Using worldsheet Hamiltonian methods we derive a charge algebra which generalizes the Courant bracket to include fluxes of general index type. This is achieved by coupling a bi-vector to the Hamiltonian of the Polyakov model. This bracket is useful to describe so-called non-geometric backgrounds and has been discussed in the mathematics literature by Dmitry Roytenberg.

In this work we classify the subalgebras satisfied by non-geometric Q-fluxes in type IIB orientifolds on T/(Z2 × Z2) with three moduli (S, T, U). We find that there are five subalgebras compatible with the symmetries, each one leading to a characteristic flux-induced superpotential. Working in the 4-dimensional effective supergravity we obtain families of supersymmetric AdS4 vacua with all modu...

It is shown that geometric phase in non-relativistic quantum mechanics is not Galilean invariant. Typeset using REVTEX E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] 1 Consider, in the context of non-relativistic quantum mechanics, a system undergoing cyclic evolution during the interval [0, T ], so that its final and...