Real homotopy theory and supersymmetric quantum mechanics

Kim, Hyungrok; Saberi, Ingmar

doi:10.1063/1.5011677

Title: Real homotopy theory and supersymmetric quantum mechanics

Abstract

In the context of observing string backgrounds, much work has been devoted to the question of how similar a general quantum field theory (specifically, a two-dimensional superconformal field theory) is to a sigma model. Put differently, one would like to know how well or poorly one can understand the physics of string backgrounds in terms of concepts of classical geometry. Much attention has also been given of late to the question of how geometry can be encoded in a microscopic physical description that makes no explicit reference to space and time. We revisit the first question and review both well-known and less well-known results about geometry and sigma models from the perspective of dimensional reduction to supersymmetric quantum mechanics. The consequences of arising as the dimensional reduction of a d-dimensional theory for the resulting quantum mechanics are explored. In this context, we reinterpret the minimal models of rational (more precisely, complex) homotopy theory as certain supersymmetric Fock spaces, with unusual actions of the supercharges. The data of the Massey products appear naturally as supersymmetric vacuum states that are entangled between different degrees of freedom. This connection between entanglement and geometry is, as far as we know, not well known tomore »« less

Authors:

Kim, Hyungrok ^[1];

^[2]

Stony Brook Univ., NY (United States). Dept. of Physics and Astronomy
Ruprecht-Karls-Univ.Heidelberg, Heidelberg (Germany). Mathematisches Inst.

Publication Date:: 2018-07-03

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

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

OSTI Identifier:: 1540144

Alternate Identifier(s):: OSTI ID: 1458783

Grant/Contract Number:: SC0011632

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Mathematical Physics

Additional Journal Information:: Journal Volume: 59; Journal Issue: 7; Journal ID: ISSN 0022-2488

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics

Citation Formats


                    Kim, Hyungrok, and Saberi, Ingmar. Real homotopy theory and supersymmetric quantum mechanics.  United States: N. p., 2018. 
Web.  doi:10.1063/1.5011677.

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                    Kim, Hyungrok, & Saberi, Ingmar. Real homotopy theory and supersymmetric quantum mechanics.  United States.  https://doi.org/10.1063/1.5011677

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                    Kim, Hyungrok, and Saberi, Ingmar. Tue .  
"Real homotopy theory and supersymmetric quantum mechanics".  United States.  https://doi.org/10.1063/1.5011677.  https://www.osti.gov/servlets/purl/1540144.

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@article{osti_1540144,

  title        = {Real homotopy theory and supersymmetric quantum mechanics},

  author       = {Kim, Hyungrok and Saberi, Ingmar},

  abstractNote = {In the context of observing string backgrounds, much work has been devoted to the question of how similar a general quantum field theory (specifically, a two-dimensional superconformal field theory) is to a sigma model. Put differently, one would like to know how well or poorly one can understand the physics of string backgrounds in terms of concepts of classical geometry. Much attention has also been given of late to the question of how geometry can be encoded in a microscopic physical description that makes no explicit reference to space and time. We revisit the first question and review both well-known and less well-known results about geometry and sigma models from the perspective of dimensional reduction to supersymmetric quantum mechanics. The consequences of arising as the dimensional reduction of a d-dimensional theory for the resulting quantum mechanics are explored. In this context, we reinterpret the minimal models of rational (more precisely, complex) homotopy theory as certain supersymmetric Fock spaces, with unusual actions of the supercharges. The data of the Massey products appear naturally as supersymmetric vacuum states that are entangled between different degrees of freedom. This connection between entanglement and geometry is, as far as we know, not well known to physicists. In addition, we take note of an intriguing numerical coincidence in the context of string compactification on hyper-Kähler eight-manifolds.},

  doi          = {10.1063/1.5011677},

  journal      = {Journal of Mathematical Physics},

  number       = 7,

  volume       = 59,

  place        = {United States},

  year         = {2018},

  month        = {7}

}

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Works referenced in this record:

