Hamiltonian truncation study of supersymmetric quantum mechanics: S-matrix and metastable states

Balthazar, Bruno; Rodriguez, Victor A.; Yin, Xi

doi:10.1007/jhep08(2019)100

Title: Hamiltonian truncation study of supersymmetric quantum mechanics: S-matrix and metastable states

Abstract

We implement the Rayleigh-Ritz method in supersymmetric quantum mechanics with flat directions, and extract the S-matrix and metastable resonances. The effectiveness of the method is demonstrated in two strongly coupled systems: an N = 1 toy supermembrane model, and an N = 4 model with a U(1) gauge multiplet and a charged chiral multiplet.

Authors:

Balthazar, Bruno ^[1]; Rodriguez, Victor A. ^[1]; Yin, Xi ^[1]

Harvard Univ., Cambridge, MA (United States)

Publication Date:: Tue Aug 20 00:00:00 EDT 2019

Research Org.:: Harvard Univ., Cambridge, MA (United States)

Sponsoring Org.:: USDOE Office of Science (SC); National Science Foundation (NSF)

OSTI Identifier:: 1610171

Grant/Contract Number:: FG02-91ER40654; DGE1144152

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 8; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Field Theories in Lower Dimensions; Nonperturbative Effects; Supersymmetric Effective Theories; Supersymmetric Gauge Theory

Citation Formats


                    Balthazar, Bruno, Rodriguez, Victor A., and Yin, Xi. Hamiltonian truncation study of supersymmetric quantum mechanics: S-matrix and metastable states.  United States: N. p., 2019. 
Web.  doi:10.1007/jhep08(2019)100.

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                    Balthazar, Bruno, Rodriguez, Victor A., & Yin, Xi. Hamiltonian truncation study of supersymmetric quantum mechanics: S-matrix and metastable states.  United States.  https://doi.org/10.1007/jhep08(2019)100

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                    Balthazar, Bruno, Rodriguez, Victor A., and Yin, Xi. Tue .  
"Hamiltonian truncation study of supersymmetric quantum mechanics: S-matrix and metastable states".  United States.  https://doi.org/10.1007/jhep08(2019)100.  https://www.osti.gov/servlets/purl/1610171.

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@article{osti_1610171,

  title        = {Hamiltonian truncation study of supersymmetric quantum mechanics: S-matrix and metastable states},

  author       = {Balthazar, Bruno and Rodriguez, Victor A. and Yin, Xi},

  abstractNote = {We implement the Rayleigh-Ritz method in supersymmetric quantum mechanics with flat directions, and extract the S-matrix and metastable resonances. The effectiveness of the method is demonstrated in two strongly coupled systems: an N = 1 toy supermembrane model, and an N = 4 model with a U(1) gauge multiplet and a charged chiral multiplet.},

  doi          = {10.1007/jhep08(2019)100},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 8,

  volume       = 2019,

  place        = {United States},

  year         = {Tue Aug 20 00:00:00 EDT 2019},

  month        = {Tue Aug 20 00:00:00 EDT 2019}

}

Copy to clipboard

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Works referenced in this record:

Supersymmetry and Morse theory
journal, January 1982

Witten, Edward
Journal of Differential Geometry, Vol. 17, Issue 4
DOI: 10.4310/jdg/1214437492

Comments on thermodynamics of supersymmetric matrix models
journal, September 2009

Smilga, A. V.
Nuclear Physics B, Vol. 818, Issue 1-2
DOI: 10.1016/j.nuclphysb.2009.03.023

Supersymmetry and quantum mechanics
journal, January 1995

Cooper, Fred; Khare, Avinash; Sukhatme, Uday
Physics Reports, Vol. 251, Issue 5-6
DOI: 10.1016/0370-1573(94)00080-M

On the ground state wave function of matrix theory
journal, November 2015

Lin, Ying-Hsuan; Yin, Xi
Journal of High Energy Physics, Vol. 2015, Issue 11
DOI: 10.1007/JHEP11(2015)027

Counting trees in supersymmetric quantum mechanics
journal, January 2018

Córdova, Clay; Shao, Shu-Heng
Annales de l’Institut Henri Poincaré D, Vol. 5, Issue 1
DOI: 10.4171/AIHPD/47

BPS Quivers and Spectra of Complete $${\mathcal{N} = 2}$$ N = 2 Quantum Field Theories
journal, August 2013

