Supergeometry in mathematics and physics
Mikhail Kapranov
TL;DR
This paper provides a comprehensive overview of supergeometry, covering its mathematical foundations, applications in physics related to supersymmetry, and explores its homotopy-theoretic roots, aiming to bridge mathematics and physics.
Contribution
It offers a detailed exposition of supergeometry from both mathematical and physical perspectives, and investigates its homotopy-theoretic origins, which is a novel interdisciplinary approach.
Findings
Mathematically formalized supergeometry
Connections between supergeometry and supersymmetry in physics
Proposed homotopy-theoretic interpretation of superformalism
Abstract
This is a chapter for a planned collective volume entitled "New spaces in mathematics and physics" (M. Anel, G. Catren Eds.). The first part contains a short formal exposition of supergeometry as it is understood by mathematicians. The second part discusses aspects of supergeometry that are used by physicists in relation to supersymmetry. Finally, the third part is an attempt to uncover homotopy-theoretic roots of the super formalism.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Nonlinear Waves and Solitons