations and conformal transformations in the context of Fermi liquids, finding three possible paths to symmetry realization: pure Goldstones, no Goldstones and DIHM, or some mixture thereof. We show that in the two dimensional degenerate electron system the DIHM route is the only consistent way to realize spontaneously broken boosts and dilatations, while in three dimensions these symmetries could just as well be realized via the inclusion of non-derivatively coupled Goldstone bosons. We present the action, including the leading order non-linearities, for the rotational Goldstone (angulon), and discuss the constraint associated with the possible DIHM that would need to be imposed to remove it from the spectrum. Finally we discuss the conditions under which Goldstone bosons are non-derivatively coupled, a necessary condition for the existence of a Dynamical Inverse Higgs Constraint (DIHC), generalizing the results for Vishwanath and Wantanabe.},
doi = {10.1007/jhep05(2018)014},
journal = {Journal of High Energy Physics (Online)},
number = 5,
volume = 2018,
place = {United States},
year = {Thu May 03 00:00:00 EDT 2018},
month = {Thu May 03 00:00:00 EDT 2018}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1007/jhep05(2018)014
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Cited by: 14 works
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Figures / Tables:

Figure 1 Figure 1: Allowed kinematic configuration for quasi-particle scattering. Diagram (a) is the BCS back to back configuration which leads to Cooper pair condensation. (b) Forward scattering, in which the final state momenta lie on top of the initial state momenta.
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Works referenced in this record:

Structure of Phenomenological Lagrangians. II
journal, January 1969

Inverse Higgs effect in nonlinear realizations
journal, November 1975

  • Ivanov, E. A.; Ogievetskii, V. I.
  • Theoretical and Mathematical Physics, Vol. 25, Issue 2
  • DOI: 10.1007/BF01028947

Nonlinear realizations of symmetries and unphysical Goldstone bosons
journal, November 2010

Renormalization group for interacting fermions in d > 1
journal, January 1992

Lorentz violation at high energy: Concepts, phenomena, and astrophysical constraints
journal, January 2006

Gravity with a dynamical preferred frame
journal, June 2001

Invariant operators in collinear effective theory
journal, September 2001

Goldstone modes in the neutron star core
journal, July 2014

Effective field theory for finite systems with spontaneously broken symmetry
journal, January 2014

Kaon condensation and Goldstone's theorem
journal, December 2001

Effective theory approach to the spontaneous breakdown of Lorentz invariance
journal, October 2010

  • Armendariz-Picon, Cristian; Diez-Tejedor, Alberto; Penco, Riccardo
  • Journal of High Energy Physics, Vol. 2010, Issue 10
  • DOI: 10.1007/JHEP10(2010)079

Renormalization-group approach to the theory of the Fermi surface
journal, December 1990

On how to count Goldstone bosons
journal, March 1976

Spontaneous Breaking of Lie and Current Algebras
journal, April 2004

New Mechanism for Superconductivity
journal, September 1965

Relativistic fluids, superfluids, solids, and supersolids from a coset construction
journal, February 2014

Renormalization group for interacting fermions in d > 1
journal, September 1991

Spontaneous Symmetry Breaking and Nambu–Goldstone Bosons in Quantum Many-Body Systems
journal, April 2010

Renormalization group scaling in nonrelativistic QCD
journal, March 2000

Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance
journal, June 2012

Effective Lagrangian for Nonrelativistic Systems
journal, September 2014

Quantum critical points of helical Fermi liquids
journal, February 2010

Broken Symmetries
journal, August 1962

  • Goldstone, Jeffrey; Salam, Abdus; Weinberg, Steven
  • Physical Review, Vol. 127, Issue 3
  • DOI: 10.1103/PhysRev.127.965

An effective field theory for heavy quarks at low energies
journal, April 1990

Reparameterisation invariance constraints on heavy particle effective field theories
journal, July 1992

Effective field theory and matching in nonrelativistic gauge theories
journal, January 1998

Zoology of condensed matter: framids, ordinary stuff, extra-ordinary stuff
journal, June 2015

  • Nicolis, Alberto; Penco, Riccardo; Piazza, Federico
  • Journal of High Energy Physics, Vol. 2015, Issue 6
  • DOI: 10.1007/JHEP06(2015)155

Nonperturbative behavior of the quantum phase transition to a nematic Fermi fluid
journal, February 2006

Spontaneous breaking of non-relativistic scale symmetry
journal, October 2017

  • Arav, Igal; Hason, Itamar; Oz, Yaron
  • Journal of High Energy Physics, Vol. 2017, Issue 10
  • DOI: 10.1007/JHEP10(2017)063

Spontaneously Broken Spacetime Symmetries and Goldstone’s Theorem
journal, February 2002

Counting Rule for Nambu-Goldstone Modes in Nonrelativistic Systems
journal, February 2013

Landau theory of relativistic Fermi liquids
journal, May 1976

Nonrelativistic effective Lagrangians
journal, March 1994

More on gapped Goldstones at finite density: more gapped Goldstones
journal, November 2013

  • Nicolis, Alberto; Penco, Riccardo; Piazza, Federico
  • Journal of High Energy Physics, Vol. 2013, Issue 11
  • DOI: 10.1007/JHEP11(2013)055

Triviality of the BCS-BEC crossover in extended dimensions: Implications for the ground state energy
journal, November 2006

Structure of Phenomenological Lagrangians. I
journal, January 1969

Implications of Relativity on Nonrelativistic Goldstone Theorems: Gapped Excitations at Finite Charge Density
journal, January 2013

Criterion for stability of Goldstone modes and Fermi liquid behavior in a metal with broken symmetry
journal, October 2014

  • Watanabe, Haruki; Vishwanath, Ashvin
  • Proceedings of the National Academy of Sciences, Vol. 111, Issue 46
  • DOI: 10.1073/pnas.1415592111

Non-linear realizations, Goldstone bosons of broken Lorentz rotations and effective actions for p-branes
journal, June 2013

Couplings of a light dilaton and violations of the equivalence principle
journal, August 2000

(Re-)inventing the relativistic wheel: gravity, cosets, and spinning objects
journal, November 2014

  • Delacrétaz, Luca V.; Endlich, Solomon; Monin, Alexander
  • Journal of High Energy Physics, Vol. 2014, Issue 11
  • DOI: 10.1007/JHEP11(2014)008

Lorentz violation at high energy: concepts, phenomena and astrophysical constraints
text, January 2005

Invariant Operators in Collinear Effective Theory
text, January 2001

Nonrelativistic effective Lagrangians
text, January 1993

Spontaneously Broken Spacetime Symmetries and Goldstone's Theorem
text, January 2001

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