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 twodimensional 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 wellknown and less wellknown 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 ddimensional 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 »
 Authors:

 Stony Brook Univ., NY (United States). Dept. of Physics and Astronomy
 RuprechtKarlsUniv.Heidelberg, Heidelberg (Germany). Mathematisches Inst.
 Publication Date:
 Research Org.:
 California Inst. of Technology (CalTech), Pasadena, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 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 00222488
 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.
Kim, Hyungrok, & Saberi, Ingmar. Real homotopy theory and supersymmetric quantum mechanics. United States. doi:https://doi.org/10.1063/1.5011677
Kim, Hyungrok, and Saberi, Ingmar. Tue .
"Real homotopy theory and supersymmetric quantum mechanics". United States. doi:https://doi.org/10.1063/1.5011677. https://www.osti.gov/servlets/purl/1540144.
@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 twodimensional 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 wellknown and less wellknown 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 ddimensional 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 hyperKähler eightmanifolds.},
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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