Carbs for Protein Synthesis
For natural lifters, it's hard to build muscle at an optimal rate when you don't consume any carbs. I'm not saying you CAN'T do it if your protein and calorie intake are high enough, but it'll be much harder.
So how can carbs consumed around the workout period increase muscle growth? After all, isn't muscle made from protein?
Yes, but carbs, and the insulin production they lead to, will increase mTOR expression from the training. If you consume carbs pre or intra-workout, the mTOR will be activated more than if you don't. And the more you activate mTOR, the greater your increase of protein synthesis will be from the workout.
This is important for natural lifters who need to trigger protein synthesis with their lifting sessions. While drug users will also benefit from workout carbs, they don't need them as much because they already get tons of protein synthesis from the steroids.
Carbs and Cortisol
Having carbs around workouts also has other benefits that'll positively increase muscle growth.
Carbs before and/or during the workout will decrease cortisol release. During the session, cortisol's main function is to mobilize nutrients to fuel the workout. And while lifting, glucose is the most efficient fuel source. (Yes, even more than ketones.) The more fuel you need to mobilize, the greater the cortisol production will be.
If you provide easily absorbed carbs like highly branched cyclic dextrin before and during your workout, you'll have less need to mobilize stored glycogen, which means you don't need to pump out as much cortisol. Less cortisol means more growth.
Having carbs around workouts can also increase your capacity to have a higher training volume (more easily available fuel, decreased cortisol) and grow from it.
Carbs and IGF-1 Levels
Low-carb diets lead to lower levels of systemic IGF-1. This is well documented in many studies. It's likely because in order to produce a large amount of IGF-1 you need both growth hormone and insulin.
They don't necessarily need to be present at the same time. One theory is that insulin makes the liver more sensitive to producing IGF-1 when growth hormone is released. Why is that important? Because IGF-1 is the most anabolic hormone in the body.
You don't need a huge amount of carbs throughout the day, but enough to stimulate insulin release once or twice a day will certainly help with the muscle-building process.
How many carbs? See the first related link below for details.