Creation of Fundamental String in M(atrix) Theory

The potential between two D4-branes at angles with partially unbroken supersymmetry is computed, and is used to discuss the creation of a fundamental string when two such D4-branes cross each other in M(atrix) theory. The effective Lagrangian is shown to be anomalous at 1-loop approximation, but it can be modified by bare Chern-Simons terms to preserve the invariance under the large gauge transformation. The resulting effective potential agrees with that obtained from the string calculations. The result shows that a fundamental string is created in order to cancel the repulsive force between two D4-branes at proper angles. [email protected] [email protected] [email protected], JSPS postdoctral fellow Recently the creation of a fundamental string when a D0-brane crosses a D8-brane in type IIA theory, and the creation of a longitudinal membrane in M-theory when two longitudinal M5-branes cross each other, have been studied from various points of view [17]. In the string theory context, by requiring RR charge conservation, it was first found in [1] that a third brane is created when two certain branes cross. In [2], the anomaly equation was exploited to show that when the two branes in question cross each other an energy level crosses zero and a single particle or hole is created, and this was interpreted as the creation of an open string or brane. It was also suggested that the induced charge on the D8-brane worldvolume indicates the creation of a string when the D0-brane crosses the D8-brane [3]. The one-loop open string calculation in ref. [4] revealed that the potential of the D0-D8 system vanishes due to the cancellation of the forces coming from the dilatongraviton exchange and a fundamental string created when two such branes cross. On the other hand, more and more evidence has accumulated to show that M-theory could be described in terms of a matrix model – M(atrix) theory [8]. Many consistency checks have been done, including the calculation of potentials between various D-branes [914]. It is then natural to study the brane creation in the context of M(atrix) theory, but only a few papers discuss this phenomenon. The authors of ref. [6] argued that the effective potential between two M5-branes is dominated by the contribution from the chiral fermionic zero mode in the off-diagonal degrees of freedom. On the other hand, ref. [13] calculated the effective potential between D0and D8-branes, with the approximation of small b and ci (b is the distance between D0and D8-branes along X9, and ci’s stand for backgrounds). Since the effective potential is computed only for small b and ci, it is hard to determine from the potential in [13] whether a fundamental string is created or not when D0-brane crosses D8-brane. The creation of a fundamental string in D0-D8 system can be related to the creation of branes of other dimensions in other systems by sequences of dualities. For example, after T-dualities, when one D4-brane along (1357) directions crosses another D4-brane in (2468) directions, the creation of a fundamental string occurs. But when two parallel D4-branes cross each other, nothing happens. This raises an obvious question: is a fundamental string created when two D4-branes at angles cross each other? In the present paper, we compute the effective potential without the approximation made in ref. [13] and use the result to discuss the brane creation in M(atrix) theory. In