Scalar Love numbers and Love symmetries of 5-dimensional Myers-Perry black holes

The near-zone ``Love'' symmetry resolves the naturalness issue of black hole Love number vanishing with $\text{SL}\left(2,\mathbb{R}\right)$ representation theory. Here, we generalize this proposal to $5$-dimensional asymptotically flat and doubly spinning (Myers-Perry) black holes. We consider the scalar response of Myers-Perry black holes and extract its static scalar Love numbers. In agreement with the naturalness arguments, these Love numbers are, in general, non-zero and exhibit logarithmic running unless certain resonant conditions are met; these conditions include new cases with no previously known analogs. We show that there exist two near-zone truncations of the equations of motion that exhibit enhanced $\text{SL}\left(2,\mathbb{R}\right)$ Love symmetries that explain the vanishing of the static scalar Love numbers in the resonant cases. These Love symmetries can be interpreted as local $\text{SL}\left(2,\mathbb{R}\right)\times\text{SL}\left(2,\mathbb{R}\right)$ near-zone symmetries spontaneously broken down to global $\text{SL}\left(2,\mathbb{R}\right)\times U\left(1\right)$ symmetries by the periodic identification of the azimuthal angles. We also discover an infinite-dimensional extension of the Love symmetry into $\text{SL}\left(2,\mathbb{R}\right)\ltimes\hat{U}\left(1\right)_{\mathcal{V}}^2$ that contains both Love symmetries as particular subalgebras, along with a family of $\text{SL}\left(2,\mathbb{R}\right)$ subalgebras that reduce to the exact near-horizon Myers-Perry black hole isometries in the extremal limit. Finally, we show that the Love symmetries acquire a geometric interpretation as isometries of subtracted (effective) black hole geometries that preserve the internal structure of the black hole and interpret these non-extremal $\text{SL}\left(2,\mathbb{R}\right)$ structures as remnants of the enhanced isometry of the near-horizon extremal geometries.