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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:
;
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:
Journal Article: Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 12; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society
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. 2018. "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 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},
url = {https://www.osti.gov/biblio/1441112}, journal = {Physical Review D},
issn = {2470-0010},
number = 12,
volume = 97,
place = {United States},
year = {Mon Jun 11 00:00:00 EDT 2018},
month = {Mon Jun 11 00:00:00 EDT 2018}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at https://doi.org/10.1103/PhysRevD.97.125006

Citation Metrics:
Cited by: 6 works
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Works referenced in this record:

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Works referencing / citing this record:

On non-relativistic supersymmetry and its spontaneous breaking
journal, June 2017


The lagrangian formulation of chiral scalars
journal, July 1987


Warped conformal field theory as lower spin gravity
journal, August 2015


A new formulation of non-relativistic diffeomorphism invariance
journal, October 2014


Schrödinger holography for z < 2
journal, January 2015


Localization of the Galilean symmetry and dynamical realization of Newton–Cartan geometry
journal, January 2015


Schrödinger holography with z = 2
journal, March 2015


Comments on string theory backgrounds with non-relativistic conformal symmetry
journal, October 2008


Holographic stress tensor for non-relativistic theories
journal, September 2009


Self-gravitating darkon fluid with anisotropic scaling
journal, November 2010


Anomalous Hall viscosity at the Weyl-semimetal–insulator transition
journal, May 2019