Difference between revisions of "Moltara"

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'''Moltara''' is a subterranean land that was introduced on November 12, 2009 as part of the [[Atlas of the Ancients]] [[plot]]. Located 7,000 feet under [[Neopia|Neopia's]] surface, Moltara is built upon a series of lava tunnels and magma lakes. The only entrance to Moltara is an immense door that sits on a remote island archipelago just east of [[Maraqua]]. Moltara is divided into two major areas: Moltara City and the Moltara Caves.

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

==History==

===Atlas of the Ancients===

''To be added...''<br style="clear:both" />

==Attractions==

Difference between revisions of "Moltara"

Revision as of 13:57, 9 May 2012

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@@ Line 12: / Line 12: @@
 '''Moltara''' is a subterranean land that was introduced on November 12, 2009 as part of the [[Atlas of the Ancients]] [[plot]]. Located 7,000 feet under [[Neopia|Neopia's]] surface, Moltara is built upon a series of lava tunnels and magma lakes.  The only entrance to Moltara is an immense door that sits on a remote island archipelago just east of [[Maraqua]].  Moltara is divided into two major areas: Moltara City and the Moltara Caves.
-bt: I realized that I was not being percise 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.
+==History==
+===Atlas of the Ancients===
+{{main|Atlas of the Ancients}}
+''To be added...''<br style="clear:both" />
 ==Attractions==

Difference between revisions of "Moltara"

Revision as of 13:57, 9 May 2012

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