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After introducing a d=10 pure spinor $lambda^alpha$, the Virasoro constraint $partial x^m partial x_m =0$ can be replaced by the twistor-like constraint $partial x^m (gamma_m lambda)_alpha=0$. Quantizing this twistor-like constraint leads to the pure spinor formalism for the superstring where the fermionic superspace variables $theta^alpha$ and their conjugate momenta come from the ghosts and antighosts of the twistor-like constraint.
We describe D=4 twistorial membrane in terms of two twistorial three-dimensional world volume fields. We start with the D-dimensional p-brane generalizations of two phase space string formulations: the one with $p+1$ vectorial fourmomenta, and the se
We consider a formulation of N=1 D=3,4 and 6 superparticle mechanics, which is manifestly supersymmetric on the worldline and in the target superspace. For the construction of the action we use only geometrical objects that characterize the embedding
After a short introduction to Matrix theory, we explain how can one generalize matrix models to describe toroidal compactifications of M-theory and the heterotic vacua with 16 supercharges. This allows us, for the first time in history, to derive the
We consider possible discretizations for a gauge-fixed Green-Schwarz action of Type IIB superstring. We use them for measuring the action, from which we extract the cusp anomalous dimension of planar $mathcal{N}=4$ SYM as derived from AdS/CFT, as wel
The algebra of spacetime supersymmetry generators in the RNS formalism for the superstring closes only up to a picture-changing operation. After adding non-minimal variables and working in the large Hilbert space, the algebra closes without picture-c