The physics of multiple overlapping branes provides a connection between brane physics and non-abelian supersymmetric field theories. Thus, it has played a crucial role in the geometrisation of the latter and the interplay between string and field theory dualities.
An heuristic argument suggesting that the abelian description may break down comes from the analysis of BIons. All half-BPS probe branes described in this review feel no force when probing the background describing parallel branes of the same nature . This means they can sit at any distance . Consider a Dp-brane in the background of parallel Dp-branes. As soon as the probe approaches the location of the Dp-branes sourcing the geometry, the properly regularised mass of the open string (BIon) stretching between the probe D-brane and the background D-branes will tend to zero . This suggests the potential emergence of extra massless modes in the spectrum of these open strings. If so, this would signal a breakdown in the effective action, since these extra modes were not included in the former. U-duality guarantees that similar considerations apply to other brane set-ups not having a microscopic theory with which to test this phenomena.
In this section, I will briefly discuss the supersymmetric effective actions describing coincident Dp-branes and M2-branes in a Minkowski background. These correspond to non-abelian super-Yang–Mills (SYM) theories in different dimensions and certain superconformal field theories with non-dynamical gauge fields having Chern–Simons actions, respectively.
Living Rev. Relativity 15, (2012), 3
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