nLab
D=10 super Yang-Mills theory

Contents

Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Quantum field theory

Contents

Idea

super Yang-Mills theory in spacetime dimension 10.

Properties

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.

References

Last revised on July 11, 2019 at 12:38:13. See the history of this page for a list of all contributions to it.