Aspects of U-duality in BLG models with Lorentzian metric 3-algebras

TL;DR

This paper explores the relationship between U-duality, Lorentzian 3-algebras, and D-brane actions, revealing how moduli parameters and dualities are encoded in the algebraic structure of BLG models.

Contribution

It establishes a detailed connection between U-duality, super Yang-Mills parameters, and Lorentzian 3-algebra moduli, extending the understanding of BLG models with Lorentzian metrics.

Findings

Derived the relation between super Yang-Mills coupling and 3-algebra moduli.

Showed SL(2,Z) duality as rotation of VEVs in the algebra.

Identified moduli parameters as deformation parameters of 3-algebras.

Abstract

In our previous paper, it was shown that BLG model based on a Lorentzian metric 3-algebra gives Dp-brane action whose worldvolume is compactified on torus T^d (d=p-2). Here the 3-algebra was a generalized one with d+1 pairs of Lorentzian metric generators and expressed in terms of a loop algebra with central extensions. In this paper, we derive the precise relation between the coupling constant of the super Yang-Mills, the moduli of T^d and some R-R flux with VEV's of ghost fields associated with Lorentzian metric generators. In particular, for d=1, we derive the Yang-Mills action with theta term and show that SL(2,Z) Montonen-Olive duality is realized as the rotation of two VEV's. Furthermore, some moduli parameters such as NS-NS 2-form flux are identified as the deformation parameters of the 3-algebras. By combining them, we recover most of the moduli parameters which are required by U-duality symmetry.