Phenomenally beautiful math was the main highlight of this week, I’d say, although none of it for the very faint of heart.
High Energy Physics and Particles:
The CMS Collaboration released results this month ruling out supersymmetric particles with masses of less than ~ 0.5 TeV/c2. This is just one of a series of ongoing SUSY related papers analyzing last years data and spitting out constraints on models (which is hugely important). We’ll be seeing results papers for years to come, but it’s nice to see evidence of the LHC being exactly what we all hoped it would be already: the thing that tells us if we’re likely on the right track or not.
For more, see Reality check at the LHC.
General Relativity, Quantum Gravity, et al.:
Silke Weinfurtner, Edmund W. Tedford, Matthew C. J. Penrice, William G. Unruh, & Gregory A. Lawrence (2010). Measurement of stimulated Hawking emission in an analogue system Phys. Rev. Lett., 106 (2), 1302-1306 arXiv: 1008.1911v2
Hawking argued that black holes emit thermal radiation via a quantum spontaneous emission. To address this issue experimentally, we utilize the analogy between the propagation of fields around black holes and surface waves on moving water. By placing a streamlined obstacle into an open channel flow we create a region of high velocity over the obstacle that can include surface wave horizons. Long waves propagating upstream towards this region are blocked and converted into short (deep-water) waves. This is the analogue of the stimulated emission by a white hole (the time inverse of a black hole), and our measurements of the amplitudes of the converted waves demonstrate the thermal nature of the conversion process for this system. Given the close relationship between stimulated and spontaneous emission, our findings attest to the generality of the Hawking process.
Analogues often make me a little uncomfortable in physics, for what are probably obvious reasons, but Bill Unruh has had a lot of success and acceptance with his analogue black hole/white hole models in the past. The line between similar and the same, and if it is actually telling us anything to observe properties in these analogue systems (which have some major fundamental differences) always gets to me in these matters, so I’m going to have to come back to this one to give further comments.
We develop an approach to Khovanov homology of knots via gauge theory (previous physics-based approches involved other descriptions of the relevant spaces of BPS states). The starting point is a system of D3-branes ending on an NS5-brane with a nonzero theta-angle. On the one hand, this system can be related to a Chern-Simons gauge theory on the boundary of the D3-brane worldvolume; on the other hand, it can be studied by standard techniques of S-duality and T-duality. Combining the two approaches leads to a new and manifestly invariant description of the Jones polynomial of knots, and its generalizations, and to a manifestly invariant description of Khovanov homology, in terms of certain elliptic partial differential equations in four and five dimensions.
So Ed Witten is one of those few authors whose work I can feel safe about getting excited over before I’ve read it, and at 146 pages, well, it’s unlikely I’ll ever make it through all of this (although its length is only due to the fact that it very thorough, and thus imaginably very useful). I’m going to defer to the University of Toronto’s Daniel Moskovich from Low Dimensional Topology (which I can’t recommend enough) on this one, as he wrote:
Based on Witten’s record on such topics, and on a preliminary visual scan of the introduction, it would not be unreasonable to surmise that this preprint could change history. Khovanov homology will never look the same again. …This is trully a momentous occasion for knot theory!
For more, see Newsflash: Witten’s new preprint.
The basic concepts from the paper:
Noncommutative (NC) geometry provides a rich mathematical framework to modify the standard formalism of quantum field theory (QFT) in order to include quantum effects of spacetime
itself. … we collect the required tools from Drinfel’d twists and their associated NC geometry… We define an action functional for a real and free scalar field on twist-deformed curved spacetimes … and derive the corresponding deformed wave operator. … The deformed Green’s operators are constructed… to construct the space of real solutions of the deformed wave equation …The quantization is performed… “
And the important conclusions:
We have shown that the deformed symplectic R[[l ]]-module is isomorphic, via symplectic isomorphisms, to the formal power series extension of the undeformed symplectic vector space.
A direct consequence of this symplectic isomorphism for the deformed QFT is that it is ∗-algebra isomorphic to the formal power series extension of the undeformed QFT. This immediately yields isomorphisms between the corresponding groups of symplectic automorphisms and bijections between
the corresponding spaces of algebraic states.
Noncommutative spacetimes, or spaces, for that matter, are not things I have spent much time looking at, so I honestly can’t speak to the real content of this paper, other than by saying that there is growing interest in QFT on noncommutative spacetimes and those in quantum gravity should perhaps take note of it.
This isn’t about new research, per se, but Fred Van Oystaeyen has an interesting article on noncommutative space that is worth a read.