Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-11-08
Prog.Theor.Phys. 109 (2003) 687-707
Physics
High Energy Physics
High Energy Physics - Theory
25 pages, minor changes, published version
Scientific paper
10.1143/PTP.109.687
We show that the Born-Infeld action with the Wess-Zumino terms for the Ramond-Ramond fields, which is the D3-brane effective action, is a solution to the Hamilton-Jacobi (H-J) equation of type IIB supergravity. Adopting the radial coordinate as time, we develop the ADM formalism for type IIB supergravity reduced on $S^5$ and derive the H-J equation, which is the classical limit of the Wheeler-De Witt equation and whose solutions are classical on-shell actions. The solution to the H-J equation reproduces the on-shell actions for the supergravity solution of a stack of D3-branes in a $B_2$ field and the near-horizon limit of this supergravity solution, which is conjectured to be dual to noncommutative Yang Mills and reduces to $AdS_5 \times S^5$ in the commutative limit. Our D3-brane effective action is that of a probe D3-brane, and the radial time corresponds to the vacuum expectation value of the Higgs field in the dual Yang Mills. Our findings can be applied to the study of the holographic renormalization group.
Sato Matsuo
Tsuchiya Asato
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