Topological Defect Lines and Renormalization Group Flows in Two Dimensions

We consider topological defect lines (TDLs) in two-dimensional conformal field theories. Generalizing and encompassing both global symmetries and Verlinde lines, TDLs together with their attached defect operators provide models of fusion categories without braiding. We study the crossing relations of TDLs, discuss their relation to the 't Hooft anomaly, and use them to constrain renormalization group flows to either conformal critical points or topological quantum field theories (TQFTs). We show that if certain non-invertible TDLs are preserved along a RG flow, then the vacuum cannot be a non-degenerate gapped state. For various massive flows, we determine the infrared TQFTs completely from the consideration of TDLs together with modular invariance.Comment: 101 pages, 63 figures, 2 tables; v3: minor changes, added footnotes and references, published versio

Little String Amplitudes (and the Unreasonable Effectiveness of 6D SYM)

We study tree level scattering amplitudes of four massless states in the double scaled little string theory, and compare them to perturbative loop amplitudes in six-dimensional super-Yang-Mills theory. The little string amplitudes are computed from correlators in the cigar coset CFT and in N=2 minimal models. The results are expressed in terms of integrals of conformal blocks and evaluated numerically in the alpha' expansion. We find striking agreements with up to 2-loop scattering amplitudes of massless gluons in 6D SU(k) SYM at a Z_k invariant point on the Coulomb branch. We comment on the issue of UV divergence at higher loop orders in the gauge theory and discuss the implication of our results.Comment: 58 pages, 5 figures, 3 tables, comments added, references adde

Risk Spillovers in Returns for Chinese and International Tourists to Taiwan

Fluctuations in the numbers of visitors directly affect the rates of return on tourism business activities. Therefore, maintaining a firm grasp of the relationship between the changes in the numbers of Chinese tourists and international travellers visiting Taiwan is conducive to the formulation of an effective and practical tourism strategy. Although the topic of international visitors to Taiwan is important, existing research has discussed the issue of the travel demand between Chinese tourists and international travellers visiting Taiwan. This paper is the first to examine the spillover effects between the rate of change in the numbers of Chinese tourist arrivals and the rate of change in the numbers of international traveller arrivals. Using daily data for Chinese tourists and international travellers visiting Taiwan over the period from 1 January 2014 to 31 October 2016, together with the Diagonal BEKK model, the paper analyses the co-volatility spillover effects between the rate of change in the numbers of international travellers and the rate of change in the numbers of Chinese tourists visiting Taiwan. The empirical results show that there is no dependency relationship between the rate of change in the numbers of Chinese tourists and the rate of change in the numbers of international travellers visiting Taiwan. However, there is a significant negative co-volatility spillover effect between the rate of change in the numbers of Chinese tourists and the rate of change in the numbers of international travellers. The empirical findings suggest that Taiwan should abandon its development strategy of focusing only on a single market, namely China, and to be pro-active in encouraging visits by international travellers to Taiwan for sightseeing purposes, thereby increasing the willingness of international travellers to visit Taiwan. Moreover, with the reduction in the numbers of Chinese tour groups visiting Taiwan, and increases in the numbers of individual travellers, the Taiwan Government should change its previous travel policies of mainly attracting Chinese tour group travellers and actively promoting in-depth tourism among international tourists, by developing tourism that focuses on the special characteristics of different localities. In this way, the government can enhance the quality of Taiwan’s tourism, and also attract travellers with high spending power