I understand that the search space is larger, but how have you determined that it is exponentially larger than in chess?
"Some of the factors responsible for the game tree's enormity are shown below. (A comparison to chess is shown in brackets)
the size of the board : 19x19 (8x8)
the average number of moves per game is around 300 (80)
the average branching factor at each turn is around 235 (35)
players can pass"
It's been 10 years since I did the math for this in my AI class but a simplified example would be to compare the start of each game. a go player has 19^2 or 361 possible moves. then on the second turn there are 360 possible moves (since one space has been taken up by the first move) so after two moves there are 361*360 or 129,960 possible go board configurations.
a chess player is more restricted by the smaller size of the board and the way pieces are permitted to move. so there are a total of 16 possible pawn moves on the first turn plus 4 possible knight moves leaving 20 total moves available. On the second turn the second player is similarly resticted to 20 possible moves causing the total number of chess board configurations after two moves to be 400. Once more room opens up on the chess board the branching factor does increase a bit but it never comes close to the hundreds of potential moves at any step during a go game.
this "branching factor" is the key to the size of a search space. in chess it gets messy to calculate due to the variety of piece types and their allowable movements but it's easy to see that at any given board configuration there are fewer possible moves. to calculate the search space you multiply the number of potential moves at each step until every board configuration has been accounted for.