Talks

The Bell Curve is an extremely beautiful and elegant mathematical object that turns up – often in surprising ways – in all spheres of human life. The Curve was first used by astronomers to correct errors in their observations, but it soon found important applications in the social and medical sciences in the eighteen hundreds. Some philosophers believe that a new kind of human being was created around this time largely due to the growth of statistical reasoning in the arts and sciences. Dr. Mighton will speak about the consequences of this new way of thinking about people, and further insights from his play called “Risk”, in which he is dramatizing these ideas. The Bell Curve also figures prominently in education as our school system is based on the implicit belief that there are natural, wide bell curves in achievement in students. In this lecture, Dr. Mighton will share evidence that this belief is false and he will describe how the arts and sciences, and society in general, might benefit if we rejected this belief.

Combining the principles of general relativity and quantum theory still remains as elusive as ever. Recent work, that concentrated on one of the points of contact (and conflict) between quantum theory and general relativity, suggests a new perspective on gravity. It appears that the gravitational dynamics in a wide class of theories - including, but not limited to, standard Einstein's theory - can be given a purely thermodynamic interpretation. In this approach gravity appears as an emergent phenomenon, like e.g., gas or fluid dynamics. I will describe the necessary background, key results and their implications as suggested by my recent work in this area.

This talk will discuss some surprising links which have emerged in the last few years between two at first sight distinct areas of mathematical physics: the spectral properties of certain simple schroedinger-like equations, and the Bethe ansatz techniques which are used to compute the energies of states in integrable quantum field theories. No knowledge of either area will be assumed.

Quantization of string theory on the AdS(3) backgrounds with the RR flux, such as AdS(3)xS(3)xT(4) or AdS(3)xS(3)xS(3)xS(1), is an unsolved problem. Since the sigma model on these backgrounds is classically integrable, one can try to implement powerful methods of integrability similar to those used to solve AdS(5)/CFT(4) and AdS(4)/CFT(3). I will describe the integrability approach to the AdS(3) backgrounds, emphasizing the differences to the better understood cases of AdS(5) and AdS(4).

I describe a novel abelian gauge theory in 2+1 dimensions which has surprising theoretical and phenomenological features. The theory has a vanishing coefficient for the square of the electric field $e_i^2$, characteristic of a quantum critical point with dynamical critical exponent $z=2$, and a level-$k$ Chern-Simons coupling, which is marginal at this critical point. For $k=0$, this theory is dual to a free $z=2$ scalar field theory describing a quantum Lifshitz transition, but $k \neq 0$ renders the scalar description non-local. The $k \neq 0$ theory exhibits properties intermediate between the (topological) pure Chern-Simons theory and the scalar theory. For instance, the Chern-Simons term does not make the gauge field massive. Nevertheless, there are chiral edge modes when the theory is placed on a space with boundary, and a non-trivial ground state degeneracy $k^g$ when it is placed on a finite-size Riemann surface of genus $g$. The coefficient of $e_i^2$ is the only relevant coupling; it tunes the system through a quantum phase transition between an isotropic fractional quantum Hall state and an anisotropic fractional quantum Hall state. I describe zero-temperature transport coefficients in both phases and at the critical point, and comment briefly on the relevance of the results to recent experiments.

The AdS/CFT correspondence has opened the door to understand a class of strongly coupled quantum field theories. Although the original correspondence has been conjectured based on string theory, it is possible that the underlying principle is more general, and a wider class of quantum field theories can be understood through holographic descriptions. In this talk, I will discuss about a prescription to construct holographic theories for general quantum field theories. As an example, I will present a holographic dual theory for the D-dimensional O(N) vector model. The phase transition and critical behaviors of the model are reproduced through the holographic theory.

The entanglement entropy of a pure quantum state of a bipartite system is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local Hamiltonians in one dimension have entanglement that diverges logarithmically in the subsystem size, with a universal coefficient that is is related to the central charge of the associated conformal field theory. In this talk I will discuss the extension of these ideas to two dimensional systems, either at a special quantum critical point or in a topological phase. We find the entanglement entropy for a standard class of z=2 quantum critical points in two spatial dimensions with scale invariant ground state wave functions: in addition to a nonuniversal ‘‘area law’’ contribution proportional to the size of the boundary of the region under observation, there is generically a universal logarithmically divergent correction, and in its absence a universal finite piece is found. This logarithmic term is completely determined by the geometry of the partition into subsystems and the central charge of the field theory that describes the equal-time correlations of the critical wavefunction. On the other hand, in a topological phase there is no such logarithmic term but instead a universal constant term. We will discuss the connection between this universal entanglement entropy and the nature of the topological phase.

Recently several proposals are made for possible spin liquid and topological insulator phases in frustrated magnets. I will review some of these efforts and present some new results. Implications to real materials will also be made.

The entanglement entropy in conformal field theory was predicted to include a boundary term which depends on the choice of conformally invariant boundary condition. We have studied this effect in the Kondo model of a magnetic impurity in a metal, which exhibits a renormalization group flow between conformally invariant fixed points.