  This thesis is devoted to the study of dynamical symmetry enhancement of
black hole horizons in string theory. In particular, we consider supersymmetric
horizons in the low energy limit of string theory known as supergravity and we
prove the $\textit{horizon conjecture}$ for a number of supergravity theories.
We first give important examples of symmetry enhancement in $D=4$ and the
mathematical preliminaries required for the analysis. Type IIA supergravity is
the low energy limit of $D=10$ IIA string theory, but also the dimensional
reduction of $D=11$ supergravity which itself the low energy limit of M-theory.
We prove that Killing horizons in IIA supergravity with compact spatial
sections preserve an even number of supersymmetries. By analyzing the global
properties of the Killing spinors, we prove that the near-horizon geometries
undergo a supersymmetry enhancement. This follows from a set of generalized
Lichnerowicz-type theorems we establish, together with an index theory
argument. We also show that the symmetry algebra of horizons with non-trivial
fluxes includes an $\mathfrak{sl}(2, \mathbb{R})$ subalgebra. As an
intermediate step in the proof, we also demonstrate new Lichnerowicz type
theorems for spin bundle connections whose holonomy is contained in a general
linear group. We prove the same result for Roman's Massive IIA supergravity. We
also consider the near-horizon geometry of supersymmetric extremal black holes
in un-gauged and gauged 5-dimensional supergravity, coupled to abelian vector
multiplets. We consider important examples in $D=5$ such as the BMPV and
supersymmetric black ring solution, and investigate the near-horizon geometry
to show the enhancement of the symmetry algebra of the Killing vectors. We
repeat a similar analysis as above to prove the horizon conjecture. We also
investigate the conditions on the geometry of the spatial horizon section
$\cal{S}$.
