Worldsheet description of a massive type IIA superstring in 10D

TL;DR

This paper develops a worldsheet description of a massive type IIA superstring in 10D by deriving it from a massive M2-brane with a genus one light cone diagram, connecting it to Romans supergravity and M9-branes.

Contribution

It introduces a novel formulation of a massive superstring as a dimensional reduction of a massive M2-brane with specific boundary conditions and topological terms, linking it to M9-branes and Romans mass.

Findings

Derived a worldsheet Hamiltonian for a massive type IIA superstring.

Established a relation between Romans mass and M2-brane moduli.

Showed the presence of a non-zero Hamiltonian shift due to topological terms.

Abstract

We construct, following \cite{mpgm14,mpgm17}, a massive M2-brane (supermembrane) as the limit of a genus two M2-brane that becomes a twice punctured Riemann surface with particular boundary conditions on the fields defined on the punctures. The target space is $M_9\times LCD$, where $LCD$ is a genus one light cone diagram. It contains mass terms and a topological term associated with the non-triviality of the target surface that, at low energies, can be associated with the presence of a cosmological constant. We show that the supergravity background of the M2-brane considered in this formulation requires the presence of M9-branes acting as sources. They correspond to the 11D uplift of the characteristic D8's of Romans supergravity. To this end, we explicitly show that some of the background singularities of the massive M2-brane can be reproduced by the M9-branes found by \cite{Bergshoeff}. This establishes a relation between the Romans mass and the moduli of the massive M2-brane. When dimensionally reduced, we obtain a worldsheet Hamiltonian of a N=2 type IIA closed superstring in 10D. We denote it \textit{massive} string. The corresponding \textit{massive} string inherits a non-vanishing constant term from the topological massive M2-brane that shifts the Hamiltonian. The non-vanishing parameter is related to the non-trivial structure of the massive M2-brane background and it can be related to the Romans mass term. It also contains a modified tension due to the non-trivial dependence on the moduli and on the punctures associated with the target torus.