How to Falsify String Theory at a Collider

The string landscape accommodates a broad range of possible effective field theories. This poses a challenge for extracting verifiable predictions as well as falsifiable signatures of string theory. Motivated by these considerations, in this work we observe that all known stringy Standard Models support only low-dimensional representations of the gauge group. While it is in principle possible to produce contrived models with higher-dimensional representations, these generically appear in a tower of states with lighter ones in lower-dimensional representations, i.e., not in isolation. With this in mind, we consider the phenomenologically well-motivated scenario given by adding a single Majorana field in a real, $n$-dimensional representation of $SU(2)_L$ with $n \geq 5$ \textit{and nothing else}. This scenario is not realized in any known string construction, and we conjecture that this is true of string theory in general. Detection of this scenario would thus amount to falsifying the (known) string landscape. We recast existing LHC searches for new electroweak states to extract updated bounds on this class of scenarios. Improved limits from future colliders and dark matter detection experiments provide additional routes to potentially falsifying string theory.