Noncommutative bion core

Abstract

We examine noncommutative solutions of the non-Abelian theory on the world-volume of N coincident D-strings. These solutions can be interpreted in terms of noncommutative geometry as funnels describing the non-Abelian D-string expanding out into an orthogonal D3-brane. These configurations are ''dual'' to the bion solutions in the Abelian world-volume theory of the D3-brane. In the latter, a charge N magnetic monopole describes N D-strings attached to the D3-brane with a spike deformation of the world volume. The noncommutative D-string solutions give a reliable account of physics at the core of the monopole, where the bion description is expected to break down. In the large N limit, we find good agreement between the two points of view, including the energy, couplings to background fields, and the shape of the funnel. We also study fluctuations traveling along the D-string, again obtaining agreement in the large N limit. At finite N, our results give a limit on the number of modes that can travel to infinity along the N D-strings attached to the D3-brane.

There and back again: a T-brane’s tale

“…The regimes of validity of the two descriptions are complementary. The non-Abelian description is valid when the commutators of the expectation values of the fields are small compared to the string scale, while the Abelian D(p + 2)-brane description is valid when these commutators are large (and hence the curvature of the two-sphere wrapped by the D(p + 2)-brane is lower than the string scale) [14,15]. As we explained above, for T-branes the naive Abelian description in terms of dielectric branes is problematic.…”

“…Remarkably, this energy density can be expressed as the square root of a sum of perfect squares [20]: 6) where STr denotes the symmetrized trace [14,21,22]. Thus any solution of (3.3)-(3.4) sets the first square to zero and, as one expects for supersymmetric solutions, also satisfies the full non-Abelian equations of motion [15]. Let us examine the profile of the configuration given by (3.4).…”

“…When the number of D6-branes and the vevs of the non-Abelian fields are very large, the physics of the brane configuration considered in the previous section is captured by a different system, consisting of a single funnel-shaped D8-brane with non-trivial worldvolume gauge flux, F 2 [15]. 9 Hence, this can be thought of as a type of Myers effect for the D6-branes, with the difference that what keeps the D6-branes polarized are the boundary conditions, and not the bulk fluxes as in [14].…”

Electrified fluctuations in D1⊥D3 and D1⊥D5 systems

“…In the coming work [22], we will focus on other interesting investigations concerning the perturbations propagating on a dyonic string in the supergravity background [19,10] of an orthogonal p-brane. We will discuss the relative transverse fluctuations in dyoinc D1-D5 system in flat background and supergravity background.…”

Non-abelian (p,q) strings in the warped deformed conifold

“…Since this S 2 is thus magnetized, it suggests that on the non-Abelian side we should attempt to describe this wrapped S 2 via a fuzzy sphere ansatz for our transverse scalars, as we know that in the large q limit we should recover the classical two-sphere geometry with q units of magnetic flux. This is not the same as constructing the dual model to that in [12], as in order to do so we would have to consider a BIon type solution [21] which blows up into a D3-brane wrapped on the two-cycle via the dielectric effect [14,20]. The non-trivial construction of such a solution is beyond the scope of this note, but would be useful to develop in the future.…”