A note on entanglement entropy for topological interfaces in RCFTs

In this paper we calculate the entanglement entropy for topological interfaces in rational conformal field theories for the case where the interface lies at the boundary of the entangling interval and for the case where it is located in the center of the entangling interval. We compare the results to each other and also to the recently calculated left/right entropy of a related BCFT. We also comment of the entanglement entropies for topological interfaces for a free compactified boson and Liouville theory.Comment: 17 pages, pdflatex, 2 figures, v2: references added, typos corrected and figure 2 improved, v3: minor correctio

Small representations, string instantons, and Fourier modes of Eisenstein series (with an appendix by D. Ciubotaru and P. Trapa)

This paper concerns some novel features of maximal parabolic Eisenstein series at certain special values of their analytic parameter s. These series arise as coefficients in the R4 and D4R4 interactions in the low energy expansion of scattering amplitudes in maximally supersymmetric string theory reduced to D=10-d dimensions on a torus T^d, d<8. For each d these amplitudes are automorphic functions on the rank d+1 symmetry group E_d+1. Of particular significance is the orbit content of the Fourier modes of these series when expanded in three different parabolic subgroups, corresponding to certain limits of string theory. This is of interest in the classification of a variety of instantons that correspond to minimal or next-to-minimal BPS orbits. In the limit of decompactification from D to D+1 dimensions many such instantons are related to charged 1/2-BPS or 1/4-BPS black holes with euclidean world-lines wrapped around the large dimension. In a different limit the instantons give nonperturbative corrections to string perturbation theory, while in a third limit they describe nonperturbative contributions in eleven-dimensional supergravity. A proof is given that these three distinct Fourier expansions have certain vanishing coefficients that are expected from string theory. In particular, the Eisenstein series for these special values of s have markedly fewer Fourier coefficients than typical ones. The corresponding mathematics involves showing that the wavefront sets of the Eisenstein series are supported on only certain coadjoint nilpotent orbits - just the minimal and trivial orbits in the 1/2-BPS case, and just the next-to-minimal, minimal and trivial orbits in the 1/4-BPS case. Thus as a byproduct we demonstrate that the next-to-minimal representations occur automorphically for E6, E7, and E8, and hence the first two nontrivial low energy coefficients are exotic theta-functions.Comment: v3: 127 pp. Minor changes. Final version to appear in the Special Issue in honor of Professor Steve Ralli

DDMF: An Efficient Decision Diagram Structure for Design Verification of Quantum Circuits under a Practical Restriction

Recently much attention has been paid to quantum circuit design to prepare for the future "quantum computation era." Like the conventional logic synthesis, it should be important to verify and analyze the functionalities of generated quantum circuits. For that purpose, we propose an efficient verification method for quantum circuits under a practical restriction. Thanks to the restriction, we can introduce an efficient verification scheme based on decision diagrams called Decision Diagrams for Matrix Functions (DDMFs). Then, we show analytically the advantages of our approach based on DDMFs over the previous verification techniques. In order to introduce DDMFs, we also introduce new concepts, quantum functions and matrix functions, which may also be interesting and useful on their own for designing quantum circuits.Comment: 15 pages, 14 figures, to appear IEICE Trans. Fundamentals, Vol. E91-A, No.1

Entanglement entropy at holographic interfaces

In this note we calculate the holographic entanglement entropy in the presence of a conformal interface for a geometric configuration in which the entangling region ${\cal A}$ lies on one side of the interface. For the supersymmetric Janus solution we find exact agreement between the holographic and CFT calculation of the entanglement entropy.Comment: 15 pages, 2 figures, pdflatex. v2: reference added, typos correcte

Relationships between land use and nitrogen and phosphorus in New Zealand lakes

Developing policies to address lake eutrophication requires an understanding of the relative contribution of different nutrient sources and of how lake and catchment characteristics interact to mediate the source–receptor pathway. We analysed total nitrogen (TN) and total phosphorus (TP) data for 101 New Zealand lakes and related these to land use and edaphic sources of phosphorus (P). We then analysed a sub-sample of lakes in agricultural catchments to investigate how lake and catchment variables influence the relationship between land use and in-lake nutrients. Following correction for the effect of co-variation amongst predictor variables, high producing grassland (intensive pasture) was the best predictor of TN and TP, accounting for 38.6% and 41.0% of variation, respectively. Exotic forestry and urban area accounted for a further 18.8% and 3.6% of variation in TP and TN, respectively. Soil P (representing naturally-occurring edaphic P) was negatively correlated with TP, owing to the confounding effect of pastoral land use. Lake and catchment morphology (zmax and lake : catchment area) and catchment connectivity (lake order) mediated the relationship between intensive pasture and in-lake nutrients. Mitigating eutrophication in New Zealand lakes requires action to reduce nutrient export from intensive pasture and quantifying P export from plantation forestry requires further consideration