# On 1/4 BPS ((F, D1), (NS5, D5)) bound states of type IIB string theory

## TL;DR

This paper constructs two new SL(2,Z) invariant 1/4 BPS bound states in type IIB string theory involving strings and 5-branes, analyzing their stability, tensions, and dualities.

## Contribution

It introduces two novel 1/4 BPS bound states of strings and 5-branes in type IIB theory, detailing their conditions for stability and their behavior under dualities.

## Key findings

- Bound states exist only under specific vacuum moduli conditions.
- The first bound state requires a no-force condition for stability.
- Tension formulas and dual states are derived and discussed.

## Abstract

We construct two new SL(2,Z) invariant vacua of type IIB string theory which are bound states of $(p,q)$ strings with $(m,n)$ 5-branes, written as ((F, D1), (NS5, D5)) and preserve 1/4 of the full space-time supersymmetries. For the first case, the strings live inside the 5-brane world-volume and in the second case the strings are perpendicular to the 5-brane world-volume. In the first case, naively one would expect an attractive interaction between the strings and the 5-branes due to attractive force between F and D5 and also between D1 and NS5. We find that 1/4 BPS bound state exists only when the vacuum moduli satisfy certain condition which is found to be consistent with the no-force condition between the branes. No such complication arises for the second case. The tension formulae and the various other descendant states which can be obtained by the application of T-duality for both these bound states are discussed.