Existence and construction of Galilean invariant $z\ne 2$ theories
Abstract
We prove a nogo theorem for the construction of a Galilean boost invariant and $$z{\ne}2$$ anisotropic scale invariant field theory with a finite dimensional basis of fields. Two point correlators in such theories, we show, grow unboundedly with spatial separation. Correlators of theories with an infinite dimensional basis of fields, for example, labeled by a continuous parameter, do not necessarily exhibit this bad behavior. Hence, such theories behave effectively as if in one extra dimension. Embedding the symmetry algebra into the conformal algebra of one higher dimension also reveals the existence of an internal continuous parameter. Consideration of isometries shows that the nonrelativistic holographic picture assumes a canonical form, where the bulk gravitational theory lives in a spacetime with one extra dimension. This can be contrasted with the original proposal by Balasubramanian and McGreevy, and by Son, where the metric of a ($d+2$)dimensional spacetime is proposed to be dual of a $$d$$dimensional field theory. We provide explicit examples of theories living at fixed point with anisotropic scaling exponent $$z=\frac{2{\ell}}{{\ell}+1}$$, $${\ell}{\in}\mathbb{Z}$$.
 Authors:

 Univ. of California, San Diego, CA (United States). Dept. of Physics
 Publication Date:
 Research Org.:
 Univ. of California, San Diego, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP)
 OSTI Identifier:
 1441112
 Alternate Identifier(s):
 OSTI ID: 1498885
 Grant/Contract Number:
 SC0009919
 Resource Type:
 Published Article
 Journal Name:
 Physical Review. D.
 Additional Journal Information:
 Journal Volume: 97; Journal Issue: 12; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; quantum field theory; continuous symmetries; spacetime symmetries; symmetries; group theory
Citation Formats
Grinstein, Benjamín, and Pal, Sridip. Existence and construction of Galilean invariant z≠2 theories. United States: N. p., 2018.
Web. doi:10.1103/physrevd.97.125006.
Grinstein, Benjamín, & Pal, Sridip. Existence and construction of Galilean invariant z≠2 theories. United States. https://doi.org/10.1103/physrevd.97.125006
Grinstein, Benjamín, and Pal, Sridip. Mon .
"Existence and construction of Galilean invariant z≠2 theories". United States. https://doi.org/10.1103/physrevd.97.125006.
@article{osti_1441112,
title = {Existence and construction of Galilean invariant z≠2 theories},
author = {Grinstein, Benjamín and Pal, Sridip},
abstractNote = {We prove a nogo theorem for the construction of a Galilean boost invariant and $z{\ne}2$ anisotropic scale invariant field theory with a finite dimensional basis of fields. Two point correlators in such theories, we show, grow unboundedly with spatial separation. Correlators of theories with an infinite dimensional basis of fields, for example, labeled by a continuous parameter, do not necessarily exhibit this bad behavior. Hence, such theories behave effectively as if in one extra dimension. Embedding the symmetry algebra into the conformal algebra of one higher dimension also reveals the existence of an internal continuous parameter. Consideration of isometries shows that the nonrelativistic holographic picture assumes a canonical form, where the bulk gravitational theory lives in a spacetime with one extra dimension. This can be contrasted with the original proposal by Balasubramanian and McGreevy, and by Son, where the metric of a ($d+2$)dimensional spacetime is proposed to be dual of a $d$dimensional field theory. We provide explicit examples of theories living at fixed point with anisotropic scaling exponent $z=\frac{2{\ell}}{{\ell}+1}$, ${\ell}{\in}\mathbb{Z}$.},
doi = {10.1103/physrevd.97.125006},
journal = {Physical Review. D.},
number = 12,
volume = 97,
place = {United States},
year = {2018},
month = {6}
}
https://doi.org/10.1103/physrevd.97.125006
Web of Science
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