Keep an eye on the Jackie and Toves tumblr for liveblogging the revelation.
http://physicistsofdiscerningtaste.tumblr.com/
Tuesday, June 26, 2012
Rumor Has It
Keep an eye on the Jackie and Toves tumblr for liveblogging the revelation.
http://physicistsofdiscerningtaste.tumblr.com/
Thursday, June 14, 2012
AdS Integrability
The idea behind this is that in the N=4 SYM on the boundary at large N, only the single trace operators will really matter.
They will be like Tr(abcdef...) so for example if they were a bunch of those scalars coming from the transverse motion of the D3 branes you would get a SO(6) spin chain. This you can then solve by Bethe Ansatz.
It's all thanks to planarity.
They will be like Tr(abcdef...) so for example if they were a bunch of those scalars coming from the transverse motion of the D3 branes you would get a SO(6) spin chain. This you can then solve by Bethe Ansatz.
It's all thanks to planarity.
Of Monsters and Mathematicians
I did a moonshining post about Matheiu, but not about it's daddy the Monster. That oversight will be fixed now.
Suppose you have a discrete subgroup of PSL(2,R) call it G. The quotient of the hyperbolic plane by G will be some surface possibly with bad stuff. When the surface is genus 0 call that a genus 0 group.
We also want two more conditions on our group. The group should contain all of the T duality subgroup. T just translates the complexified coupling by 1. Shifting the action by multiples of 2 pi would make sense to include. Let us also have it contain the the congruence subgroup for some N.
Because the group contains those translations, we can Fourier expand on the quotient in powers of q.
The field of functions on this surface is the rational functions of a single function J called the Hauptmodul.
If you do this for SL(2,Z) you get the familiar one.
Finally the monster raises it's head.
The Hauptomodul looks like
where V is a infinite dimensional graded module for the Monster. This was originally constructed from looking at those numbers in the SL(2,Z) J function and noticing the fact that 196884=1+196883 and those were known irreps of the Monster. The fact that you could break up those numbers in such combinations of the dimensions of Monster irreps was the distilling information illegally from character tables.
You can apply Hecke operator like constructions to those weighted characters.
This is modular and can only blow up at the cusps so it is a polynomial in the original Tg.
These are called replication formulae because they relate repeated applications of g.
We're still relying on coincidences between the numbers to establish connection between these two series. We need to construct the representation V.
This is done by compactifying the 26 dimensional bosonic string target space on the 24 dimensional Leech lattice and also quotienting by the -1 involution of this lattice. Recall the heterotic string construction.
I enjoy our Little Talks
Suppose you have a discrete subgroup of PSL(2,R) call it G. The quotient of the hyperbolic plane by G will be some surface possibly with bad stuff. When the surface is genus 0 call that a genus 0 group.
We also want two more conditions on our group. The group should contain all of the T duality subgroup. T just translates the complexified coupling by 1. Shifting the action by multiples of 2 pi would make sense to include. Let us also have it contain the the congruence subgroup for some N.
Because the group contains those translations, we can Fourier expand on the quotient in powers of q.
The field of functions on this surface is the rational functions of a single function J called the Hauptmodul.
If you do this for SL(2,Z) you get the familiar one.
Finally the monster raises it's head.
The Hauptomodul looks like
where V is a infinite dimensional graded module for the Monster. This was originally constructed from looking at those numbers in the SL(2,Z) J function and noticing the fact that 196884=1+196883 and those were known irreps of the Monster. The fact that you could break up those numbers in such combinations of the dimensions of Monster irreps was the distilling information illegally from character tables.
You can apply Hecke operator like constructions to those weighted characters.
This is modular and can only blow up at the cusps so it is a polynomial in the original Tg.
These are called replication formulae because they relate repeated applications of g.
We're still relying on coincidences between the numbers to establish connection between these two series. We need to construct the representation V.
This is done by compactifying the 26 dimensional bosonic string target space on the 24 dimensional Leech lattice and also quotienting by the -1 involution of this lattice. Recall the heterotic string construction.
I enjoy our Little Talks
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