user2716: The following is suggested by my computer (Stockfish) as an improvement to a line in the Fried Liver played in Shirov v Sulskis 2014 and suggested as a definite refutation in some places - Shirov's key move was 9. a3. 
As an improvement, instead of the Sulskis move 11... Kd6, play 11... Qh4 as follows, with suggested follow-up (I have tested at some depth, but the positions are not straightforward and there are alternative moves).
[FEN ""]
1. e4 e5
2. Nf3 Nc6
3. Bc4 Nf6
4. Ng5 d5
5. exd5 Nxd5
6. Nxf7 Kxf7
7. Qf3+ Ke6
8. Nc3  Ncb4
9. a3   Nc2+
10. Kd1  Nxa1
11. Nxd5 Qh4
12. d3  Kd6
13. h3  Be6
14. Ne3  e4
15. Nf5+ Kc6
16. Nxh4 exf3
17. Bxe6 fxg2
18. Nxg2

With advantage to black. 11... Qh4 is an extraordinary move so I'd appreciate any commentary on that. Is it really advantage black? Can anyone find an improvement in this line (from move 11) for white?
My computer (at significant depth) would play 9 Bb3 as an improvement for white, instead of Shirov's move (I'm taking the position after move 8 as basic) - but this secures only a modest advantage for white and it looks as though the position can be defended. Is there any deep published analysis of these lines?

user7473: This does not actually answer your question, but if you are asking about this from the perspective of the white player, you are probably better off playing the modern move 6.d4 and studying the lines that follow from that. The reason for this is that most black players don't play 5...Nxd5, so it would not be very good use of your time to look into a line like this. GMs play like this because they prepared beforehand, and such lines are not an actual part of their main repertoire.
Anyway, to attempt to answer your question: 9.Bb3 was the old main move and is a well-known line; in fact, it would be the first line anyone would learn about if they somehow decide to incorporate 5...Nxd5 into their opening repertoire as black. After 11... Qh4, if GM analysis tells you that the position is advantageous for black, you should probably believe it. In the final position, white's pawn structure is shattered; the d- and f-pawns are on open files which makes them easy targets for the black rooks. More importantly, white's pieces are poorly coordinated, and he needs to spend time to pick up the knight on a1.
In the line you have, most of white's moves are almost forced (in today's age, you can simply check this with your engine) after 11... Qh4. Nevertheless, it is indeed an incredible move that your opponent is unlikely to find over the board, which makes this line a good surprise weapon for an unprepared opponent.
As for improvements, you are not likely to find them published until an actual game has been played in that line, especially if the move is something that the computer has evaluated wrongly (but this is very unlikely to happen in sharp positions like this one).
(The last time I checked, which was about 5 years ago, the evaluation of the immediate Fried Liver with 6.Nxf7 is not favourable for white; however, the position after 6.d4 exd4 7.O-O is indeed better for white. The evaluation may have changed recently, but it's quite unlikely, again because this is an open position, and most genuine improvements were probably found by computers already.)

user4588: Recently, GM L'Ami made a DVD covering the Two Knights and the Fried Liver attack. According to the article, he suggests ideas for both white and black, so maybe he discusses 9.Bb3 (instead of 9.a3) and 11....Qh4 (instead of 11....Kd6).
Furthermore I'd like to add that, although it has been played by a couple of grandmasters, 5....Nxd5 is considered to be very risky for black.
The main line of the variation is 5....Na5. According to the Game Database of ChessTempo, it is by far the most popular response to 4.Ng5. After 6.Bb5+ c6 7.dxc6 bxc6, black is a pawn down, but is ahead in development. This position is one of the tabiyas of 1.e4 e5: has black sufficient compensation for the pawn or not?

