arXiv subjects

Shotaro Shiba

Publications and source records attributed to Shotaro Shiba.

21 records · Page 2Linked to original sources

arXiv2009

Lorentzian Lie (3-)algebra and toroidal compactification of M/string theory

We construct a class of Lie 3-algebras with an arbitrary number of pairs of generators with Lorentzian signature metric. Some examples are given and corresponding BLG models are studied. We show that such a system in general describes a supersymmetric massive vector multiplets after the ghost fields are Higgsed. Simple systems with nontrivial interaction are realized by infinite dimensional Lie 3-algebras associated with the loop algebras. The massive fields are then naturally identified with the Kaluza-Klein modes by the toroidal compactification triggered by the ghost fields. For example, Dp-brane with an (infinite dimensional) affine Lie algebra symmetry $\hat g$ can be identified with D(p+1)-brane with gauge symmetry $g$.

hep-th↗

arXiv2008

Truncated Nambu-Poisson Bracket and Entropy Formula for Multiple Membranes

We show that there exists a cut-off version of Nambu-Poisson bracket which defines a finite dimensional Lie 3-algebra. The algebra still satisfies the fundamental identity and thus produces N=8 supersymmetric BLG type equation of motion for multiple M2 branes. By counting the number of the moduli and the degree of freedom, we derive an entropy formula which scales as N^{3/2} as expected for the multiple M2 branes.

hep-th↗

arXiv2008

M5-brane in three-form flux and multiple M2-branes

We investigate the Bagger-Lambert-Gustavsson model associated with the Nambu-Poisson algebra as a theory describing a single M5-brane. We argue that the model is a gauge theory associated with the volume-preserving diffeomorphism in the three-dimenisonal internal space. We derive gauge transformations, actions, supersymmetry transformations, and equations of motions in terms of six-dimensional fields. The equations of motions are written in gauge-covariant form, and the equations for tensor fields have manifest self-dual structure. We demonstrate that the double dimensional reduction of the model reproduces the non-commutative U(1) gauge theory on a D4-brane with a small non-commutativity parameter. We establish relations between parameters in the BLG model and those in M-theory. This shows that the model describes an M5-brane in a large C-field background.

hep-th↗