nLab D=10 super Yang-Mills theory




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super Yang-Mills theory in spacetime dimension 10.


Equations of motion from the Bianchi identity

The equations of motion of 10d super Yang-Mills happen to be equivalent in superspace to the Bianchi identity

DF=0 D F = 0

subject to the constraint that the bispinorial part of the curvature 2-form vanishes

F αβ=0 F_{\alpha \beta} = 0

(e.g. Witten 86, Atick-Dhar-Ratra 86, (4.14), Bonora-Bregola-Lechner-Pasti-Tonin 87, above (2.7)).

After embedding into heterotic supergravity this becomes parts of the torsion constraints of supergravity. See there.

In this superspace formulation the gaugino χ\chi appears as the even-odd component of the super-curvature form

(1)F (1,1)(ψ¯Γ aχ)e a F_{(1,1)} \;\propto\; \left(\overline{\psi} \Gamma_a \chi\right) \wedge e^a

(where (e a,ψ α)(e^a, \psi^\alpha) is the super vielbein). This is (Witten 86 (8), Bonora-Pasti-Tonin 87, below (11), Bonora-Bregola-Lechner-Pasti-Tonin 87, (2.27)).

Compactification to the point

The KK-compactification of D=10D=10 super-Yang-Mills to the point is a theory whose fields are simply elements of the gauge Lie algebra, hence matrices if we have a matrix Lie algebra. The theory defined by this reduction is called the IKKT matrix model.


On scattering amplitudes in pure spinor-formalism:

Last revised on March 10, 2024 at 14:36:04. See the history of this page for a list of all contributions to it.