2716: <p>The following is suggested by my computer (Stockfish) as an improvement to a line in the Fried Liver played in Shirov v Sulskis 2014 and suggested as a definite refutation in some places - Shirov's key move was 9. a3. </p>

<p>As an improvement, instead of the Sulskis move 11... Kd6, play 11... Qh4 as follows, with suggested follow-up (I have tested at some depth, but the positions are not straightforward and there are alternative moves).</p>

<pre><code>[FEN ""]
1. e4 e5
2. Nf3 Nc6
3. Bc4 Nf6
4. Ng5 d5
5. exd5 Nxd5
6. Nxf7 Kxf7
7. Qf3+ Ke6
8. Nc3  Ncb4
9. a3   Nc2+
10. Kd1  Nxa1
11. Nxd5 Qh4
12. d3  Kd6
13. h3  Be6
14. Ne3  e4
15. Nf5+ Kc6
16. Nxh4 exf3
17. Bxe6 fxg2
18. Nxg2
</code></pre>

<p>With advantage to black. 11... Qh4 is an extraordinary move so I'd appreciate any commentary on that. Is it really advantage black? Can anyone find an improvement in this line (from move 11) for white?</p>

<p>My computer (at significant depth) would play 9 Bb3 as an improvement for white, instead of Shirov's move (I'm taking the position after move 8 as basic) - but this secures only a modest advantage for white and it looks as though the position can be defended. Is there any deep published analysis of these lines?</p>
 7473: <p>This does not actually answer your question, but if you are asking about this from the perspective of the white player, you are probably better off playing the modern move 6.d4 and studying the lines that follow from that. The reason for this is that most black players don't play 5...Nxd5, so it would not be very good use of your time to look into a line like this. GMs play like this because they prepared beforehand, and such lines are not an actual part of their main repertoire.</p>

<p>Anyway, to attempt to answer your question: 9.Bb3 was the old main move and is a well-known line; in fact, it would be the first line anyone would learn about if they somehow decide to incorporate 5...Nxd5 into their opening repertoire as black. After 11... Qh4, if GM analysis tells you that the position is advantageous for black, you should probably believe it. In the final position, white's pawn structure is shattered; the d- and f-pawns are on open files which makes them easy targets for the black rooks. More importantly, white's pieces are poorly coordinated, and he needs to spend time to pick up the knight on a1.</p>

<p>In the line you have, most of white's moves are almost forced (in today's age, you can simply check this with your engine) after 11... Qh4. Nevertheless, it is indeed an incredible move that your opponent is unlikely to find over the board, which makes this line a good surprise weapon for an unprepared opponent.</p>

<p>As for improvements, you are not likely to find them published until an actual game has been played in that line, especially if the move is something that the computer has evaluated wrongly (but this is very unlikely to happen in sharp positions like this one).</p>

<p>(The last time I checked, which was about 5 years ago, the evaluation of the immediate Fried Liver with 6.Nxf7 is <em>not</em> favourable for white; however, the position after 6.d4 exd4 7.O-O is indeed better for white. The evaluation may have changed recently, but it's quite unlikely, again because this is an open position, and most genuine improvements were probably found by computers already.)</p>
 4588: <p>Recently, <a href="http://en.chessbase.com/post/erwin-l-ami-the-modern-two-knights" rel="nofollow noreferrer">GM L'Ami</a> made a DVD covering the Two Knights and the Fried Liver attack. According to the article, he suggests ideas for both white and black, so maybe he discusses 9.Bb3 (instead of 9.a3) and 11....Qh4 (instead of 11....Kd6).</p>

<p>Furthermore I'd like to add that, although it has been played by a couple of grandmasters, 5....Nxd5 is considered to be very risky for black.</p>

<p>The main line of the variation is 5....Na5. According to the <a href="http://chesstempo.com/game-database.html" rel="nofollow noreferrer">Game Database of ChessTempo</a>, it is by far the most popular response to 4.Ng5. After 6.Bb5+ c6 7.dxc6 bxc6, black is a pawn down, but is ahead in development. This position is one of the <a href="https://chess.stackexchange.com/questions/2097/what-is-a-tabiya-and-what-is-their-importance">tabiyas</a> of 1.e4 e5: has black sufficient compensation for the pawn or not?</p>
