New E77 invariants and amplitudes

TL;DR

This paper introduces new E7 invariants for supergravity amplitude studies, revealing their limitations with UV divergences and connecting them to D3 brane models, thus shedding light on supergravity UV behavior.

Contribution

It constructs novel four-linear E7 invariants for supergravity amplitudes and analyzes their compatibility with UV divergences, extending understanding of duality invariants.

Findings

New E7 invariants generalize the Cartan quartic invariant.

Invariants are inconsistent with expected UV divergent amplitudes.

Degeneration to U(1) reproduces known D3 brane deformation sources.

Abstract

We construct a new class of manifest E77 duality invariants, which generalize the Cartan quartic invariant, familiar from studies of the black hole entropy. The new ones, being four-linear, are designed for studies of the four-vector amplitudes and to be used, upon supersymmetrization, as initial sources of deformation for the non-linear higher-derivative generalizations of the linear twisted self-duality condition. We show, however, that the new invariants are inconsistent with the expected UV divergent amplitudes in extended supergravities with non-degenerate duality groups of type E7. When E77 degenerates into U(1) the new invariants reproduce the recently discovered source of deformation for the Born-Infeld duality invariant model with higher derivatives relevant to UV divergences of the D3 brane action. These facts may explain the UV properties of perturbative supergravity.