Brane Effective Actions, Kappa-Symmetry and Applications

TL;DR

This paper provides a comprehensive survey of brane effective actions, detailing how a single abelian brane—Dp, M2, and M5—propagates in on-shell supergravity backgrounds using Green–Schwarz-inspired formalisms. It develops the kinematic framework, including worldvolume diffeomorphisms and kappa symmetry, to achieve manifest spacetime covariance and supersymmetry, and then connects these actions to physical applications via worldvolume solitons and AdS/CFT probe dynamics. The review also addresses consistency checks under dualities, covariantization to curved backgrounds, and the bridge to nonabelian brane theories and 3-algebra approaches for M2-branes. Finally, it surveys a rich spectrum of solitonic configurations—BIons, dyons, supertypes, baryon vertices, giant gravitons, and their connections to calibrations and black hole microphysics—highlighting the deep interplay between brane dynamics, supersymmetry, and holography.

Abstract

This is a review on brane effective actions, their symmetries and some of its applications. Its first part uncovers the Green-Schwarz formulation of single M- and D-brane effective actions focusing on kinematical aspects : the identification of their degrees of freedom, the importance of world volume diffeomorphisms and kappa symmetry, to achieve manifest spacetime covariance and supersymmetry, and the explicit construction of such actions in arbitrary on-shell supergravity backgrounds. Its second part deals with applications. First, the use of kappa symmetry to determine supersymmetric world volume solitons. This includes their explicit construction in flat and curved backgrounds, their interpretation as BPS states carrying (topological) charges in the supersymmetry algebra and the connection between supersymmetry and hamiltonian BPS bounds. When available, I emphasise the use of these solitons as constituents in microscopic models of black holes. Second, the use of probe approximations to infer about non-trivial dynamics of strongly coupled gauge theories using the AdS/CFT correspondence. This includes expectation values of Wilson loop operators, spectrum information and the general use of D-brane probes to approximate the dynamics of systems with small number of degrees of freedom interacting with larger systems allowing a dual gravitational description. Its final part briefly discusses effective actions for N D-branes and M2-branes. This includes both SYM theories, their higher order corrections and partial results in covariantising these couplings to curved backgrounds, and the more recent supersymmetric Chern-Simons matter theories describing M2-branes using field theory, brane constructions and 3-algebra considerations.

Figures (11)

• Figure 1: Layout of the main relations uncovered in this review.
• Figure 2: Different superstring formulations require curved backgrounds to be on-shell.
• Figure 3: Set of half-BPS branes discussed in this review, their tensions and some of their connections under T-duality and the strongly coupled limit of type IIA.
• Figure 4: Schematic diagram describing the derivation of Buscher's T-duality rules using type IIA/IIB supergravities.
• Figure 5: Kappa symmetry and world volume diffeomorphisms allow to couple the brane degrees of freedom to the superfield components of supergravity in a manifestly covariant and supersymmetric way. Invariance under kappa symmetry forces the background to be on-shell. The gauge fixing of these symmetries connects the GS formulation with world volume supersymmetry, whose on-shell degrees of freedom match the Goldstone modes of the brane supergravity configurations.