Type IIB parabolic ($p,q$)-strings from M2-branes with fluxes

TL;DR

This paper explores the connection between M2-branes with fluxes on a symplectic torus bundle and type IIB ($p,q$)-strings, revealing how fluxes and monodromies classify bound states and relate to supergravity gauge symmetries.

Contribution

It extends previous work by linking M2-brane flux configurations to type IIB ($p,q$)-strings and analyzes the role of parabolic monodromy in the Hamiltonian formulation.

Findings

Hamiltonian defined via coinvariant modules

Mass operator invariant under coinvariant transformations

($p,q$)-strings classified by parabolic subgroup of SL(2,ℚ)

Abstract

We extend the work of Schwarz [1] to show that bound states of type IIB supersymmetric ($p, q$)-strings on a circle are associated with M2-branes irreducibly wrapped on $T^2$, or equivalently with nontrivial worldvolume fluxes. Beyond this extension we consider the Hamiltonian of an M2-brane with $C_{\pm}$ fluxes formulated on a symplectic torus bundle with monodromy. In particular, we analyze the relevant case when the monodromy is parabolic. We show that the Hamiltonian is defined in terms of the coinvariant module. We also find that the mass operator is invariant under transformations between inequivalent coinvariants. These coinvariants classify the inequivalent classes of twisted torus bundles with nontrivial monodromy for a given flux. We obtain their associated ($p,q$)-strings via double dimensional reduction, which are invariant under a parabolic subgroup of $SL(2,\mathbb{Q})$. This is the origin of the gauge symmetry of the associated gauged supergravity. These bound states could also be related to the parabolic Scherk-Schwarz reductions of type IIB string theory.