Built on

N. Mermin and H. Wagner, Absence of ferromagnetism or antiferromagnetism in one-dimensional or two-dimensional isotropic Heisenberg models
1966
Earlier work this paper cites.
P. Hohenberg, Existence of long-range order in one and two dimensions
1967
Earlier work this paper cites.
S. R. Coleman, J. Wess, and B. Zumino, Structure of phenomenological Lagrangians. 1
1969
Earlier work this paper cites.
J. Callan, Curtis G., S. R. Coleman, J. Wess, and B. Zumino, Structure of phenomenological Lagrangians. 2
1969
Earlier work this paper cites.
S. R. Coleman, There are no Goldstone bosons in two dimensions
1973
Earlier work this paper cites.
D. V. Volkov, Phenomenological lagrangians
1973
Earlier work this paper cites.
V. Ogievetsky, Nonlinear realizations of internal and space-time symmetries
1974
Earlier work this paper cites.
E. A. Ivanov and V. I. Ogievetskii, Inverse Higgs effect in nonlinear realizations
1975
Earlier work this paper cites.
G. ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking
1980
Earlier work this paper cites.
Cambridge University Press, 1998
J. A. de Azcárraga and J. M. Izquierdo, Lie groups, Lie algebras, cohomology and some applications in physics · 1998
Earlier work this paper cites.
S. Kachru, X. Liu, and M. Mulligan, Gravity duals of Lifshitz-like fixed points
Original
2008
Earlier work this paper cites.

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2014

Scalar Field Theories with Polynomial Shift Symmetries

Griffin, Tom, Grosvenor, Kevin T., Horava, Petr et al.

Understand

We continue our study of naturalness in nonrelativistic QFTs of the Lifshitz type, focusing on scalar fields that can play the role of Nambu-Goldstone (NG) modes associated with spontaneous symmetry breaking.

Such systems allow for an extension of the constant shift symmetry to a shift by a polynomial of degree $P$ in spatial coordinates.
These "polynomial shift symmetries" in turn protect the technical naturalness of modes with a higher-order dispersion relation, and lead to a refinement of the proposed classification of infrared Gaussian fixed points available to describe NG modes in nonrelativistic theories.
Generic interactions in such theories break the polynomial shift symmetry explicitly to the constant shift.

Built on

N. Mermin and H. Wagner, Absence of ferromagnetism or antiferromagnetism in one-dimensional or two-dimensional isotropic Heisenberg models
1966
Earlier work this paper cites.
P. Hohenberg, Existence of long-range order in one and two dimensions
1967
Earlier work this paper cites.
S. R. Coleman, J. Wess, and B. Zumino, Structure of phenomenological Lagrangians. 1
1969
Earlier work this paper cites.
J. Callan, Curtis G., S. R. Coleman, J. Wess, and B. Zumino, Structure of phenomenological Lagrangians. 2
1969
Earlier work this paper cites.
S. R. Coleman, There are no Goldstone bosons in two dimensions
1973
Earlier work this paper cites.
D. V. Volkov, Phenomenological lagrangians
1973
Earlier work this paper cites.
V. Ogievetsky, Nonlinear realizations of internal and space-time symmetries
1974
Earlier work this paper cites.
E. A. Ivanov and V. I. Ogievetskii, Inverse Higgs effect in nonlinear realizations
1975
Earlier work this paper cites.
G. ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking
1980
Earlier work this paper cites.
Cambridge University Press, 1998
J. A. de Azcárraga and J. M. Izquierdo, Lie groups, Lie algebras, cohomology and some applications in physics · 1998
Earlier work this paper cites.
S. Kachru, X. Liu, and M. Mulligan, Gravity duals of Lifshitz-like fixed points
Original
2008
Earlier work this paper cites.