New Exceptional Effective Field Theories in de Sitter Space from Generalized Energy Conservation

We discover a surprising relationship between exceptional effective field theories (EFTs) in de Sitter space and a notion of (GEC) of an <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>S</a:mi> </a:mrow> </a:math> matrix defined in an extended Poincaré patch of four-dimensional de Sitter. By demanding that such an <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mi>S</c:mi> </c:mrow> </c:math> matrix has support only when the total energies of in and out states are equal, we constrain the coupling constants in theories of self-interacting scalars living in the exceptional series of de Sitter representations. We rediscover the theories of Dirac-Born-Infeld (DBI) and special Galileon, and when increasing the conformal dimension, we find evidence for new exceptional theories where the four-point scalar self-interactions are uniquely fixed in terms of a single coupling constant. We conjecture that for each integer conformal dimension <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi mathvariant="normal">Δ</e:mi> <e:mo>≥</e:mo> <e:mn>4</e:mn> </e:math> , there is at least one exceptional EFT that can be entirely fixed by GEC.