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Title: Unitarity and universality in nonrelativistic conformal field theory

Abstract

We relate the notion of unitarity of a ($0+1$)-D conformally ($$SL(2,\mathbf{R})$$) invariant field theory with that of a nonrelativistic conformal (Schrödinger) field theory using the fact that $$SL(2,\mathbf{R})$$ is a subgroup of nonrelativistic conformal (Schrödinger) group. Exploiting $$SL(2,\mathbf{R})$$ unitarity, we derive the unitarity bounds and null conditions for a Schrödinger field theory (for the neutral as well as the charged sector). In noninteger dimensions the theory is shown to be nonunitary. The use of the $$SL(2,\mathbf{R})$$ subgroup opens up the possibility of borrowing results from ($0+1$)-D $$SL(2,\mathbf{R})$$ invariant field theory to explore Schrödinger field theory, in particular, the neutral sector, which has otherwise been unexplored.

Authors:
 [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:
1439761
Alternate Identifier(s):
OSTI ID: 1498883
Grant/Contract Number:  
SC0009919
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 97; Journal Issue: 10; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Fermi gases; heavy-fermion systems; conformal field theory; conformal symmetry

Citation Formats

Pal, Sridip. Unitarity and universality in nonrelativistic conformal field theory. United States: N. p., 2018. Web. doi:10.1103/physrevd.97.105031.
Pal, Sridip. Unitarity and universality in nonrelativistic conformal field theory. United States. doi:10.1103/physrevd.97.105031.
Pal, Sridip. Thu . "Unitarity and universality in nonrelativistic conformal field theory". United States. doi:10.1103/physrevd.97.105031.
@article{osti_1439761,
title = {Unitarity and universality in nonrelativistic conformal field theory},
author = {Pal, Sridip},
abstractNote = {We relate the notion of unitarity of a ($0+1$)-D conformally ($SL(2,\mathbf{R})$) invariant field theory with that of a nonrelativistic conformal (Schrödinger) field theory using the fact that $SL(2,\mathbf{R})$ is a subgroup of nonrelativistic conformal (Schrödinger) group. Exploiting $SL(2,\mathbf{R})$ unitarity, we derive the unitarity bounds and null conditions for a Schrödinger field theory (for the neutral as well as the charged sector). In noninteger dimensions the theory is shown to be nonunitary. The use of the $SL(2,\mathbf{R})$ subgroup opens up the possibility of borrowing results from ($0+1$)-D $SL(2,\mathbf{R})$ invariant field theory to explore Schrödinger field theory, in particular, the neutral sector, which has otherwise been unexplored.},
doi = {10.1103/physrevd.97.105031},
journal = {Physical Review D},
number = 10,
volume = 97,
place = {United States},
year = {2018},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/physrevd.97.105031

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Cited by: 5 works
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Works referenced in this record:

Scale and Conformal Transformations in Galilean-Covariant Field Theory
journal, January 1972


Four loop mass anomalous dimension in the Gross–Neveu model
journal, October 2008


On Newton-Cartan local renormalization group and anomalies
journal, November 2016

  • Auzzi, Roberto; Baiguera, Stefano; Filippini, Francesco
  • Journal of High Energy Physics, Vol. 2016, Issue 11
  • DOI: 10.1007/JHEP11(2016)163

Operator bases, S-matrices, and their partition functions
journal, October 2017

  • Henning, Brian; Lu, Xiaochuan; Melia, Tom
  • Journal of High Energy Physics, Vol. 2017, Issue 10
  • DOI: 10.1007/JHEP10(2017)199

On the vanishing of evanescent operators
journal, March 1991


Schrödinger invariance and strongly anisotropic critical systems
journal, June 1994

  • Henkel, Malte
  • Journal of Statistical Physics, Vol. 75, Issue 5-6
  • DOI: 10.1007/BF02186756

Cut-touching linear functionals in the conformal bootstrap
journal, June 2017


Unitarity violation at the Wilson-Fisher fixed point in 4 ε dimensions
journal, June 2016


Conformal invariance for non-relativistic field theory
journal, February 2000


Heat kernel for Newton-Cartan trace anomalies
journal, July 2016

  • Auzzi, Roberto; Nardelli, Giuseppe
  • Journal of High Energy Physics, Vol. 2016, Issue 7
  • DOI: 10.1007/JHEP07(2016)047

Weyl consistency conditions in non-relativistic quantum field theory
journal, December 2016

  • Pal, Sridip; Grinstein, Benjamín
  • Journal of High Energy Physics, Vol. 2016, Issue 12
  • DOI: 10.1007/JHEP12(2016)012

Dynamical Response near Quantum Critical Points
journal, February 2017


Extremal bootstrapping: go with the flow
journal, March 2018

  • El-Showk, Sheer; Paulos, Miguel F.
  • Journal of High Energy Physics, Vol. 2018, Issue 3
  • DOI: 10.1007/JHEP03(2018)148

