Twelve-Dimensional Supersymmetric Gauge Theory as the Large N Limit

Starting with the ordinary ten-dimensional supersymmetric Yang-Mills theory for the gauge group U(N), we obtain a twelve-dimensional supersymmetric gauge theory as the large N limit. The two symplectic canonical coordinates parametrizing the unitary N X N matrices for U(N) are identified with the extra coordinates in twelve dimensions in the $N\to\infty$ limit. Applying further a strong/weak duality, we get the `decompactified' twelve-dimensional theory. The resulting twelve-dimensional theory has peculiar gauge symmetry which is compatible also with supersymmetry. We also establish a corresponding new superspace formulation with the extra coordinates. By performing a dimensional reduction from twelve dimensions directly into three dimensions, we see that the Poisson bracket terms which are needed for identification with supermembrane action arises naturally. This result indicates an universal duality mechanism that the 't Hooft limit of an arbitrary supersymmetric theory promotes the original supersymmetric theory in (D-1,1) dimensions into a theory in (D,2) dimensions with an additional pair of space-time coordinates. This also indicates interesting dualities between supermembrane theory, type IIA superstring with D0-branes, and the recently-discovered twelve-dimensional supersymmetric theories.Comment: 14 pages, latex, no figure

Supergravity in 10 + 2 Dimensions as Consistent Background for Superstring

We present a consistent theory of N=1 supergravity in twelve-dimensions with the signature (10,2). Even though the formulation uses two null vectors violating the manifest Lorentz covariance, all the superspace Bianchi identities are satisfied. After a simple dimensional reduction to ten-dimensions, this theory reproduces the N=1 supergravity in ten-dimensions, supporting the consistency of the system. We also show that our supergravity can be the consistent backgrounds for heterotic or type-I superstring in Green-Schwarz formulation, by confirming the kappa-invariance of the total action. This theory is supposed to be the purely N=1 supergravity sector for the field theory limit of the recently predicted F-theory in twelve-dimensions.Comment: An amendment in eq.(3.3a), a paragraph added in pages 6 - 7 with new eq.(3.12), other minor changes like wording and updated references, 14 pages, latex, no figure

Supergravity Theories in D≥12D\ge 12 Coupled to Super p-Branes

We construct supergravity theories in twelve and thirteen dimensions with the respective signatures (10,2) and (11,2) with some technical details. Starting with N=1 supergravity in 10+2 dimensions coupled to Green-Schwarz superstring, we give N=2 chiral supergravity in 10+2 dimensions with its couplings to super (2+2)-brane. We also build an N=1 supergravity in 11+2 dimensions, coupled to supermembrane. All of these formulations utilize scalar (super)fields intact under supersymmetry, replacing the null-vectors introduced in their original formulations. This method makes all the equations SO(10,2) or SO(11,2) Lorentz covariant, up to modified Lorentz generators. We inspect the internal consistency of these formulations, in particular with the usage of the modified Lorentz generators for the extra coordinates.Comment: 47 pages, latex, minor corrections of typos, mismatched indices, updated references, et

Two-scale momentum theory for very large wind farms

A new theoretical approach is proposed to predict a practical upper limit to the efficiency of a very large wind farm. The new theory suggests that the efficiency of ideal turbines in an ideal very large wind farm depends primarily on a non-dimensional parameter λ/Cf0, where λ is the ratio of the rotor swept area to the land area (for each turbine) and Cf0 is a natural friction coefficient observed before constructing the farm. When X/Cf approaches to zero, the new theory goes back to the classical actuator disc theory, yielding the well-known Betz limit. When λ/Cf0 increases to a large value, the maximum power coefficient of each turbine reduces whilst a normalised power density of the farm increases asymptotically to an upper limit. A CFD analysis of an infinitely large wind farm with 'aligned' and 'displaced' array configurations is also presented to validate a key assumption used in the new theory

Lagrangian and Covariant Field Equations for Supersymmetric Yang-Mills Theory in 12D

We present a lagrangian formulation for recently-proposed supersymmetric Yang-Mills theory in twelve dimensions. The field content of our multiplet has an additional auxiliary vector field in the adjoint representation. The usual Yang-Mills field strength is modified by a Chern-Simons form containing this auxiliary vector field. This formulation needs no constraint imposed on the component field from outside, and a constraint on the Yang-Mills field is generated as the field equation of the auxiliary vector field. The invariance check of the action is also performed without any reference to constraints by hand. Even though the total lagrangian takes a simple form, it has several highly non-trivial extra symmetries. We couple this twelve-dimensional supersymmetric Yang-Mills background to Green-Schwarz superstring, and confirm fermionic kappa-invariance. As another improvement of this theory, we present a set of fully Lorentz-covariant and supercovariant field equations with no use of null-vectors. This system has an additional scalar field, whose gradient plays a role of the null-vector. This system exhibits spontaneous breaking of the original Lorentz symmetry SO(10,2) for twelve-dimensions down to SO(9,1) for ten-dimensions.Comment: 14 pages, latex, no figure