it may no longer be possible to view a gauge symmetry as what you get from “gauging” a global symmetry through introducing space-time dependence.

A possibility of this generalization was already suggested [@Ho:2001as] for even-dimensional spherical brane configurations in the matrix theory. For example, for the fuzzy-$S^4$ configuration of $n$ D4-branes, the algebra of functions on the 4-dimensional base space is non-associative, but there is an associative algebra for gauge transformations. For large $n$, the gauge symmetry algebra is approximately that of a $U(n)$-bundle (or equivalently a fuzzy-$S^2$ bundle) over $S^4$ [@Ho:2001as].

Another example is the low energy effective theory of a D3-brane in large R-R 2-form field background [@Ho:2013opa]. This theory is S-dual to the noncommutative gauge theory for a D3-brane in large NS-NS $B$-field background. The gauge symmetry to all orders in the dual theory is not given by the noncommutative gauge symmetry, but is characterized by a bracket $\{\cdot, \cdot\}_{**}$ which defines a non-associative algebra on the base space [@Ho:2013opa]. (The gauge symmetry algebra is of course associative.)

In this paper, we will show that the gauge symmetry of space-time diffeomorphism is also an example of the generalized gauge symmetry. Accordingly, a class of gravity theories can be interpreted as YM theories. Generically, these theories include a graviton, a dilaton and an anti-symmetric tensor. We will point out that the connection between Yang-Mills theory and gravity (through the color-kinematics duality) is manifest at tree level in 3-point amplitudes.

Attempts to interpret gravity as a gauge theory have a long history since the works of Utiyama [@Utiyama], Kibble [@Kibble] and Sciama [@Sciama]. It is well known that General Relativity (GR) can be rewritten as the Chern-Simons theory in 3 dimensions [@Witten:1988hc], and a YM-like theory in 4 dimensions [@MacDowell:1977jt; @Stelle-West], as well as higher dimensions [@Vasiliev:2001wa]. The vielbein and the connec