Talks

The space of convex polyhedra can be given a dynamical structure. Exploiting this dynamics we have performed a Bohr-Sommerfeld quantization of the volume of a tetrahedral grain of space, which is in excellent agreement with loop gravity. Here we present investigations of the volume of a 5-faced convex polyhedron. We give for the first time a constructive method for finding these polyhedra given their face areas and normals to the faces and find an explicit formula for the volume. This results
in new information about cylindrical consistency in loop gravity and a couple of surprises about polyhedra. In particular, we are interested in discovering whether the evolution generated by this volume is chaotic or integrable as this will impact the interpretation of the spin network basis in loop gravity. 

There is strong theoretical evidence that black holes have a finite thermodynamic entropy equal to one quarter the area A of the horizon. Providing a microscopic derivation of the entropy of the horizon is a major task for a candidate theory of quantum gravity. Loop quantum gravity has been shown to provide a geometric explanation of the finiteness of the entropy and of the proportionality to the area of the horizon. The microstates are quantum geometries of the horizon. What has been missing until recently is the identification of the near-horizon quantum dynamics and a derivation of the universal form of the Bekenstein-Hawking entropy with its 1/4 prefactor. I report recent progress in this direction. In particular, I discuss the covariant spin foam dynamics and and show that the entropy of the quantum horizon reproduces the Bekenstein-Hawking entropy S=A/4 with the proper one-fourth coefficient for all values of the Immirzi parameter.

It is certainly possible to express ordinary quantum mechanics in the framework of a real vector space: by adopting a suitable restriction on all operators--Stueckelberg’s rule--one can make the real-vector-space theory exactly equivalent to the standard complex theory.  But can we achieve a similar effect without invoking such a restriction?  In this talk I explore a model within real-vector-space quantum theory in which the role of the complex phase is played by a separate physical system called the ubit (for “universal rebit”).  The ubit is a single binary real-vector-space quantum object that is allowed to interact with everything in the world.  It also rotates in its two-dimensional state space.  In the limit of infinitely fast rotation, one recovers standard quantum theory.  When the rotation rate is large but not infinite, one finds small deviations from the standard theory.  Here I describe a few such deviations that we have seen numerically and explained analytically.

We add a gravitational background lattice to the simplest holographic model of matter at finite density and calculate the optical conductivity. With the lattice, the zero frequency delta function found in previous calculations (resulting from translation invariance) is broadened and the DC conductivity is finite. The optical conductivity exhibits a Drude peak with a cross-over to power-law behavior at higher frequencies. Surprisingly, these results bear a strong resemblance to the properties of some of the cuprates.

Precision timepieces are marvels of human ingenuity. Over the past half-a-century, precision time-keeping has been carried out with atomic clocks. I will review a novel and rapidly developing class of atomic clocks, optical lattice clocks. At their projected accuracy level, these would neither lose nor gain a fraction of a second over estimated age of the Universe. In other words, if someone were to build such a clock at the Big Bang and if such a timepiece were to survive the 14 billion years, the clock would be off by no more than a mere second. What can we do with this new-found precision? How can we exploit this exquisite ability to listen carefully for probing new physics?

In the second part of my talk I will overview atomic searches for new physics beyond the Standard Model of elementary particles.  I will report on a refined analysis of table-top experiments on violation of mirror symmetry in atoms. This analysis sets new constraints on a hypothesized particle, the extra
Z-boson. Our raised bound on the Z' masses improves upon the Tevatron results and carves out a
lower-energy part of the discovery reach of the Large Hadron Collider.

In spacetime physics any set C of events—a causal set—is taken to be partially ordered by the relation £ of possible causation: for p, q Î C,   p £ q means that q is in p’s future light cone. Fotini Markopoulou has proposed that the causal structure of spacetime itself be represented by “sets evolving over C” —that is, in essence, by the topos Set C of presheaves on Cop.  In this talk I am going to show how Set  C may be effectively replaced by a certain model V(H) of intuitionistic set theory—frame-valued set theory—with (I hope) illuminating results. In particular, Markopoulou’s idea of viewing the universe “from the inside” will amount to placing oneself “inside” V(H). I will also sketch the role played in this framework by covering schemes and sheaves.

A local renormalization group procedure is proposed where length scale is changed in spacetime dependent manner. Combining this scheme with an earlier observation that high energy modes in renormalization group play the role of dynamical sources for low energy modes at each scale, we provide a prescription to derive background independent holographic duals for field theories. From a first principle construction, it is shown that the holographic theory dual to a D-dimensional matrix field theory is a (D+1)-dimensional quantum theory of gravity coupled with matter fields of various spins.The (D+1)-dimensional diffeomorphism invariance is a consequence of the freedom to choose different local RG schemes.

A beautiful understanding of the smallness of the neutrino masses may be obtained via the seesaw mechanism, whereby one takes advantage of the key qualitative distinction between the neutrinos and the other fermions: right-handed neutrinos are gauge singlets, and may therefore have large Majorana masses. The standard seesaw mechanism, however, does not address the apparent lack of hierarchy in the neutrino masses compared to the quarks and charged leptons, nor the large leptonic mixing angles compared to the small angles of the CKM matrix. In this talk, I will show that the singlet nature of the right-handed neutrinos may be taken advantage of in one further way in order to solve these remaining problems: Unlike particles with gauge interactions, whose numbers are constrained by anomaly cancellation, the number of gauge singlet particles is essentially undetermined. If large numbers of gauge singlet fermions are present at high energies - as is suggested, for example, by various string constructions - then the effective low energy neutrino mass matrix may be determined as a sum over many distinct Yukawa couplings, with the largest ones being the most important. This can reduce hierarchy, and lead to large mixing angles. Assuming a statistical distribution of fundamental parameters, we will show that this scenario leads to a good fit to low energy phenomenology, with only a few qualitative assumptions guided by the known quark and lepton masses. The scenario leads to predictions of a normal hierarchy for the neutrino masses, and a value for the |m_ee| mass matrix element of about 1-6 meV.

How did inflation actually happen? Precision measurements of statistical properties of primordial fluctuations generated during inflation offer a direct probe of the physics of inflation. When we calculate statistical properties of primordial fluctuations generated during inflation, we usually assume that the initial state of quantum fluctuations is in a preferred vacuum state called Bunch-Davies vacuum. While there is some motivation for choosing such a state, this is an assumption, and thus needs to be tested by observations. In this talk I will present new probes of initial state of quantum fluctuations during inflation: the 3-point function of the cosmic microwave background anisotropy, the 2-point function of galaxies, and a spectral distortion of the thermal spectrum of the cosmic microwave background.