Search Talks

In the de Broglie-Bohm pilot-wave formulation of quantum theory, standard quantum probabilities arise spontaneously through a process of dynamical relaxation that is broadly similar to thermal relaxation in classical physics. If we are to regard this process as the cause of the quantum probabilities we observe today, then we must infer a primordial ‘quantum nonequilibrium’ in the remote past. Such quantum nonequilibrium may have left observable traces today, perhaps in the cosmic microwave background, or in relic particle species that decoupled in the very early universe and that have been sufficiently minimally interacting ever since. The search for the dark matter–that we observe today only through its gravitational interactions–has provided a compendium of particle species that could at least in
principle carry quantum nonequilibrium. If they did indeed exist, nonequilibrium distributions would not only demonstrate the need to reevaluate the canonical quantum formalism, but also generate new phenomena that lie outside the domain of conventional quantum theory, potentially opening up a large domain for investigation. We will develop a simple, parameter free, quantum field theoretical model of spectral measurement, and use it to demonstrate some of the novel effects that could occur to the profiles of the line spectra of such relic particles. We find for instance, line broadening effects that scale with the resolution of the telescope, the possibility of line narrowing and other effects that could cause multiple bumps to form. We use this discussion to comment on possible implications on the indirect search for dark matter.

I will explain how to axiomatize the notion of a chiral WZW model using the formalism of VOAs (vertex operator algebras). This class of models is in almost bijective correspondence with pairs (G,k), where G is a connected (not necessarily simply connected) Lie group and k in H^4(BG,Z) is a degree four cohomology class subject to a certain positivity condition. To my surprise, I have found a couple extra models which satisfy all the defining properties of chiral WZW models, but which don't come from pairs (G,k) as above. The simplest such model is the simple current extension of the affine VOA E8xE8 at level (2,2) by the group Z/2. Thus from a quantum perspective, the Lie group E8 x E8 behaves as if it had a non-trivial center.

It is interesting to note that, unlike Chern–Simons theories whose gauge group can be disconnected, the gauge group of a chiral WZW model is necessarily connected. This raises the question of what is the chiral WZW model associated to a disconnected gauge group? Whatever the answer turns out to be, mathematicians will probably need to enlarge the class of objects that they agree to call ‘chiral conformal field theories’ in order to accommodate these yet to be defined models.

I will present some speculations on the matter.