Quantum Conserved Charges and S-matrices in N=2 Supersymmetric Sine-Gordon Theory

We study the quantum conserved charges and S-matrices of N=2 supersymmetric sine-Gordon theory in the framework of perturbation theory formulated in N=2 superspace. The quantum affine algebras ${\widehat {sl_{q}(2)}}$ and super topological charges play important roles in determining the N=2 soliton structure and S-matrices of soliton-(anti)soliton as well as soliton-breather scattering.Comment: 22 page

Density of States Scaling at the Semimetal to Metal Transition in Three Dimensional Topological Insulators

The quantum phase transition between the three dimensional Dirac semimetal and the diffusive metal can be induced by increasing disorder. Taking the system of disordered $\mathbb{Z}_2$ topological insulator as an important example, we compute the single particle density of states by the kernel polynomial method. We focus on three regions: the Dirac semimetal at the phase boundary between two topologically distinct phases, the tricritical point of the two topological insulator phases and the diffusive metal, and the diffusive metal lying at strong disorder. The density of states obeys a novel single parameter scaling, collapsing onto two branches of a universal scaling function, which correspond to the Dirac semimetal and the diffusive metal. The diverging length scale critical exponent $\nu$ and the dynamical critical exponent $z$ are estimated, and found to differ significantly from those for the conventional Anderson transition. Critical behavior of experimentally observable quantities near and at the tricritical point is also discussed.Comment: 5 pages, 5 figures, to appear in PR

The Orbifolds of N=2 Superconformal Theories with c=3

We construct Z_M, M= 2, 3, 4, 6 orbifold models of the N=2 superconformal field theories with central charge c=3. Then we check the description of the Z_3, Z_4 and Z_6 orbifolds by the N=2 superconformal Landau-Ginzburg models with c=3, by comparing the spectrum of chiral fields, in particular the Witten index Tr(-1)^F.Comment: 20 pages; typos corrected, references adde

A dynamic code for economic object valuation in prefrontal cortex neurons.

Neuronal reward valuations provide the physiological basis for economic behaviour. Yet, how such valuations are converted to economic decisions remains unclear. Here we show that the dorsolateral prefrontal cortex (DLPFC) implements a flexible value code based on object-specific valuations by single neurons. As monkeys perform a reward-based foraging task, individual DLPFC neurons signal the value of specific choice objects derived from recent experience. These neuronal object values satisfy principles of competitive choice mechanisms, track performance fluctuations and follow predictions of a classical behavioural model (Herrnstein's matching law). Individual neurons dynamically encode both, the updating of object values from recently experienced rewards, and their subsequent conversion to object choices during decision-making. Decoding from unselected populations enables a read-out of motivational and decision variables not emphasized by individual neurons. These findings suggest a dynamic single-neuron and population value code in DLPFC that advances from reward experiences to economic object values and future choices.Wellcome Trust, Behavioural and Clinical Neuroscience Institute (BCNI) Cambridg