# (F1, D1, D3) Bound State, Its Scaling Limits and SL(2,Z) Duality

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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## Details (F1, D1, D3) Bound State, Its Scaling Limits and SL(2,Z) Duality (F1, D1, D3) Bound State, Its Scaling Limits and SL(2,Z) Duality

20 pages, Latex, minor corrections, final version to appear in Prog. Theor. Phys

Scientific paper

10.1143/PTP.104.1073

We discuss the properties of the bound state (F1, D1, D3) in IIB supergravity in three different scaling limits and the $SL(2,{\bf Z})$ transformation of the resulting theories. In the simple decoupling limit with finite electric and magnetic components of NS $B$ field, the worldvolume theory is the ${\cal N}$=4 super Yang-Mills (SYM) and the supergravity dual is still the $AdS_5 \times S^5$. In the large magnetic field limit with finite electric field, the theory is the noncommutative super Yang-Mills (NCSYM), and the supergravity dual is the same as that without the electric background. We show how to take the decoupling limit of the closed string for the critical electric background and finite magnetic field, and that the resulting theory is the noncommutative open string (NCOS) with both space-time and space-space noncommutativities. It is shown that under the $SL(2, {\bf Z})$ transformation, the SYM becomes itself with a different coupling constant, the NCSYM is mapped to a NCOS, and the NCOS in general transforms into another NCOS and reduces to a NCSYM in a special case.

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