And ATLAS comes in with 5 Sigma
Wednesday, July 4, 2012
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
Thursday, May 24, 2012
Tuesday, April 24, 2012
Spooky Action from the FUTURE!
I have 2 machines that produce entangled pairs of photons. Call them thing 1 and thing 2.
Thing 1 sends a photon to Dick. Thing 2 sends a photon to Sally. They both send the other photons to the cat.
Dick and Sally measure their photons in whatever basis they choose.
Later, the cat decides whether or not to entangle the two photons it got.
If the cat did nothing, Dick and Sally's measurements have nothing to do with each other. There is no way they could talk to each other.
But if the cat did entangle them, the two measurements are correlated. That's weird, the cat acted in the future and influenced what Dick and Sally saw before.
An actual experiment
It reminds me of those time travelling neutrinos that came back and loosened that cable so they wouldn't be found out. (Credit Kate)
Sunday, April 15, 2012
Some cute integrals
Normally I would hate evaluating integrals with trig functions with the white hot intensity of a thousand suns, but these are so cute they can get away with it.
Everybody get
. Good!
Next one
Everybody get. Good!
Next one
Keep doing these all the way until
Big surprise! What did you get?
Before doing the next one, guess the next one.
If you guessed , you would be wrong. It is actually about 2.31e-11 lower than that. Still a rational multiple of 
though. If you managed to guess that I tip my hat to you.
You can't possibly be satisfied with this. Something has to explain why the jump suddenly happened so far into the sequence.
Well, to do these better double the integral by going over the entire real line. Now use the property that integrating in real space and in momentum space gives the same results. The products of sincs becomes convolutions of box functions. In fact you might as well do this with a general sequence like so:
instead of the reciprocals of the odd integers like we did before.
Look at the running sums of the alphas we had before. You see that
The step where things mess up is when the sum jumps above 2. This is generally true as well. To show why this is true you need to look at the widths of the convolutions and how that grows.
Next time someone tells you to fill in the pattern
you can confidently tell them you have no fucking clue.
Everybody get
. Good!Next one
Everybody get
. Good!Next one
Keep doing these all the way until
Big surprise! What did you get?
Before doing the next one, guess the next one.
If you guessed
, you would be wrong. It is actually about 2.31e-11 lower than that. Still a rational multiple of though. If you managed to guess that I tip my hat to you.You can't possibly be satisfied with this. Something has to explain why the jump suddenly happened so far into the sequence.
Well, to do these better double the integral by going over the entire real line. Now use the property that integrating in real space and in momentum space gives the same results. The products of sincs becomes convolutions of box functions. In fact you might as well do this with a general sequence like so:
instead of the reciprocals of the odd integers like we did before.Look at the running sums of the alphas we had before. You see that
The step where things mess up is when the sum jumps above 2. This is generally true as well. To show why this is true you need to look at the widths of the convolutions and how that grows.
Next time someone tells you to fill in the pattern
you can confidently tell them you have no fucking clue.
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