Higher-derivative 3-algebras

TL;DR

This paper derives higher-derivative corrections to Lorentzian 3-algebra theories from N=8 supersymmetric Yang-Mills theory on D2-branes, expressing corrections in terms of intrinsic 3-algebra quantities and exploring their relevance.

Contribution

It introduces a method to incorporate higher-derivative corrections into Lorentzian 3-algebra theories derived from D2-branes, emphasizing intrinsic algebraic structures.

Findings

Corrections are expressed via 3-bracket and covariant derivatives.

Analysis includes both bosonic and fermionic terms.

Conjecture on relevance to Euclidean 3-algebra theories.

Abstract

Starting with the N=8 supersymmetric Yang-Mills theory on D2-branes and incorporating higher-derivative corrections to lowest nontrivial order, we perform a duality to derive the Lorentzian 3-algebra theory along with a set of derivative corrections. We find that these corrections can be expressed entirely in terms of intrinsic 3-algebra quantities: the 3-bracket and covariant derivatives. Our analysis is performed for both bosonic and fermionic terms. We conjecture that the derivative corrections we obtain are relevant for Euclidean 3-algebra theories as well.