Bootstrapping the 3d Ising twist defect
journal, March 2014

  • Gaiotto, Davide; Mazac, Dalimil; Paulos, Miguel F.
  • Journal of High Energy Physics, Vol. 2014, Issue 3
  • DOI: 10.1007/JHEP03(2014)100

Operator product expansions on the vacuum in conformal quantum field theory in two spacetime dimensions
journal, February 1976

  • Lüscher, M.
  • Communications in Mathematical Physics, Vol. 50, Issue 1
  • DOI: 10.1007/BF01608553

High precision Feshbach spectroscopy of ultracold cesium collisions
journal, March 2001


Operator product expansion and conservation laws in non-relativistic conformal field theories
journal, December 2014


Conformal field theories at nonzero temperature: Operator product expansions, Monte Carlo, and holography
journal, December 2014


Hilbert series and operator bases with derivatives in effective field theories
journal, December 2015

  • Henning, Brian; Lu, Xiaochuan; Melia, Tom
  • Communications in Mathematical Physics, Vol. 347, Issue 2
  • DOI: 10.1007/s00220-015-2518-2

Nonrelativistic conformal field theories
journal, October 2007


Aspects of hot Galilean field theory
journal, April 2015


Entanglement entropy in non-relativistic field theories
journal, April 2010


Duality in quantum field theory
journal, February 1977


A tauberian theorem for the conformal bootstrap
journal, December 2017


Schrödinger invariance and spacetime symmetries
journal, June 2003


Spacetime symmetries of the quantum Hall effect
journal, February 2015


Gravity Duals for Nonrelativistic Conformal Field Theories
journal, August 2008


Tensor representations of conformal algebra and conformally covariant operator product expansion
journal, March 1973


Analytic bounds and emergence of AdS2 physics from the conformal bootstrap
journal, April 2017


Condensation of Pairs of Fermionic Atoms near a Feshbach Resonance
journal, March 2004


The Plancherel formula for the universal covering group ofSL(R, 2)
journal, April 1964


2, 84, 30, 993, 560, 15456, 11962, 261485, . . .: higher dimension operators in the SM EFT
journal, August 2017

  • Henning, Brian; Lu, Xiaochuan; Melia, Tom
  • Journal of High Energy Physics, Vol. 2017, Issue 8
  • DOI: 10.1007/JHEP08(2017)016

Crossing symmetry in alpha space
journal, November 2017

  • Hogervorst, Matthijs; van Rees, Balt C.
  • Journal of High Energy Physics, Vol. 2017, Issue 11
  • DOI: 10.1007/JHEP11(2017)193

A new expansion for nucleon-nucleon interactions
journal, April 1998


Heavy quark effective theory and nonrelativistic QCD Lagrangian to order α s / m 3
journal, July 1997


NRQED Lagrangian at order 1 / M 4
journal, March 2013


On HQET and NRQCD operators of dimension 8 and above
journal, July 2017


Heat kernel and Weyl anomaly of Schrödinger invariant theory
journal, December 2017


Non-relativistic scale anomalies
journal, June 2016

  • Arav, Igal; Chapman, Shira; Oz, Yaron
  • Journal of High Energy Physics, Vol. 2016, Issue 6
  • DOI: 10.1007/JHEP06(2016)158

Bounding scalar operator dimensions in 4 D CFT
journal, December 2008


Two-nucleon systems from effective field theory
journal, November 1998


Resonant Magnetic Field Control of Elastic Scattering in Cold R 85 b
journal, December 1998


Gapless quantum spin chains: multiple dynamics and conformal wavefunctions
journal, October 2017

  • Chen, Xiao; Fradkin, Eduardo; Witczak-Krempa, William
  • Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 46
  • DOI: 10.1088/1751-8121/aa8dbc

Hilbert series and operator basis for NRQED and NRQCD/HQET
journal, September 2017


Resonant Control of Elastic Collisions in an Optically Trapped Fermi Gas of Atoms
journal, April 2002


Plancherel Formula for the 2 x 2 Real Unimodular Group
journal, April 1952

  • Harish-Chandra,
  • Proceedings of the National Academy of Sciences, Vol. 38, Issue 4
  • DOI: 10.1073/pnas.38.4.337

All unitary ray representations of the conformal group SU(2,2) with positive energy
journal, February 1977

  • Mack, G.
  • Communications in Mathematical Physics, Vol. 55, Issue 1
  • DOI: 10.1007/BF01613145

Observation of Resonance Condensation of Fermionic Atom Pairs
journal, January 2004


Quantum critical response: from conformal perturbation theory to holography
journal, July 2017

  • Lucas, Andrew; Sierens, Todd; Witczak-Krempa, William
  • Journal of High Energy Physics, Vol. 2017, Issue 7
  • DOI: 10.1007/JHEP07(2017)149

Conformal four point functions and the operator product expansion
journal, April 2001


Unitarity violation in noninteger dimensional Gross-Neveu-Yukawa model
journal, May 2018


    Works referencing / citing this record:

    Existence and construction of Galilean invariant z 2 theories
    journal, June 2018