ar X iv : 0 80 6 . 16 14 v 1 [ he p - th ] 1 0 Ju n 20 08 Finite - gap systems , tri - supersymmetry and self - isospectrality

ar X iv : 0 80 6 . 16 14 v 2 [ he p - th ] 1 8 Ju n 20 08 Finite - gap systems , tri - supersymmetry and self - isospectrality

We show that an n-gap periodic quantum system with parity-even smooth potential admits 2n − 1 isospectral super-extensions. Each is described by a tri-supersymmetry that originates from a higher-order differential operator of the Lax pair and two-term nonsingular decompositions of it; its local part corresponds to a spontaneously partially broken centrally extended nonlinear N = 4 supersymmetry...

ar X iv : 0 80 6 . 16 14 v 3 [ he p - th ] 2 4 O ct 2 00 8 Finite - gap systems , tri - supersymmetry and self - isospectrality

We show that an n-gap periodic quantum system with parity-even smooth potential admits 2n − 1 isospectral super-extensions. Each is described by a tri-supersymmetry that originates from a higher-order differential operator of the Lax pair and two-term nonsingular decompositions of it; its local part corresponds to a spontaneously partially broken centrally extended nonlinear N = 4 supersymmetry...

ar X iv : 0 80 6 . 22 70 v 2 [ he p - th ] 2 0 Ju n 20 08 An N = 1 Superfield Action for M 2 branes

We present an octonionic N = 1 superfield action that reproduces in components the action of Bagger and Lambert for M2 branes. By giving an expectation value to one of the scalars we obtain the maximally supersymmetric superfield action for D2 branes.

ar X iv : 0 80 6 . 46 34 v 1 [ he p - ex ] 3 0 Ju n 20 08 LPHE 2008 - 05 June 30 , 2008 B 0 – B 0 MIXING

ar X iv : 0 80 6 . 27 19 v 1 [ m at h . G N ] 1 7 Ju n 20 08 A property of C p [ 0 , 1 ]

We prove that for every finite dimensional compact metric space X there is an open continuous linear surjection from Cp[0, 1] onto Cp(X). The proof makes use of embeddings introduced by Kolmogorov and Sternfeld in connection with Hilbert’s