Non-abelian Born-Infeld Action Research Articles

On the Supersymmetric non-Abelian Born-Infeld Action

We review an iterative construction of the supersymmetric non-abelian Born-Infeld action. We obtain the action through second order in the field strength. Kappa-invariance fixes the ordenings which turn out to deviate from the symmetrized trace proposal.

On the Polarization of Unstable D0-Branes into Noncommutative Odd Spheres

We consider the polarization of unstable type IIB D0-branes in the presence of a background five-form field strength. This phenomenon is studied from the point of view of the leading terms in the non-abelian Born Infeld action of the unstable D0-branes. The equations have SO(4) invariant solutions describing a non-commutative 3-sphere, which becomes a classical 3-sphere in the large N limit. We discuss the interpretation of these solutions as spherical D3-branes. The tachyon plays a tantalizingly geometrical role in relating the fuzzy S^3 geometry to that of a fuzzy S^4.

Non-abelian Born-Infeld action and solitons for critical non-BPS branes

The non-abelian flat directions in the tachyon potential of stable non-BPS branes recently found are shown to persist to all orders in alpha' at tree level in the string coupling. We also obtain the non-abelian Born-Infeld action including the tachyon potential for a stack of stable non-BPS branes on a critical orbifold. Finally we discuss stable soliton states on the non-BPS brane.

The non-abelian Born-Infeld action and noncommutative gauge theory

In this paper we explicitly show the equivalence between the non-Abelian Born-Infeld action, which was proposed by Tseytlin as an effective action on several D-branes, and its noncommutative counterpart for slowly varying fields. This confirms the equivalence between the two descriptions of the D-branes using an ordinary gauge theory with a constant B field background and a noncommutative gauge theory, claimed by Seiberg and Witten. We also construct the general forms of the 2 n-derivative terms for non-Abelian gauge fields which are consistent with the equivalence in the approximation of neglecting (2 n+2)-derivative terms.

On the general structure of the non-abelian Born–Infeld action

We discuss the general structure of the non-abelian Born-Infeld action, together with all of the alpha-prime derivative corrections, in flat D-dimensional space-time. More specifically, we show how the connection between open strings propagating in background magnetic fields and gauge theories on non-commutative spaces can be used to constrain the form of the effective action for the massless modes of open strings at week coupling. In particular, we exploit the invariance in form of the effective action under a change of non-commutativity scale of space-time to derive algebraic equations relating the various terms in the alpha- prime expansion. Moreover, we explicitly solve these equations in the simple case D=2, and we show, in particular, how to construct the minimal invariant derivative extension of the NBI action.

BPS states of the non-abelian Born–Infeld action

We argue that the trace structure of the non-abelian Born–Infeld action can be fixed by demanding that the action be linearised by certain energy-minimising BPS-like configurations. It is shown how instantons in D4-branes, SU(2) monopoles and dyons in D3-branes, and vortices in D2-branes are all BPS states of the action recently proposed by Tseytlin. All such configurations can be dealt with exactly within the context of non-abelian Born–Infeld theory since, given the relevant BPS-like condition, the action reduces to that of Yang–Mills theory. It would seem, moreover, that such an analysis holds for the symmetrised trace structure of Tseytlin's proposal only.

TAMING THE NON-ABELIAN BORN–INFELD ACTION

We show how to reduce the non-Abelian Born–Infeld action describing the interaction of two D-particles to the sum of elliptic integrals depending on simple kinematic invariants. This representation gives explicitly all α′ corrections to D-particle dynamics. The α′ corrections induce a stabilization of the classical trajectories such as the "eikonal" which are unstable within the Yang–Mills approximation.

Bound states of D-branes and the non-abelian Born-Infeld action

We attempt to settle the issue as to what is the correct non-abelian generalisation of the Born-Infeld action, via a consideration of the two-loop β-function for the non-abelian background gauge field in open string theory. An analysis of the bosonic theory alone shows the recent proposal of Tseytlin [A.A. Tseytlin, Nucl. Phys. B 501 (1997) 41] to be somewhat lacking. For the superstring, however, this proposal would seem to be correct, and not just within the approximation used. Since it is this latter case that is relevant to the description of D-branes, we, in effect, obtain an independent verification of Tseytlin's result. Some issues involved in the concept of non-abelian T-duality are discussed; and it is shown how the interaction between separated and parallel branes, in the form of massive string states, emerges.

Fluctuation spectra of tilted and intersecting D-branes from the Born-Infeld action

We consider the spectra of excitations around diagonal and intersecting D-brane configurations on tori. These configurations are described by constant curvature connections in a dual gauge theory description. The low-energy string fluctuation spectrum is reproduced exactly by the gauge theory in the case of vanishing field strength; however, this correspondence breaks down for fixed non-zero field strength. We show that in many cases the full Born-Infeld action correctly captures the low-energy spectrum in the case of non-vanishing field strength. This gives a field theory description of the low-energy physics of systems of diagonally wound branes and branes at angles as considered by Berkooz, Douglas and Leigh. This description extends naturally to non-supersymmetric configurations, where the tachyonic instability associated with brane-antibrane systems appears as an instability around a saddle point solution of the corresponding Yang-Mills/Born-Infeld theory. In some cases, the field theory description requires a non-abelian generalization of the Born-Infeld action. We follow Tseytlin's recent proposal for formulating such an action. In the case of intersecting branes, the non-abelian Bom-Infeld theory produces a transcendental relation which comes tantalizingly close to reproducing the correct spectrum; however, a discrepancy remains which indicates that a further clarification of the non-abelian Born-Infeld action may be necessary.