Supersymmetric reduced models with a symmetry based on Filippov algebra

Generalizations of the reduced model of super Yang-Mills theory obtained by replacing the Lie algebra structure to Filippov $n$-algebra structures are studied. Conditions for the reduced model actions to be supersymmetric are examined. These models are related with what we call \{cal N}_{min}=2 super $p$-brane actions.Comment: v3: In the previous versions we overlooked that Eq.(3.9) holds more generally, and missed some supersymmetric actions. Those are now included and modifications including a slight change in the title were made accordingly. 1+18 page

Classical and Quantum Nambu Mechanics

The classical and quantum features of Nambu mechanics are analyzed and fundamental issues are resolved. The classical theory is reviewed and developed utilizing varied examples. The quantum theory is discussed in a parallel presentation, and illustrated with detailed specific cases. Quantization is carried out with standard Hilbert space methods. With the proper physical interpretation, obtained by allowing for different time scales on different invariant sectors of a theory, the resulting non-Abelian approach to quantum Nambu mechanics is shown to be fully consistent.Comment: 44 pages, 1 figure, 1 table Minor changes to conform to journal versio

Constructing Self-Dual Strings

We present an ADHMN-like construction which generates self-dual string solutions to the effective M5-brane worldvolume theory from solutions to the Basu-Harvey equation. Our construction finds a natural interpretation in terms of gerbes, which we develop in some detail. We also comment on a possible extension to stacks of multiple M5-branes.Comment: 1+19 pages, presentation improved, minor corrections, published versio

Three-algebra for supermembrane and two-algebra for superstring

While string or Yang-Mills theories are based on Lie algebra or two-algebra structure, recent studies indicate that M-theory may require a one higher, three-algebra structure. Here we construct a covariant action for a supermembrane in eleven dimensions, which is invariant under global supersymmetry, local fermionic symmetry and worldvolume diffeomorphism. Our action is classically on-shell equivalent to the celebrated Bergshoeff-Sezgin-Townsend action. However, the novelty is that we spell the action genuinely in terms of Nambu three-brackets: All the derivatives appear through Nambu brackets and hence it manifests the three-algebra structure. Further the double dimensional reduction of our action gives straightforwardly to a type IIA string action featuring two-algebra. Applying the same method, we also construct a covariant action for type IIB superstring, leading directly to the IKKT matrix model.Comment: 1+15 pages, no figure; Refs added, Accepted for publication in JHE

Taking off the square root of Nambu-Goto action and obtaining Filippov-Lie algebra gauge theory action

We propose a novel prescription to take off the square root of Nambu-Goto action for a p-brane, which generalizes the Brink-Di Vecchia-Howe-Tucker or also known as Polyakov method. With an arbitrary decomposition as d+n=p+1, our resulting action is a modified d-dimensional Polyakov action which is gauged and possesses a Nambu n-bracket squared potential. We first spell out how the (p+1)-dimensional diffeomorphism is realized in the lower dimensional action. Then we discuss a possible gauge fixing of it to a direct product of $d$-dimensional diffeomorphism and n-dimensional volume preserving diffeomorphism. We show that the latter naturally leads to a novel Filippov-Lie n-algebra based gauge theory action in d-dimensions.Comment: 1+13 pages, No figure; Expanded, published version. Title change