Alim, Murad; Cecotti, Sergio; Córdova, Clay
Communications in Mathematical Physics, Vol. 323, Issue 3
DOI: 10.1007/s00220-013-1789-8

M(atrix) theory: matrix quantum mechanics as a fundamental theory
journal, June 2001

Taylor, Washington
Reviews of Modern Physics, Vol. 73, Issue 2
DOI: 10.1103/RevModPhys.73.419

Asymptotic form of zero energy wave functions in supersymmetric matrix models
journal, February 2000

Fröhlich, J.; Graf, G. M.; Hasler, D.
Nuclear Physics B, Vol. 567, Issue 1-2
DOI: 10.1016/S0550-3213(99)00649-5

Wall-crossing made smooth
journal, April 2015

Pioline, Boris
Journal of High Energy Physics, Vol. 2015, Issue 4
DOI: 10.1007/JHEP04(2015)092

D -Particle Bound States and Generalized Instantons
journal, January 2000

Moore, Gregory; Nekrasov, Nikita; Shatashvili, Samson
Communications in Mathematical Physics, Vol. 209, Issue 1
DOI: 10.1007/s002200050016

Constraints on supersymmetry breaking
journal, July 1982

Witten, Edward
Nuclear Physics B, Vol. 202, Issue 2
DOI: 10.1016/0550-3213(82)90071-2

D-Brane Bound States Redux
journal, June 1998

Sethi, Savdeep; Stern, Mark
Communications in Mathematical Physics, Vol. 194, Issue 3
DOI: 10.1007/s002200050374

The supermembrane is unstable
journal, June 1989

De Wit, B.; Lüscher, M.; Nicolai, H.
Nuclear Physics B, Vol. 320, Issue 1
DOI: 10.1016/0550-3213(89)90214-9

The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999

Maldacena, Juan
International Journal of Theoretical Physics, Vol. 38, Issue 4, p. 1113-1133
DOI: 10.1023/A:1026654312961

Schwarzschild Black Holes from Matrix Theory
journal, January 1998

Banks, T.; Fischler, W.; Klebanov, I. R.
Physical Review Letters, Vol. 80, Issue 2
DOI: 10.1103/PhysRevLett.80.226

Counting SO(9) × SU(2) representations in coordinate independent state space of SU(2) matrix theory
journal, December 2010

Michishita, Yoji
Journal of Mathematical Physics, Vol. 51, Issue 12
DOI: 10.1063/1.3527280

Quantum Quivers and Hall/Hole Halos
journal, October 2002

Denef, Frederik
Journal of High Energy Physics, Vol. 2002, Issue 10
DOI: 10.1088/1126-6708/2002/10/023

Witten index and wall crossing
journal, January 2015

Hori, Kentaro; Kim, Heeyeon; Yi, Piljin
Journal of High Energy Physics, Vol. 2015, Issue 1
DOI: 10.1007/JHEP01(2015)124

Witten index and threshold bound states of D-branes
journal, November 1997

Yi, Piljin
Nuclear Physics B, Vol. 505, Issue 1-2
DOI: 10.1016/S0550-3213(97)00486-0

Asymptotics of ground state degeneracies in quiver quantum mechanics
journal, January 2016

Córdova, Clay; Shao, Shu-Heng
Communications in Number Theory and Physics, Vol. 10, Issue 2
DOI: 10.4310/CNTP.2016.v10.n2.a4

Dyon-monopole bound states, self-dual harmonic forms on the multi-monopole moduli space, and SL (2,Z) invariance in string theory
journal, June 1994

Sen, Ashoke
Physics Letters B, Vol. 329, Issue 2-3
DOI: 10.1016/0370-2693(94)90763-3

Monte Carlo Studies of Supersymmetric Matrix Quantum Mechanics with Sixteen Supercharges at Finite Temperature
journal, January 2008

Anagnostopoulos, Konstantinos N.; Hanada, Masanori; Nishimura, Jun
Physical Review Letters, Vol. 100, Issue 2
DOI: 10.1103/PhysRevLett.100.021601

Monopole and dyon bound states in N = 2 supersymmetric Yang-Mills theories
journal, December 1995

Sethi, S.; Stern, M.; Zaslow, E.
Nuclear Physics B, Vol. 457, Issue 3
DOI: 10.1016/0550-3213(95)00517-X

Truncated Comformal Space Approach to Scaling Lee-Yang Model
journal, August 1990

