Unitarity and universality in nonrelativistic conformal field theory

Pal, Sridip

doi:10.1103/PhysRevD.97.105031

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:: Pal, Sridip

Publication Date:: Thu May 31 00:00:00 EDT 2018

Research Org.:: Univ. of California, San Diego, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

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 Name: Physical Review D Journal Volume: 97 Journal Issue: 10; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

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

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                    Pal, Sridip. Unitarity and universality in nonrelativistic conformal field theory.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevD.97.105031.

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                    Pal, Sridip. Unitarity and universality in nonrelativistic conformal field theory.  United States.  https://doi.org/10.1103/PhysRevD.97.105031

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                    Pal, Sridip. Thu .  
"Unitarity and universality in nonrelativistic conformal field theory".  United States.  https://doi.org/10.1103/PhysRevD.97.105031.

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@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         = {Thu May 31 00:00:00 EDT 2018},

  month        = {Thu May 31 00:00:00 EDT 2018}

}

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Works referencing / citing this record:

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

Grinstein, Benjamín; Pal, Sridip
Physical Review D, Vol. 97, Issue 12
DOI: 10.1103/physrevd.97.125006

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

Grinstein, Benjamín; Pal, Sridip
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Similar Records

Title: Unitarity and universality in nonrelativistic conformal field theory

Abstract

Citation Formats

Renormalization-group fixed points, universal phase diagram, and 1 ∕ N expansion for quantum liquids with interactions near the unitarity limit journal, March 2007

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

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

On the vanishing of evanescent operators journal, March 1991

Schrödinger invariance and strongly anisotropic critical systems journal, June 1994

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

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

Dynamical Response near Quantum Critical Points journal, February 2017

Extremal bootstrapping: go with the flow journal, March 2018

Bootstrapping the 3d Ising twist defect journal, March 2014

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

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

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

Crossing symmetry in alpha space journal, November 2017

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

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

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

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

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

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

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

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

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

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

Renormalization-group fixed points, universal phase diagram, and $1 ∕ N$ expansion for quantum liquids with interactions near the unitarity limit
journal, March 2007

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

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

On the vanishing of evanescent operators
journal, March 1991

Schrödinger invariance and strongly anisotropic critical systems
journal, June 1994

Cut-touching linear functionals in the conformal bootstrap
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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

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

Dynamical Response near Quantum Critical Points
journal, February 2017

Extremal bootstrapping: go with the flow
journal, March 2018

Bootstrapping the 3d Ising twist defect
journal, March 2014

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

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

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

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A new expansion for nucleon-nucleon interactions
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Heavy quark effective theory and nonrelativistic QCD Lagrangian to order $α_{s} {/ m}^{3}$
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Heat kernel and Weyl anomaly of Schrödinger invariant theory
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Two-nucleon systems from effective field theory
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Hilbert series and operator basis for NRQED and NRQCD/HQET
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Resonant Control of Elastic Collisions in an Optically Trapped Fermi Gas of Atoms
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Plancherel Formula for the 2 x 2 Real Unimodular Group
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All unitary ray representations of the conformal group SU(2,2) with positive energy
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Observation of Resonance Condensation of Fermionic Atom Pairs
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Quantum critical response: from conformal perturbation theory to holography
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Conformal four point functions and the operator product expansion
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Unitarity violation in noninteger dimensional Gross-Neveu-Yukawa model
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Existence and construction of Galilean invariant $z \neq 2$ theories
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