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Real homotopy theory and supersymmetric quantum mechanics

Kim, Hyungrok and Saberi, Ingmar (2015) Real homotopy theory and supersymmetric quantum mechanics. . (Submitted)

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In the context of studying string backgrounds, much work has been devoted to the question of how similar a general quantum field theory (specifically, a two-dimensional superconformal 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-Kahler eight-manifolds.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:We thank B. Knudsen, M. Kologlu, L. McCloy, T. McKinney, S. Nawata, D. Pei, and B. Stoica for many fruitful conversations as these ideas were taking shape. We are especially grateful to S. Gukov and H. Ooguri for comments, inspiration, and support. Our work is funded by support from the Department of Energy (through grant DE-SC0011632) and the Walter Burke Institute for Theoretical Physics at Caltech.
Group:Walter Burke Institute for Theoretical Physics
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Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
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Record Number:CaltechAUTHORS:20151104-123907522
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:61835
Deposited By: Joy Painter
Deposited On:04 Nov 2015 21:13
Last Modified:02 Jun 2023 00:24

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