Quantum criticality between topological and band insulators in 3+1 dimensions

Four-component massive and massless Dirac fermions in the presence of long range Coulomb interaction and chemical potential disorder exhibit striking fermionic quantum criticality. For an odd number of flavors of Dirac fermions, the sign of the Dirac mass distinguishes the topological and the trivial band insulator phases, and the gapless semimetallic phase corresponds to the quantum critical point that separates the two. Up to a critical strength of disorder, the semimetallic phase remains stable, and the universality class of the direct phase transition between two insulating phases is unchanged. Beyond the critical strength of disorder the semimetallic phase undergoes a phase transition into a disorder controlled diffusive metallic phase, and there is no longer a direct phase transition between the two types of insulating phases.     

Quantum gravity in 2 + ε dimensions

We examine quantum gravity in 2 + ε dimensions, where the theory is formally renormalizable. Paying due attention to surface integrals (which prove crucial), we calculate the one-loop counterterms and establish a criterion for asymptotic freedom. We find, incidentally, that the β function vanishes to one-loop order for all models which are supersymmetric in two dimensions.     

Quantum theory of dilaton gravity in 1+1 dimensions

We discuss the quantum theory of 1+1 dimensional dilaton gravity, which is an interesting model with features analogous to the spherically symmetric gravitational systems in 3+1 dimensions. The functional measures over the metrics and the dilaton field are explicitly evaluated and the diffeomorphism invariance is completely fixed in the conformal gauge by using the technique developed in two dimensional quantum gravity. We derive the Wheeler-DeWitt like equations as physical state conditions. In the ADM formalism the measures of fields are very ambiguous, but in our formalism they are explicitly defined. A singularity appears at ²=κ(>0), where and N is the number of matter fields. The final stage of the black hole evaporation corresponds to the region ²κ, where the Liouville term becomes important, which just comes from the measure of the metrics. If κ<0, the singularity disappears.     

（2+1）维动态黑洞的量子熵

在Tortoise坐标系中，利用brick-wall模型研究了来源于标量场的(2+1)维动态黑洞的量子熵.结果表明，在视界附近的薄区域内标量场的熵与黑洞熵有相同结构.特别是在静态情况下，量子熵满足熵的周长律. 关键词： 标量场 brick-wall模型 (2+1)维动态黑洞 量子熵     

Integrable nonlinear evolution partial differential equations in 4 + 2 and 3 + 1 dimensions

The derivation and solution of integrable nonlinear evolution partial differential equations in three spatial dimensions has been the holy grail in the field of integrability since the late 1970s. The celebrated Korteweg-de Vries and nonlinear Schr?dinger equations, as well as the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations, are prototypical examples of integrable evolution equations in one and two spatial dimensions, respectively. Do there exist integrable analogs of these equations in three spatial dimensions? In what follows, I present a positive answer to this question. In particular, I first present integrable generalizations of the KP and DS equations, which are formulated in four spatial dimensions and which have the novelty that they involve complex time. I then impose the requirement of real time, which implies a reduction to three spatial dimensions. I also present a method of solution.     

Skyrmion dynamics in 2 + 1 dimensions

The classical dynamics of slowly moving CP¹ skyrmions in 2 + 1 dimensions is shown to be described by the geodesic motion on a Kähler manifold of “quark” and “anti-quark” constituents. Including a Hopf term in the lagrangian gives rise to interpolating quantum statistics and evaluation of the virial expansion amounts to the calculation of heat kernels for operators in a flux tube field background.     

Einstein-Maxwell theory in 2+1 dimensions

Einstein-Maxwell theory in 2+1 dimensions is considered as a toy model for the 3+1 theory and as a means for understanding field theories without a background space-time geometry. Two possible approaches to the quantization of this theory are presented, one based on a Schwinger-Tomonaga time evolution equation and the other on a loop space construction, and the problems arising in both of these are discussed.     

Quantum antiferromagnetism in 2 dimensions

We study the spin dynamics of the 2-dimensional spin 1/2 Heisenberg model at finite temperatureT, in particular the frequency region <TJ (the coupling constant). The main conclusion reached is that the spin fluctuations have relaxational character, no propagating spin waves exist for <T. Comparison with experimental results on La₂CuO₄ give good agreement. Similarities and differences to previous theoretical treatments are discussed.     

Skyrmions in (3+1) dimensions

We derive an analytical approximation to the skyrmion profile function. We check the quality of this approximation by using it to study various properties of the two skyrmion interactions. We find a good agreement with the numerical results of Verbaarschot et al. and Jackson et al.     

Quantum codimension-two cosmology

We generalize the 2-codimensional quantum cosmological model with the vacuum seed instanton to that with a non-vacuum seed instanton associated with the Gibbons–Townsend monopole. The confusion in the literature that substituting a field configuration into an action and varying that action is not equivalent to substituting it into the field equations is clarified.