<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Q</mml:mi></mml:math>-ball-like solitons on the M2-brane with worldvolume fluxes

We present a novel family of analytical and numerical classical solitonic solutions to the nonlinear equations governing the dynamics of the bosonic part of a supermembrane (M2-brane) mass operator formulated on a flat spacetime toroidally compactified with worldvolume fluxes. The dynamics of membrane excitations is associated with sectors of the supermembrane theory that exhibit a discrete spectrum at the supersymmetric level, which is an expected property of any well-defined sector of the M-theory. Contrary to expectations, the presence of worldvolume fluxes facilitates the acquisition of novel solutions while preserving the theory’s nonlinear character even in the absence of bosonic scalar potential. The theory remains nonlinear due to the coupling of the scalars with the fluxes and with a symplectic gauge field that arises in the theory. It is noteworthy that the theory also permits the existence of quasiharmonic solutions to the nonlinear equations. We then focus on the M2 brane theory realization of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>Q</a:mi></a:math>-ball-like solitons. In order to ascertain the behavior of these solutions, we examine the existence of M2-brane solitonic nondispersive solutions, their composition rules, their dynamics, and the existence of localized solutions along the worldvolume. We also establish a relation between the worldvolume fluxes and the nontopological <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>Q</c:mi></c:math>-ball charges.