It's a very good question and I can't match the expert knowledge of those who have already answered, but I also can't resist making a few points.

In LQG it is hard to calculate anything because it does not give a classical limit that looks like smooth spacetime. If such a limit existed we would expect to be able to look at small deviations from flat spacetime and it is hard to see how that could lead anywhere except to a perturbative theory of gravitons. From the particle physics world we know that the supergravity/superstring route is probably the only way to do that. Some people might say that there could be another unknown way or that LQG would somehow avoid such a perturbative limit but let's assume otherwise until there is some good explanation of how that would work.

In that case LQG could only work if it included matter as string theory does. Matter might be emergent but that would mean that LQG has to work as it is with a classical limit and that does not seem to be the case, so probably LQG needs matter put in as some additional degrees of freedom. I think Lee Smolin tried to generalise LQG to look more like string theory in the early days before he gave up and became more dismissive of string theory. For example, he and others looked for higher dimensional version and supersymmetric version of LQG but there was nothing very promising. I think it would be wrong for a younger generation to assume that no progress can be made with such a connection just because others could not find it.

On the string theory side the fundamental issue is that it's degrees of freedom and underlying principles are not known or fully understood. LQG has spins and knots. Spin half entities are qubits which also arise in string theory. This does not mean there is a connection because such entities arise everywhere as representations of symmetries. However, LQG and string theory share similar origins out of gauge theories and they share some mathematical structures. The areas where they are least well understood are also the areas where we might expect to see connections if there are any.

Personally I think that theorists have to take Dirac's advise to look for elegant mathematical structures and be driven by them. When they find them in relation to one approach it suggests that the approach has some promise. Both string theory and LQG passed this test when trying to solve the same problem but failed so far to make contact with experiment. I think you have to keep a broad view and look for connections between the mathematics of these and other approaches that look interesting. Unfortunately sociological issues driven by the way funding is allocated seems to discourage people from looking at the bigger picture.

Of course some experimental input would also help.

It's a very good question and I can't match the expert knowledge of those who have already answered, but I also can't resist making a few points.

In LQG it is hard to calculate anything because it does not give a classical limit that looks like smooth spacetime. If such a limit existed we would expect to be able to look at small deviations from flat spacetime and it is hard to see how that could lead anywhere except to a perturbative theory of gravitons. From the particle physics world, we know that the supergravity/superstring route is probably the only way to do that. Some people might say that there could be another unknown way or that LQG would somehow avoid such a perturbative limit but let's assume otherwise until there is some good explanation of how that would work.

In that case, LQG could only work if it included matter as string theory does. Matter might be emergent but that would mean that LQG has to work as it is with a classical limit and that does not seem to be the case, so probably LQG needs matter put in as some additional degrees of freedom. I think Lee Smolin tried to generalise LQG to look more like string theory in the early days before he gave up and became more dismissive of string theory. For example, he and others looked for a higher dimensional version and supersymmetric version of LQG but there was nothing very promising. I think it would be wrong for a younger generation to assume that no progress can be made with such a connection just because others could not find it.

On the string theory side, the fundamental issue is that its degrees of freedom and underlying principles are not known or fully understood. LQG has spins and knots. Spin half entities are qubits which also arise in string theory. This does not mean there is a connection because such entities arise everywhere as representations of symmetries. However, LQG and string theory share similar origins out of gauge theories and they share some mathematical structures. The areas where they are least well understood are also the areas where we might expect to see connections if there are any.

Personally, I think that theorists have to take Dirac's advice to look for elegant mathematical structures and be driven by them. When they find them in relation to one approach it suggests that the approach has some promise. Both string theory and LQG passed this test when trying to solve the same problem but failed so far to make contact with the experiment. I think you have to keep a broad view and look for connections between the mathematics of these and other approaches that look interesting. Unfortunately, sociological issues driven by the way funding is allocated seem to discourage people from looking at the bigger picture.

Of course, some experimental input would also help.