Standard Model as a Double Field Theory

We show that, without any extra physical degree introduced, the Standard Model can be readily reformulated as a Double Field Theory. Consequently, the Standard Model can couple to an arbitrary stringy gravitational background in an $\mathbf{O}(4,4)$ T-duality covariant manner and manifest two independent local Lorentz symmetries, $\mathbf{Spin}(1,3)\times\mathbf{Spin}(3,1)$. While the diagonal gauge fixing of the twofold spin groups leads to the conventional formulation on the flat Minkowskian background, the enhanced symmetry makes the Standard Model more rigid, and also stringy, than it appeared. The CP violating $\theta$-term may no longer be allowed by the symmetry, and hence the strong CP problem is solved. There are now stronger constraints imposed on the possible higher order corrections. We speculate that the quarks and the leptons may possibly belong to the two different spin classes.