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Title: Existence and construction of Galilean invariant z 2 theories

Abstract

We prove a no-go 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 space-time 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 space-time 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:
 [1];  [1]
  1. 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) (SC-25)
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 2470-0010
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. doi:10.1103/physrevd.97.125006.
Grinstein, Benjamín, and Pal, Sridip. Mon . "Existence and construction of Galilean invariant z≠2 theories". United States. doi: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 no-go 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 space-time 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 space-time 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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/physrevd.97.125006

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Cited by: 1 work
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