# Counting spinning dyons in maximal supergravity: The Hodge-elliptic genus for tori

## TL;DR

This paper refines the counting of spinning 1/8-BPS states in M-theory on T^4 x T^2, connecting physical state counts with advanced mathematical invariants related to Donaldson-Thomas theory.

## Contribution

It introduces a refined counting method for spinning BPS states in M-theory compactified on T^4 x T^2, linking physics with recent mathematical invariants.

## Key findings

- Refined count of 1/8-BPS states in M-theory on T^4 x T^2
- Predictions for motivic curve counts related to angular momenta
- Connections established between physical state counts and Donaldson-Thomas invariants

## Abstract

We consider $M$-theory compactified on $T^4 \times T^2$ and describe the count of spinning $1/8$-BPS states. This refines the classic count of Maldacena-Moore-Strominger in the physics literature and the recent mathematical work of Bryan-Oberdieck-Pandharipande-Yin, which studied reduced Donaldson-Thomas invariants of abelian surfaces and threefolds. As in previous work on $K3 \times T^2$ compactification, we track angular momenta under both the $SU(2)_L$ and $SU(2)_R$ factors in the 5d little group, providing predictions for the relevant motivic curve counts.