Reflection branes, bordisms, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>U</mml:mi> </mml:math> dualities

The U-dualities of maximally supersymmetric nonchiral supergravity (SUGRA) theories lead to strong constraints on the nonperturbative structure of quantum gravity. In this paper, we determine spin- and pin-lifts of these dualities, which extend this action to fermionic degrees of freedom. Among other things, this allows us to access nonsupersymmetric sectors of these low energy effective field theories in which bosonic and fermionic degrees of freedom are treated differently. We use this refinement of the duality groups, in tandem with the Swampland cobordism conjecture, to predict new codimension-two branes. These are a natural generalization of the recently discovered R7-branes of type II string theories. The first bordism groups for Spin-twisted duality bundles that follow directly from the Abelianization of the duality groups. Viewing the SUGRA theory as the low energy limit of a toroidal compactification of M-theory, winding around these codimension-two defects enacts a reflection around one of the torus directions, which, in the effective field theory, appears as a charge conjugation symmetry. We establish some basic properties of such branes, including determining Bogomol’nyi-Prasad-Sommerfield objects which can end on it, as well as braiding rules and bound states realized by multiple reflection branes.