Yurov, V. P.; Zamolodchikov, Al. B.
International Journal of Modern Physics A, Vol. 05, Issue 16
DOI: 10.1142/S0217751X9000218X

Approximations for strongly-coupled supersymmetric quantum mechanics
journal, April 2000

Kabat, Daniel; Lifschytz, Gilad
Nuclear Physics B, Vol. 571, Issue 1-2
DOI: 10.1016/S0550-3213(99)00818-4

Construction of the zero-energy state of -matrix theory: Near the origin
journal, August 2009

Hoppe, Jens; Lundholm, Douglas; Trzetrzelewski, Maciej
Nuclear Physics B, Vol. 817, Issue 3
DOI: 10.1016/j.nuclphysb.2009.01.020

Dynamical breaking of supersymmetry
journal, October 1981

Witten, Edward
Nuclear Physics B, Vol. 188, Issue 3
DOI: 10.1016/0550-3213(81)90006-7

D-brane approach to black hole quantum mechanics
journal, July 1996

Callan, Curtis G.; Maldacena, Juan M.
Nuclear Physics B, Vol. 472, Issue 3
DOI: 10.1016/0550-3213(96)00225-8

A low temperature expansion for matrix quantum mechanics
journal, May 2015

Lin, Ying-Hsuan; Shao, Shu-Heng; Wang, Yifan
Journal of High Energy Physics, Vol. 2015, Issue 5
DOI: 10.1007/JHEP05(2015)136

Monte Carlo Studies of Matrix Theory Correlation Functions
journal, April 2010

Hanada, Masanori; Nishimura, Jun; Sekino, Yasuhiro
Physical Review Letters, Vol. 104, Issue 15
DOI: 10.1103/PhysRevLett.104.151601

Truncated conformal space approach in $d$ dimensions: A cheap alternative to lattice field theory?
journal, January 2015

Hogervorst, Matthijs; Rychkov, Slava; van Rees, Balt C.
Physical Review D, Vol. 91, Issue 2
DOI: 10.1103/PhysRevD.91.025005

Hamiltonian truncation study of the $ϕ^{4}$ theory in two dimensions. II. The $Z_{2}$ -broken phase and the Chang duality
journal, March 2016

Rychkov, Slava; Vitale, Lorenzo G.
Physical Review D, Vol. 93, Issue 6
DOI: 10.1103/PhysRevD.93.065014

D -Particle Bound States and Generalized Instantons
journal, January 2000

Moore, Gregory; Nekrasov, Nikita; Shatashvili, Samson
Communications in Mathematical Physics, Vol. 209, Issue 1
DOI: 10.1007/s002200050016

Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions II. The Z_2-Broken Phase and the Chang Duality
text, January 2015

Rychkov, Slava; Vitale, Lorenzo G.
arXiv
DOI: 10.48550/arxiv.1512.00493

Quantum Quivers and Hall/Hole Halos
text, January 2002

Denef, Frederik
arXiv
DOI: 10.48550/arxiv.hep-th/0206072

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Similar Records

Title: Hamiltonian truncation study of supersymmetric quantum mechanics: S-matrix and metastable states

Abstract

Citation Formats

Supersymmetry and Morse theory journal, January 1982

Comments on thermodynamics of supersymmetric matrix models journal, September 2009

Supersymmetry and quantum mechanics journal, January 1995

On the ground state wave function of matrix theory journal, November 2015

Counting trees in supersymmetric quantum mechanics journal, January 2018

BPS Quivers and Spectra of Complete $${\mathcal{N} = 2}$$ N = 2 Quantum Field Theories journal, August 2013

M(atrix) theory: matrix quantum mechanics as a fundamental theory journal, June 2001

Asymptotic form of zero energy wave functions in supersymmetric matrix models journal, February 2000

Wall-crossing made smooth journal, April 2015

D -Particle Bound States and Generalized Instantons journal, January 2000

Constraints on supersymmetry breaking journal, July 1982

D-Brane Bound States Redux journal, June 1998

The supermembrane is unstable journal, June 1989

The Large-N Limit of Superconformal Field Theories and Supergravity journal, January 1999

Schwarzschild Black Holes from Matrix Theory journal, January 1998

Counting SO(9) × SU(2) representations in coordinate independent state space of SU(2) matrix theory journal, December 2010

