### Around the Blogs

I thought I’d take some time out for a little tour around the physics blogosphere. While there’s plenty of sturm und drang to be found in the usual places, there is also also some really nifty and worthwhile stuff out there

Georg, over at Life on the Lattice has a nice post on NRQCD on the lattice. In studying heavy quark bound states on the lattice, it is often very convenient to replace the Wilson (or Kogut-Susskind) action for the fermions with its non-relativistic counterpart. Obviously, halving the number of degrees of freedom simplifies the task of computing a fermi determinant. But that’s not where the saving really lies. It’s really in removing the rest-energy contribution to the Hamiltonian, (which, otherwise would dominate the decay of Euclidean correlation functions, $C(t,0) \sim e^{-m t}$) that makes the nonrelativistic approximation worthwhile.

I’d love to hear more about the tradeoffs in tuning the higher-order terms in the NRQCD Lagrangian and what the added complexity buys you, in terms of better numerical stability and faster convergence to the continuum.

Urs has a series of posts on Mathai’s approach to the “topological” aspects of T-duality. How T-duality acts on the K-theory of $M\times T^n$ is more-or-less understood. Mathai would like to bootstrap this to some statement about the algebra of functions $C(M\times T^n)$ (in which the K-theory is the algebraic K-theory of modules over this algebra).

Personally, I’m rather dubious of the approach, in that T-duality is more naturally described in terms of the loop space of $X$, rather than $X$ itself (remember, it exchanges momenta and windings). It’s neat, but somehow seemingly accidental, that it reduces to a simple mapping of the K-theories of $X$ and its T-dual.

Travis Stewart reports that the LHC’s ATLAS detector has seen cosmic ray events, an excellent sign that things are working as they should.

Mike Schmitt and Tomasso Dorigo have some posts about techniques for tagging b-jets.

Finally, on a more elmentary level, Dmitri Terryn has a nice little post about the elastic electromagnetic scattering cross-section, from its nonrelativistic, classical expression (Rutherford scattering) to its more complicated, fully quantum-mechanical variations.

Posted by distler at June 4, 2006 3:37 AM
## Re: Around the Blogs

Jacques Distler wrote:

Since, as you say, the approach to T-duality as followed by Mathai (and others) knows nothing about loop space, let alone about CFT (which is really where the duality lives), it is clearly just some sort of “shadow” of the full thing in terms of topological notions on target space.

(The question about the apparent “continuous orbifolding” which I mentioned is probably related to that, since clarifying it seems to call for a a setup that knows about the T-dual CFTs.)

I am not sure, though, how accidental the mapping between K-theories on T-dual target spaces is. Since these classes are where the RR-charges live, it seems necessary that such an isomorphism exists.

But that’s more a gut feeling than a precise statement.

It is no secret that “topological T-duality theorists” (like for instance also Ulrich Bunke math.GT/0501487) pretty mich just take the K-theory setup as given and are happy doing their math in that framework, without actively worrying about the connection to physics/CFT. The “abstract T-duality” definition which I mention at the end of part III certainly certifies this.

I would like to see the connection of the topological T-duality technology to CFT. As I tried to indicate before, there is an interesting analogy, which might point in the right direction.

So on the one hand side we see in the topological T-duality approach the Fourier-Mukai transformation on the correspondence space of the torus and its dual. In as far as the sheaves on $M \times \mathbf{T}$ that we are dealing with are modules for the structure sheaf, the Fourier-Mukai correspondence is a bimodule, and its operation on these sheaves by pullback can be understood alternatively in terms of the tensor product of modules.

Now, this is rather reminiscent of the way T-duality is realized in the Frobenius-algebraic approch to (R)CFT ($\to$).

As will be detailed in upcoming work that has been announced in cond-mat/0404051, T-duality (like other dualities) is induced by the action of certain bimodules internal to the representation category of the chiral vertex algebra.

I am hoping that this can be used to make the connection between T-duality in full CFT and the topological T-duality on target space studied by Mathai, Bunke et. al.

But that’s just me.