D-Branes and Scheme Theory

Abstract

In this highly speculative note we conjecture that it may be possible to understand features of coincident D-branes, such as the appearance of enhanced non-abelian gauge symmetry, in a purely geometric fashion, using a form of geometry known as scheme theory. We give a very brief introduction to some relevant ideas from scheme theory, and point out how these ideas work in special cases.

10 pages, LaTeX

References in corpus (4)

• D-Branes and Topological Field Theories
• Arithmetic and Attractors
• Attractors and Arithmetic
• Deformation quantization as the origin of D-brane non-Abelian degrees of freedom

Cited by in corpus (11)

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• D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck
• D-branes and Azumaya/matrix noncommutative differential geometry, I: D-branes as fundamental objects in string theory and differentiable maps from Azumaya/matrix manifolds with a fundamental module to real manifolds
• Azumaya noncommutative geometry and D-branes - an origin of the master nature of D-branes
• Generalized Toric Polygons, T-branes, and 5d SCFTs
• D-branes of A-type, their deformations, and Morse cobordism of A-branes on Calabi-Yau 3-folds under a split attractor flow: Donaldson/Alexander-Hilden-Lozano-Montesinos-Thurston/Hurwitz/Denef-Joyce meeting Polchinski-Grothendieck
• Derived categories and stacks in physics
• D-branes and synthetic/$C^{\infty }$-algebraic symplectic/calibrated geometry, I: Lemma on a finite algebraicness property of smooth maps from Azumaya/matrix manifolds