Signs and signatures in SL(2) x R+ exceptional field theory: Hull's starred theories from a non-Euclidean generalised metric
Year: 2026
Type: preprint
Abstract: We determine, with every sign kept, which eleven- and ten-dimensional theories the SL(2) x R+ exceptional field theory describes when its generalised metric is not positive definite. For all twelve sign cells we derive the signature and the signs of all bosonic kinetic terms on both sections. The three-form sign on the M-theory section is lambda = epsilon sigma, the IIB circle is spacelike or timelike according to tau = epsilon, and the IIB axion and four-form signs equal sigma. The ExFT duality relation gives a real (anti-)self-dual five-form exactly when epsilon (-1)^t9 = -1, which on the M-theory section reads lambda = -(-1)^t11, in agreement with Hull's three-form sign rule. The four shrinking two-torus limits of Hull that fit this ExFT are reproduced with their circle characters. All statements are checked numerically against eleven- and ten-dimensional supergravity, with the curvature computed from its definition; the check also finds two probable misprints in the internal-derivative part of the published scalar potential (quadratic order). A short methods note. The source archive contains the LaTeX source, all scripts (run_all.sh reproduces every result), their outputs, and the pre-registered plan.
Author: Nguyen, Danny
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214773153