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On the shape of a D-brane bound state and its topology change

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Shimada,  Hidehiko
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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0901.4073v1.pdf
(Preprint), 975KB

JHEP_2009_121.pdf
(Any fulltext), 949KB

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Citation

Azeyanagi, T., Hanada, M., Hirata, T., & Shimada, H. (2009). On the shape of a D-brane bound state and its topology change. Journal of high energy physics: JHEP, 2009(03): 121. doi:10.1088/1126-6708/2009/03/121.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-6047-2
Abstract
As is well known, coordinates of D-branes are described by NxN matrices. From generic non-commuting matrices, it is difficult to extract physics, for example, the shape of the distribution of positions of D-branes. To overcome this problem, we generalize and elaborate on a simple prescription, first introduced by Hotta, Nishimura and Tsuchiya, which determines the most appropriate gauge to make the separation between diagonal components (D-brane positions) and off-diagonal components. This prescription makes it possible to extract the distribution of D-branes directly from matrices. We verify the power of it by applying it to Monte-Carlo simulations for various lower dimensional Yang-Mills matrix models. In particular, we detect the topology change of the D-brane bound state for a phase transition of a matrix model; the existence of this phase transition is expected from the gauge/gravity duality, and the pattern of the topology change is strikingly similar to the counterpart in the gravity side, the black hole/black string transition. We also propose a criterion, based on the behavior of the off-diagonal components, which determines when our prescription gives a sensible definition of D-brane positions. We provide numerical evidence that our criterion is satisfied for the typical distance between D-branes. For a supersymmetric model, positions of D-branes can be defined even at a shorter distance scale. The behavior of off-diagonal elements found in this analysis gives some support for previous studies of D-brane bound states.