Quantum Quivers and Hall/Hole Halos journal, October 2002

Witten index and wall crossing journal, January 2015

Witten index and threshold bound states of D-branes journal, November 1997

Asymptotics of ground state degeneracies in quiver quantum mechanics journal, January 2016

Dyon-monopole bound states, self-dual harmonic forms on the multi-monopole moduli space, and SL (2,Z) invariance in string theory journal, June 1994

Monte Carlo Studies of Supersymmetric Matrix Quantum Mechanics with Sixteen Supercharges at Finite Temperature journal, January 2008

Monopole and dyon bound states in N = 2 supersymmetric Yang-Mills theories journal, December 1995

Truncated Comformal Space Approach to Scaling Lee-Yang Model journal, August 1990

Approximations for strongly-coupled supersymmetric quantum mechanics journal, April 2000

Construction of the zero-energy state of -matrix theory: Near the origin journal, August 2009

Dynamical breaking of supersymmetry journal, October 1981

D-brane approach to black hole quantum mechanics journal, July 1996

A low temperature expansion for matrix quantum mechanics journal, May 2015

Monte Carlo Studies of Matrix Theory Correlation Functions journal, April 2010

Truncated conformal space approach in d dimensions: A cheap alternative to lattice field theory? journal, January 2015

Hamiltonian truncation study of the ϕ 4 theory in two dimensions. II. The Z 2 -broken phase and the Chang duality journal, March 2016

D -Particle Bound States and Generalized Instantons journal, January 2000

Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions II. The Z_2-Broken Phase and the Chang Duality text, January 2015

Quantum Quivers and Hall/Hole Halos text, January 2002

Supersymmetry and Morse theory
journal, January 1982

Comments on thermodynamics of supersymmetric matrix models
journal, September 2009

Supersymmetry and quantum mechanics
journal, January 1995

On the ground state wave function of matrix theory
journal, November 2015

Counting trees in supersymmetric quantum mechanics
journal, January 2018

BPS Quivers and Spectra of Complete $${\mathcal{N} = 2}$$ N = 2 Quantum Field Theories
journal, August 2013

M(atrix) theory: matrix quantum mechanics as a fundamental theory
journal, June 2001

Asymptotic form of zero energy wave functions in supersymmetric matrix models
journal, February 2000

Wall-crossing made smooth
journal, April 2015

D -Particle Bound States and Generalized Instantons
journal, January 2000

Constraints on supersymmetry breaking
journal, July 1982

D-Brane Bound States Redux
journal, June 1998

The supermembrane is unstable
journal, June 1989

The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999

Schwarzschild Black Holes from Matrix Theory
journal, January 1998

Counting SO(9) × SU(2) representations in coordinate independent state space of SU(2) matrix theory
journal, December 2010

Quantum Quivers and Hall/Hole Halos
journal, October 2002

Witten index and wall crossing
journal, January 2015

Witten index and threshold bound states of D-branes
journal, November 1997

Asymptotics of ground state degeneracies in quiver quantum mechanics
journal, January 2016

Dyon-monopole bound states, self-dual harmonic forms on the multi-monopole moduli space, and SL (2,Z) invariance in string theory
journal, June 1994

Monte Carlo Studies of Supersymmetric Matrix Quantum Mechanics with Sixteen Supercharges at Finite Temperature
journal, January 2008

Monopole and dyon bound states in N = 2 supersymmetric Yang-Mills theories
journal, December 1995

Truncated Comformal Space Approach to Scaling Lee-Yang Model
journal, August 1990

Approximations for strongly-coupled supersymmetric quantum mechanics
journal, April 2000

Construction of the zero-energy state of -matrix theory: Near the origin
journal, August 2009

Dynamical breaking of supersymmetry
journal, October 1981

D-brane approach to black hole quantum mechanics
journal, July 1996

A low temperature expansion for matrix quantum mechanics
journal, May 2015

Monte Carlo Studies of Matrix Theory Correlation Functions
journal, April 2010

Truncated conformal space approach in $d$ dimensions: A cheap alternative to lattice field theory?
journal, January 2015

Hamiltonian truncation study of the $ϕ^{4}$ theory in two dimensions. II. The $Z_{2}$ -broken phase and the Chang duality
journal, March 2016

D -Particle Bound States and Generalized Instantons
journal, January 2000

Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions II. The Z_2-Broken Phase and the Chang Duality
text, January 2015

Quantum Quivers and Hall/Hole Halos
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