Difference between revisions of "Slorg"

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bt: I realized that I was not being psceire 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~~.

==Trivia==

*The Red Slorg is a prize from the [[Test Your Strength]] games. As such it can not be painted and other Slorgs can't be painted red.

*There are two [[Avatar|Avatars]] featuring Slorgs.

*There are over 50 items featuring Slorgs.

*The Slorg has been chosen for the [[Petpet Protection League]] award four times: The Faerie Slorg was featured in ''Week 4'', the Plushie Slorg was featured in ''Week 63'', the normal Slorg was featured in ''Week 114'', and the Mutant Slorg was featured in ''Week 413''.

==See also==

Revision as of 14:28, 4 March 2013

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-bt: I realized that I was not being psceire 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.
+==Trivia==
+*The Red Slorg is a prize from the [[Test Your Strength]] games. As such it can not be painted and other Slorgs can't be painted red.
+*There are two [[Avatar|Avatars]] featuring Slorgs.
+*There are over 50 items featuring Slorgs.
+*The Slorg has been chosen for the [[Petpet Protection League]] award four times: The Faerie Slorg was featured in ''Week 4'', the Plushie Slorg was featured in ''Week 63'', the normal Slorg was featured in ''Week 114'', and the Mutant Slorg was featured in ''Week 413''.
 ==See also==

Difference between revisions of "Slorg"

Revision as of 14:28, 4 March 2013

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