Anomalous Creation of Branes

In certain circumstances when two branes pass through each other a third brane is produced stretching between them. We explain this phenomenon by the use of chains of dualities and the in ow of charge that is required for the absence of chiral gauge anomalies when pairs of D-branes intersect. At large distances D-branes [1, 2] interact through the long-range elds of supergravity. At substringy scales, on the other hand, their interaction is more usefully described in terms of the creation and subsequent annihilation of (virtual) pairs of open strings stretching between the branes. Such pairs may materialize from the vacuum [3], a phenomenon analogous to pair creation in an electric eld. There are however special situations, to be discussed here, in which a single open string must materialize when two D-branes cross. Hanany and Witten [4] pointed out a similar phenomenon, in which a stretched D3-brane is produced when a D5-brane and a NS 5-brane cross. In this note we will explain how such phenomena can be related by chains of dualities to the (abelian) anomaly equation describing charge in ow [5] on the intersection of branes [6]. A set of m coincident type-II D-branes is described by a supersymmetric eld theory with gauge group U(m). When two such sets of D-branes intersect, the eld content in the intersection domain includes the pull-backs of the corresponding U(m) and ~ U( ~ m) gauge potentials, as well as the pull-back of the bulk graviton eld. There are circumstances in which this e ective eld theory is chiral [6]. For this to arise the two sets of coincident branes must intersect in such a manner that the space-time dimension of the intersection domain is 2 mod 4, and there are no spatial directions transverse to both sets. Two distinct con gurations of intersecting type-II D-branes that result in chiral supersymmetry in the intersection region are: (a) two D5-branes of type-IIB theory intersecting on a string, or (b) two D7-branes of type-IIB theory intersecting on a 5-brane. Other chiral con gurations in either type IIA or IIB are obtained from these by T-dualizing coordinates transverse to the intersection region. Let us denote the world-volume actions of the two individual branes and of the intersection region by S, ~ S and I, respectively. Under a gauge transformation, the variation of S and ~ S has a (boundary) piece localized at the intersection, which precisely cancels the anomalous variation of I [6]. Physically, since the embedding theory as well as the theory on either of the two D-branes is non-anomalous, the apparent charge violation in the presence of background elds in the intersection region has to be accounted for by in ow of charge from the branes. This is an application of the `anomaly in ow' argument of [5]. Let us focus rst on con guration (a) with two intersecting D5-branes lying in the planes (12345) and (16789), respectively. We will take the direction X1 to be a circle with radius L1. Furthermore, it will be su cient to consider the abelian case, in which there is an independent maximally-supersymmetric U(1) vector multiplet living in each brane. The spectrum in the intersection region consists of the pull-backs of these two abelian gauge potentials, together with a single Weyl fermion with U(1) ~ U(1) charge (+; ). This fermion, the lightest state of an oriented open string stretching between the two intersecting branes, does not transform under (0; 8) supersymmetry. Now consider switching on time-dependent Wilson lines A1(t) and ~ A1(t) on the two branes. The anomaly equation implies that the net in ow of fermion number