I have just played a game in which there was a thematic sacrifice of the b pawn. I cannot understand why this is useful. The opening of the file cannot be attacked by White as apart from Black bishop, there is also the a pawn that could defend it if needs be.
Please check the link of the game below as Stockfish suggests this move later in the game too. https://lichess.org/Ak6GNtwL/white#38
Looking at the engine output, it seems that after Black plays cxb4, White can play a3. If Black takes, this opens up the b-file, and if White is allowed to play axb4, that opens the a-file. Either way, lines towards the Black king will open up.
Just a point, but my eye was first attracted to the move h4, keeping the Bh7 entombed for a long time, but there is much better still. If there were not a direct attack, this would be a highly favorable idea since many games have been won at the highest level by excluding just one piece from participating in the game.
b4 is, indeed, much better, since it opens the way for Qa4. There are a lot of choices for black to try to defend, but the computer does not like any of them. I will give a few that try to make a sensible try at defending.
The Kc8 is incredibly weak there, especially combined with that big pawn on h7 that looks like a bishop, and the f7 weakness. Even the Bf8 cannot really do anything. When it goes to d6, it really attacks nothing, or bc gains a tempo for the attack. In short, the black king is defenseless.
[FEN "2kr1b1r/2q2p1b/p1p1p1pp/2p3P1/2PpP1N1/1P1P1N1P/P5P1/R2Q1RK1 w - - 0 1"]
1. b4 $1 (1. h4 hxg5 2. hxg5 Be7 3. b4 {Still can be played with great force.}) 1... cxb4 (1... hxg5 2. Qa4 Kb7 (2... f5 3. Nge5 a5 4. Nxc6 Rd6 5. Nfe5 cxb4 6. a3 $18) 3. bxc5 Bxc5 4. Rab1+ Ka7 5. Nfe5 Rdf8 (5... Rc8 6. Rxf7 Be7 7. c5 {And Rb6.}) 6. Nxc6+ $18) 2. Qa4 Kb7 (2... a5 3. Nge5 c5 4. a3 Bd6 5. axb4 $1 Bxe5 6. Nxe5 Qxe5 7. Rxf7 Qd6 8. Qxa5 $18) 3. a3 a5 4. Rfb1 h5 5. Nge5 c5 6. axb4 cxb4 7. Nxf7 Qxf7 8. Qxa5 $18
