We present affine Lie algebras generated by the supercovariant derivatives and the supersymmetry generators for the left and right moving modes in the doubled space. Chirality is manifest in our doubled space as well as the T-duality symmetry. We pre
sent gauge invariant bosonic and superstring actions preserving the two-dimensional diffeomorphism invariance and the kappa-symmetry where doubled spacetime coordinates are chiral fields. The doubled space becomes the usual space by dimensional reduction constraints.
A superspace with manifest T-duality including Ramond-Ramond gauge fields is presented. The superspace is defined by the double nondegenerate super-Poincare algebras where Ramond-Ramond charges are introduced by central extension. This formalism allo
ws a simple treatment that all the supergravity multiplets are in a vielbein superfield and all torsions with dimension 1 and less are trivial. A Green-Schwarz superstring action is also presented where the Wess-Zumino term is given in a bilinear form of local currents. Equations of motion are separated into left and right modes in a suitable gauge.
We consider the dynamics of the motion of a particle of mass M and spin J in AdS_3. The study reveals the presence of different dynamical sectors depending on the relative values of M, J and the AdS_3 radius R. For the subcritical M^2 R^2-J^2 >0 and
supercritical M^2 R^2-J^2<0 cases, it is seen that the equations of motion give the geodesics of AdS_3. For the critical case M^2R^2=J^2 there exist extra gauge transformations which further reduce the physical degrees of freedom, and the motion corresponds to the geodesics of AdS_2. This result should be useful in the holographic interpretation of the entanglement entropy for 2d conformal field theories with gravitational anomalies.
A superspace formulation of type II superstring background with manifest T-duality symmetry is presented. This manifestly T-dual formulation is constructed in a space spanned by two sets of nondegenerate super-Poincare algebra. Supertorsion constrain
ts are obtained from consistency of the kappa-symmetric Virasoro constraints. All superconnections and vielbein fields are solved in terms of a prepotential which is one of the vielbein components. AdS5xS5 background is explained in this formulation.
We reconsider a model of two relativistic particles interacting via a multiplicative potential, as an example of a simple dynamical system with sectors, or branches, with different dynamics and degrees of freedom.The presence or absence of sectors de
pends on the values of rest masses. Some aspects of the canonical quantization are described. The model could be interpreted as a bigravity model in one dimension.
We present M5 algebra to derive Courant brackets of the generalized geometry of $Toplus Lambda^2T^ast oplus Lambda^5T^ast$: The Courant bracket generates the generalized diffeomorphism including gauge transformations of three and six form gauge field
s. The Dirac bracket between selfdual gauge fields on a M5-brane gives a $C^{[3]}$-twisted contribution to the Courant brackets. For M-theory compactified on a five dimensional torus the U-duality symmetry is SO(5,5) and the M5 algebra basis is in the 16-dimensional spinor representation. The M5 worldvolume diffeomorphism constraints can be written as bilinear forms of the basis and transform as a SO(5,5) vector. We also present an extended space spanned by the 16-dimensional coordinates with section conditions determined from the M5 worldvolume diffeomorphism constraints.
We study all the symmetries of the free Schrodinger equation in the non-commutative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean
boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schrodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.
We examine AdS Galileon Lagrangians using the method of non-linear realization. By contractions 1) flat curvature limit and 2) non-relativistic brane algebra limit and 3) (1)+(2) limits we obtain DBI, Newton-Hoock and Galilean Galileons respectively.
We make clear how these Lagrangians appear as invariant 4-forms and/or pseudo-invariant Wess-Zumino terms using Maurer-Cartan equations on the coset $G/SO(3,1)$. We show the equations of motion are written in terms of the MC forms only and explain why the inverse Higgs condition is obtained as the equation of motion for all cases. The supersymmetric extension is also examined using SU(2,2|1)/(SO(3,1)x U(1)) supercoset and five WZ forms are constructed. They are reduced to the corresponding five Galileon WZ forms in the bosonic limit and are candidates of for supersymmetric Galileon.
We show how the SL(5) duality in M-theory is explained from a canonical analysis of M2-brane mechanics. Diffeomorphism constraints for a M2-brane coupled to supergravity background in d=4 are reformulated in a SL(5) covariant form, in which spatial d
iffeomorphism constraints are recast into a SL(5) vector and the generalized metric in the Hamiltonian constraint is quartic in the SL(5) generalized vielbein. The Hamiltonian for a M2 brane has the SL(5) duality symmetry in a background dependent gauge.
We consider the non-linear realizations of the Poincare group for p-branes with local subgroup SO(1,p)*SO(D-(p+1)). The Nambu-Goto p-brane action is constructed using the Maurer Cartan forms of the unbroken translations. We perform a throughout phase
space analysis of the action and show that it leads to the canonical action of a p-brane. We also construct some higher order derivative terms of the effective p-brane action using the MC forms of the broken Lorentz transformations.
