(F, D5) Bound State, SL(2, Z) Invariance and The Descendant States in Type IIB/A String Theory

TL;DR

This paper constructs and analyzes various bound states in type IIB and type IIA string theories, emphasizing SL(2, Z) invariance and duality transformations to generate a comprehensive set of bound states.

Contribution

The authors explicitly construct new SL(2, Z) invariant bound states in type IIB and IIA theories, extending previous work on (F, Dp) states and exploring dualities.

Findings

Explicit construction of (F, Dp) bound states for p=2 to 7.

Development of SL(2, Z) invariant bound states combining (F, D1) and (NS5, D5).

Generation of a list of bound states via T- and S-dualities.

Abstract

Recently the space-time configurations of a set of non-threshold bound states, called the (F, Dp) bound states, have been constructed explicitly for every $p$ with $2 \le p \le 7$ in both type IIA (for $p$ even) and type IIB (for $p$ odd) string theories by the present authors. By making use of the SL(2, Z) symmetry of type IIB theory we construct a more general SL(2, Z) invariant bound state of the type ((F, D1), (NS5, D5)) in this theory from the (F, D5) bound state. There are actually an infinite number of $(m,n)$ strings forming bound states with $(m',n')$ 5-branes, where strings lie along one of the spatial directions of the 5-branes. By applying T-duality along one of the transverse directions we also construct the bound state ((F, D2), (KK, D6)) in type IIA string theory. Then we give a list of possible bound states which can be obtained from these newly constructed bound states by applying T-dualities along the longitudinal directions as well as S-dualities to those in type IIB theory.