Supergravity currents and linearized interactions for Matrix Theory configurations with fermionic backgrounds

TL;DR

This paper calculates one-loop long-range interactions in matrix theory with fermionic backgrounds, matching supergravity predictions and deriving key currents for arbitrary configurations, advancing the understanding of M-theory dynamics.

Contribution

It generalizes previous matrix theory interaction calculations by including fermionic backgrounds and derives explicit expressions for supergravity currents in arbitrary configurations.

Findings

Interaction potentials match supergravity predictions at 1/r^7 and 1/r^8

Derived general expressions for stress tensor, membrane and 5-brane currents including fermionic effects

Proposed an explicit matrix theory formulation in arbitrary backgrounds

Abstract

The leading terms in the long-range interaction potential between an arbitrary pair of matrix theory objects are calculated at one-loop order. This result generalizes previous calculations by including arbitrary fermionic background field configurations. The interaction potential at orders 1/r^7 and 1/r^8 is shown to correspond precisely with the leading terms expected from linearized supergravity interactions between arbitrary objects in M-theory. General expressions for the stress tensor, membrane current and 5-brane current of an arbitrary matrix configuration are derived, including fermionic contributions. Supergravity effects which are correctly reproduced include membrane/5-brane interactions, 0-brane/6-brane interactions, supercurrent/supercurrent interactions and the spin contributions to moments of the supergravity currents. The matrix theory description of the supergravity stress tensor, membrane current and 5-brane current are used to propose an explicit formulation of matrix theory in an arbitrary background metric and 3-form field.