Difference between revisions of "Ugga Smash"
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= | bt: I realized that I was not being prsceie in saying that multi-trace operators dominate the thermodynamics at high temperature. Let us consider the free energy F(T) in the high temperature limit, of a U(N) gauge theory on the sphere (say N=4 SYM). F(T) goes like N^2 T^{d+1}, where d is the number of spatial dimensions. There is also a dependence on the t Hooft coupling, and we know it is a function of order 1, and let's ignore it for now. e^{F(T)/T} goes like d(E) e^{-E/T}, where d(E) is the number of states of a typical energy E, the latter scales like N^2 T^{d+1}, the same way as the free energy, by saddle point approximation. So the energy of a typical state scales with N like N^2. In the weakly coupled theory, at least, this means that we have an operator made out of the product of N^2 fields, and for operators of such high dimension there are nontrivial relations between single and multi-trace operators ( despite that N is large, normally we ignore the relation between single and multiple traces, but this breaks down when the dimension of the operator is high enough). Indeed, this phenomenon is the origin of the Hagedorn like phase transition in the free large N gauge theory on the sphere. | ||
==External Links== | ==External Links== | ||
Revision as of 04:05, 27 July 2012
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This page is under construction |
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| Wikified article, and working out how an old version of the game will appear with the new version |
| Ugga Smash | |
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| |
| ID # | 726 |
| World | Tyrannia |
| Category | Action, Multiplayer |
| High Scores | |
| Game Page | |
Ugga Smash is an action and multiplayer game released on November 21, 2006.
The Tyrannian Plateau has never seen a demolition derby like this before! Are you tough enough to ram one of four vehicles into your opponents as you swerve and speed across the rocky flats of Tyrannia?
The goal of Ugga Smash is to crash your way to victory by bashing your vehicle into those of the other players. There are four different vehicles to choose from and a whole host of powerups to help you (or perhaps hurt you) along the way. Challenge up to three of your friends and play on the same keyboard using the four different keyboard controls, or take on the computer by yourself. Only the strong will survive, so get smashing!
Bumper Cars
| Bumper Cars | |
|---|---|
| |
| ID # | 61 |
| World | Neopia Central |
| Category | Action |
| Replacement | Ugga Smash |
| High Scores | |
| Game Page | |
Bumper Cars is the original version of Ugga Smash, released on (need date). It was immediately retired when Ugga Smash was released, and was placed in the Game Graveyard on November 28, 2006.
Bang and Smash your way to the top in our new game - BUMPER CARS. Up to 4 players can play at the same time! For 1 player use the arrow keys to move left right, accelerate and brake. If you wish to play with more than one person at the keyboard, each person gets to use their own keys (it will tell you which keys when you start playing).
bt: I realized that I was not being prsceie in saying that multi-trace operators dominate the thermodynamics at high temperature. Let us consider the free energy F(T) in the high temperature limit, of a U(N) gauge theory on the sphere (say N=4 SYM). F(T) goes like N^2 T^{d+1}, where d is the number of spatial dimensions. There is also a dependence on the t Hooft coupling, and we know it is a function of order 1, and let's ignore it for now. e^{F(T)/T} goes like d(E) e^{-E/T}, where d(E) is the number of states of a typical energy E, the latter scales like N^2 T^{d+1}, the same way as the free energy, by saddle point approximation. So the energy of a typical state scales with N like N^2. In the weakly coupled theory, at least, this means that we have an operator made out of the product of N^2 fields, and for operators of such high dimension there are nontrivial relations between single and multi-trace operators ( despite that N is large, normally we ignore the relation between single and multiple traces, but this breaks down when the dimension of the operator is high enough). Indeed, this phenomenon is the origin of the Hagedorn like phase transition in the free large N gauge theory on the sphere.
External Links
- Game Link: Ugga Smash, Bumper Cars (Old Game)