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

TL;DR

This paper explores the properties and dualities of the (F1, D1, D3) bound state in IIB supergravity across different scaling limits, revealing how various theories like SYM, NCSYM, and NCOS relate through SL(2,Z) transformations.

Contribution

It systematically analyzes the scaling limits of the (F1, D1, D3) bound state and demonstrates the SL(2,Z) duality relations among SYM, NCSYM, and NCOS theories.

Findings

Decoupling limits yield SYM, NCSYM, and NCOS theories.

SL(2,Z) transformations relate these theories and map NCSYM to NCOS.

The supergravity dual remains consistent across different limits.

Abstract

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.