4 World Volume Solitons: Generalities

Brane effective actions capture the relevant dynamics of M-theory or string theory in some appropriate regimes of validity. Thus, they contain reliable information about its spectrum and its dynamics in those regimes. In this section, I will develop the tools to study the world volume realisation of supersymmetric states carrying the extra bosonic (topological) charges appearing in the maximal supersymmetry algebras introduced in Sections 3.6.1 and 3.6.2.

One such realisation is in terms of classical bosonic on-shell configurations. As it often occurs with supersymmetric configurations, instead of focusing on the integration of the equations of motion, I will focus on the conditions ensuring preservation of supersymmetry and on their physical interpretation. In particular,

The framework and set of relations covered in this section are summarised in Figure 6View Image.

View Image

Figure 6: Set of relations involving kappa symmetry, spacetime supersymmetry algebras, their bounds and their realisation as field theory BPS bounds in terms of brane solitons using the Hamiltonian formulation of brane effective actions.
 4.1 Supersymmetric bosonic configurations and kappa symmetry
 4.2 Hamiltonian formalism
  4.2.1 D-brane Hamiltonian
  4.2.2 M2-brane Hamiltonian
  4.2.3 M5-brane Hamiltonian
 4.3 Calibrations

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