Brane Effective Actions, Kappa-Symmetry and Applications

TL;DR

This review discusses brane effective actions, their symmetries like kappa symmetry, and their applications in supersymmetric solitons, black hole models, and gauge/gravity duality, highlighting recent advances in M- and D-brane theories.

Contribution

It provides a comprehensive overview of the Green-Schwarz formulation of brane actions, their symmetries, and recent developments in M2-brane and multiple D-brane effective theories.

Findings

Explicit construction of brane actions in supergravity backgrounds

Use of kappa symmetry to identify supersymmetric solitons

Insights into gauge/gravity duality via probe branes

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.