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Title: Real homotopy theory and supersymmetric quantum mechanics

Abstract

Citation Formats

On the Betti Numbers of Irreducible Compact Hyperkähler Manifolds of Complex Dimension Four journal, January 2001

Electric-magnetic duality and the geometric Langlands program journal, January 2007

On the Decomposition of KÄHler Manifolds with Trivial Canonical Class journal, April 1974

Supersymmetry and Morse theory journal, January 1982

Action of the Lie algebra SO(5) on the cohomology of a hyperk�hler manifold journal, January 1991

Supersymmetry and the cohomology of (hyper) Kähler manifolds journal, October 1997

N = 4 topological strings journal, January 1995

Aspects of NT ⩾ 2 topological gauge theories and D-branes journal, May 1997

Superstrings and manifolds of exceptional holonomy journal, September 1995

On the cohomology of Kahler and hyper-Kähler manifolds journal, January 1996

Twisted N =2 Supersymmetry with Central Charge and Equivariant Cohomology journal, April 1997

Cohomology of compact hyperkähler manifolds and its applications journal, July 1996

Supersymmetry and the Atiyah-Singer index theorem journal, June 1983

Structures différentiables sur les types d'homotopie rationnelle simplement connexes journal, January 1976

Constraints on supersymmetry breaking journal, July 1982

On the Algebras of BPS States journal, October 1998

Defect perturbations in Landau-Ginzburg models journal, March 2010

Sequencing BPS spectra journal, March 2016

Infinitesimal computations in topology journal, December 1977

Chiral rings in N = 2 superconformal theories journal, September 1989

Real homotopy theory of K�hler manifolds journal, October 1975

Defect perturbations in Landau-Ginzburg models text, January 2010

Supersymmetry and the Atiyah-Singer index theorem journal, March 1984

Sequencing BPS Spectra text, January 2015

Electric-Magnetic Duality And The Geometric Langlands Program preprint, January 2006

N=4 Topological Strings text, January 1994

On the algebras of BPS states text, January 1996

On the Betti Numbers of Irreducible Compact Hyperkähler Manifolds of Complex Dimension Four
journal, January 2001

Electric-magnetic duality and the geometric Langlands program
journal, January 2007

On the Decomposition of KÄHler Manifolds with Trivial Canonical Class
journal, April 1974

Supersymmetry and Morse theory
journal, January 1982

Action of the Lie algebra SO(5) on the cohomology of a hyperk�hler manifold
journal, January 1991

Supersymmetry and the cohomology of (hyper) Kähler manifolds
journal, October 1997

N = 4 topological strings
journal, January 1995

Aspects of NT ⩾ 2 topological gauge theories and D-branes
journal, May 1997

Superstrings and manifolds of exceptional holonomy
journal, September 1995

On the cohomology of Kahler and hyper-Kähler manifolds
journal, January 1996

Twisted N =2 Supersymmetry with Central Charge and Equivariant Cohomology
journal, April 1997

Cohomology of compact hyperkähler manifolds and its applications
journal, July 1996

Supersymmetry and the Atiyah-Singer index theorem
journal, June 1983

Structures différentiables sur les types d'homotopie rationnelle simplement connexes
journal, January 1976

Constraints on supersymmetry breaking
journal, July 1982

On the Algebras of BPS States
journal, October 1998

Defect perturbations in Landau-Ginzburg models
journal, March 2010

Sequencing BPS spectra
journal, March 2016

Infinitesimal computations in topology
journal, December 1977

Chiral rings in N = 2 superconformal theories
journal, September 1989

Real homotopy theory of K�hler manifolds
journal, October 1975

Defect perturbations in Landau-Ginzburg models
text, January 2010

Supersymmetry and the Atiyah-Singer index theorem
journal, March 1984

Sequencing BPS Spectra
text, January 2015

Electric-Magnetic Duality And The Geometric Langlands Program
preprint, January 2006

N=4 Topological Strings
text, January 1994

On the algebras of BPS states
text, January 1996