Extended DBI and its generalizations from graded soft theorems

TL;DR

This paper introduces extended DBI theories that interpolate between known models, revealing new symmetries and soft theorems, and demonstrates their on-shell constructibility and generalizations like 2-scale DBI theory.

Contribution

It uncovers symmetries and soft theorems in extended DBI theories, establishing their on-shell constructibility and proposing new generalized models.

Findings

Revealed new graded soft theorems for extended DBI.

Proved on-shell constructibility of the full extended DBI theory.

Introduced 2-scale DBI as a generalization with preserved constructibility.

Abstract

We analyze a theory known as extended DBI, which interpolates between DBI and the $U(N)\times U(N)/U(N)$ non-linear sigma model and represents a nontrivial example of theories with mixed power counting. We discuss symmetries of the action and their geometrical origin; the special case of SU(2) extended DBI theory is treated in great detail. The revealed symmetries lead to a new type of graded soft theorem that allows us to prove on-shell constructibility of the tree-level S-matrix. It turns out that the on-shell constructibility of the full extended DBI remains valid, even if its DBI sub-theory is modified in such a way to preserve its own on-shell constructibility. We thus propose a slight generalization of the DBI sub-theory, which we call 2-scale DBI theory. Gluing it back to the rest of the extended DBI theory gives a new set of on-shell reconstructible theories -- the 2-scale extended DBI theory and its descendants. The uniqueness of the parent theory is confirmed by the bottom-up approach that uses on-shell amplitude methods exclusively.