  We present high-statistics results for the isovector and flavor diagonal
charges of the proton using 11 ensembles of 2+1+1 flavor HISQ fermions. In the
isospin symmetric limit, results for the neutron are given by the $u
\leftrightarrow d$ interchange. A chiral-continuum fit with leading order
corrections was made to extract the connected and disconnected contributions in
the continuum limit and at $M_\pi=135$ MeV. All results are given in the
$\overline{MS}$ scheme at 2 GeV. The isovector charges, $g_A^{u-d} =
1.218(25)(30)$, $g_S^{u-d} = 1.022(80)(60) $ and $g_T^{u-d} = 0.989(32)(10)$,
are used to obtain low-energy constraints on novel scalar and tensor
interactions, $\epsilon_{S}$ and $\epsilon_{T}$, at the TeV scale. The flavor
diagonal axial charges are: $g_A^u \equiv \Delta u \equiv \langle 1
\rangle_{\Delta u^+} = 0.777(25)(30)$, $g_A^d \equiv \Delta d \equiv \langle 1
\rangle_{\Delta d^+} = -0.438(18)(30)$, and $g_A^s \equiv \Delta s \equiv
\langle 1 \rangle_{\Delta s^+} = -0.053(8)$. Their sum gives the total quark
contribution to the proton spin, $\sum_{q=u,d,s} (\frac{1}{2} \Delta q) =
0.143(31)(36)$. This result is in good agreement with the recent COMPASS
analysis $0.13 < \frac{1}{2} \Delta \Sigma < 0.18$. Implications of results for
the flavor diagonal tensor charges, $g_T^u = 0.784(28)(10)$, $g_T^d =
-0.204(11)(10)$ and $g_T^s = -0.0027(16)$ for constraining the quark electric
dipole moments and their contributions to the neutron electric dipole moment
are discussed. These flavor diagonal charges also give the strength of the
interaction of dark matter with nucleons via axial and tensor mediators.
