Fluxes, Twisted Tori, Monodromy and $U(1)$ supermembranes

Abstract: In this talk I will discuss about recent advances in the characterization of Supermembrane Theory with constant fluxes. I will show that the $D=11$ Supermembrane theory (M2-brane) compactified on a $M_9\times T^2$ target space, with constant fluxes $C_\pm$ naturally incorporates the geometrical structure of a twisted torus. Its global formulation corresponds to a twisted torus bundle fibered over the world volume of the supermembrane. This structure allows to understand better its effective limit described by the Type II Gauged supergravities. The spectrum of the theory is purely discrete, with finite multiplicity. The theory is invariant under symplectomorphisms connected and non-connected to the identity, a result relevant to guarantee the U-dual invariance of the theory. The Hamiltonian of the theory exhibits interesting new $U(1)$ gauge and global symmetries on the world volume induced by the symplectomorphism transformations. I will discuss also its supersymmetric algebra. The zero modes decouple from the nonzero ones. The nonzero mode algebra corresponds to a massive superalgebra that preserves either $1/2$ or $1/4$ of the original supersymmetry depending on the state considered.

This talk is based on:

1.Fluxes, Twisted tori, Monodromy and $U(1)$ Supermembranes. arXiv: 2005.06397 By MPGM, Camilo Las Heras, Pablo León, Joselen Peña and Alvaro Restuccia.

2. M2-branes in a constant flux background. Physics Letters B, 797, 2019. By MPGM, Camilo Las Heras, Pablo León, Joselen Peña and Alvaro Restuccia.

mathematical physics

Audience: researchers in the topic

( slides )

Seminario de Geometría y Física - Matemática UCN-USP