visayanbraindoctor: When a reigning World Champion loses, it's always news in the chess world. Most comments express shock at how Carlsen played so badly. Or did he? Did Aronian just play a better game?
Rather than discuss the World's Champion's propensity to under perform when playing for his home country, or the vagaries of his changing Elo ratings, let's go to the middlegame itself, from which we can learn a thing or two.
1. When Aronian played 11.. Ba7 in order to preserve his Bishop, he blocked his Rook on a8 from protecting his a5 Pawn. This pawn is now left protected only by the Black Queen on d8.
Carlsen saw that the maneuver Bg5 and Bxf6 would deflect the lone defender of the a5 pawn away after Qxf6, unless Black was willing to accept a destroyed pawn structure with gxf6. He would then be able to grab the a5 pawn with Nxa5. However he first blocks the a5 pawn with 12. a4, because Black threatens to advance it to a4, and White can't just take it with Bxa4 because of Black's b5 counter, forking the White Bishop and Knight.
Thus White plays 12. a4 first. Black develops with 12.. O-O.
2. With the a5 pawn blocked, Carlsen proceeds with the pawn winning maneuver explained above. Aronian, who must have been fully aware of what was happening and surely knows that Carlsen has a predilection for pawn grabbing, allows it.
13. Bg5 h6 14. Bxf6 Qxf6 and now 15. Nxa5.
3. In other words, Aronian has just purposely sacrificed a pawn, but what kind of a sac is that? The game is in transition from opening to middlegame, with some pieces still undeveloped, ans so I believe it's a sacrifice for tempo and rapid development. White loses at least two tempi grabbing the pawn and removing his Knight later from the a5 square. Meanwhile, Aronian sees that he can take advantge of White's loss of tempi by opening up the center and developing rapidly.
15. Nxa5 d5!
Black now opens up the center for possible exploitation of his rooks. White can grab another pawn with 16. exd5 cxd5 17. Bxd5, but Black has the nifty retreat 17.. Qd8, forking the Bishop on d5 and the Knight on a5.
4. Rather than give black the center with 16. exd5 cxd5, Carlsen as typical of his style proceeds conservatively, defending his e4 central pawn with 16. Bc2
However, this allows Black to open up the d-file and exploit it with his Rooks with 16.. dxe4 17. dxe4 Rd8, developing the Black Rook with tempo.
Now we see the effect of the pawn sac on both players' development. White has an undeveloped Rook on a1, with a misplaced Knight on a5, and is about to lose more tempi as his Queen has to move somewhere along the 1st rank. Developing his Queen to the second rank 18. Qe2 allows 18.. Qg5 threatening Rd2, and the Queen has to move again. So White's Rooks remain unconnected and his Queen is misplaced. His Knight remains misplaced on a5.
5. Carlsen makes the most reasonable move 18. Qe1, but now Qg5 threatens both Ba3 and Rd2. So Carlsen avoids the pins by the Black Queen on g5 and the Bishop on a7 by the good move 19. Kh1!
6. Aronian proceeds with 19.. Rd2. The White Bishop has to move, but developing it to b3 is met by Rxb2, and White has to move it again after losing a pawn. But Carlsen has prepared another good move 20. Bd1! If Rxb2, he sees that he can trap the Rook by Nc4.
7. Aronian makes the most logical move, 20.. Be6 developing his Bishop and taking control of the c4 square that White would like to occupy with his Knight. But Carlsen makes another good move 21. b4!
This removes his b-pawn from being a target by the Black Rook on his second rank, and at the same time threatens Bb3 with the plan to exchange off the Black Bishop on e6. Once this Black Bishop is gone, White can bring back his misplaced knight into the game into a good square by Nb3. The Knight here controls the d2 square on which the Black Rook is sitting on controlling the second rank. With a Knight at b3, Black takes away this d2 square for the use of Black's Rooks and consequently Black won't be able to maintain his hold on White's second rank. If Black moves his Rook along the second rank say by a future Rb2, White can perpetually challenge the Rook with Rb1, which he can't do if it remains on the d-file supported there by another Black Rook on d8.