Tentative Detection of Deuterated Methane toward the Low-Mass Protostar IRAS 04368+2557 in L1527

The millimeter-wave rotational transition line ($J_K = 1_0 - 0_0$) of deuterated methane CH$_3$D has tentatively been detected toward the low-mass Class 0 protostar IRAS 04368+2557 in L1527 with the Heinrich Hertz Submillimeter Telescope. This is the first detection of CH$_3$D in interstellar clouds, if confirmed. The column density and fractional abundance of CH$_3$D are determined to be $(9.1\pm3.4) \times 10^{15}$ cm$^{-2}$ and $(3.0\pm1.1) \times 10^{-7}$, respectively, where we assume the rotational temperature of 25 K. The column density and fractional abundance of the gaseous CH$_4$ are estimated to be $(1.3-4.6) \times 10^{17}$ cm$^{-2}$ and $(4.3-15.2) \times 10^{-6}$, respectively, by adopting the molecular D/H ratios of 2--7% reported for various molecules in L1527. The fractional abundance of CH$_4$ is higher than or comparable to that found in high-mass star-forming cores by infrared observations. It is sufficiently high for triggering the efficient production of various carbon-chain molecules in a lukewarm region near the protostar, which supports the picture of the warm carbon-chain chemistry.Comment: 13 page

Lace expansion for the Ising model

The lace expansion has been a powerful tool for investigating mean-field behavior for various stochastic-geometrical models, such as self-avoiding walk and percolation, above their respective upper-critical dimension. In this paper, we prove the lace expansion for the Ising model that is valid for any spin-spin coupling. For the ferromagnetic case, we also prove that the expansion coefficients obey certain diagrammatic bounds that are similar to the diagrammatic bounds on the lace-expansion coefficients for self-avoiding walk. As a result, we obtain Gaussian asymptotics of the critical two-point function for the nearest-neighbor model with d>>4 and for the spread-out model with d>4 and L>>1, without assuming reflection positivity.Comment: 54 pages, 12 figure

A note on higher spin symmetry in the IIB matrix model with the operator interpretation

We study the IIB matrix model in an interpretation where the matrices are differential operators defined on curved spacetimes. In this interpretation, coefficients of higher derivative operators formally appear to be massless higher spin fields. In this paper, we examine whether the unitary symmetry of the matrices includes appropriate higher spin gauge symmetries. We focus on fields that are bosonic and relatively simple in the viewpoint of the representation of Lorentz group. We find that the additional auxiliary fields need to be introduced in order to see the higher spin gauge symmetries explicitly. At the same time, we point out that a part of these extra fields are gauged-away, and the rest of part can be written in terms of a totally symmetric tensor field. The transformation to remove its longitudinal components exists as well. As a result, we observe that the independent physical DoF are the transverse components of that symmetric field, and that the theory describes the corresponding higher spin field. We also find that the field is not the Fronsdal field, rather the generalization of curvature.Comment: 1+14 pages, 1 figure; discussion on EOM added, Version to appear in NPB (v2

Topological string amplitudes for the local half K3 surface

We study topological string amplitudes for the local half K3 surface. We develop a method of computing higher-genus amplitudes along the lines of the direct integration formalism, making full use of the Seiberg-Witten curve expressed in terms of modular forms and E_8-invariant Jacobi forms. The Seiberg-Witten curve was constructed previously for the low-energy effective theory of the non-critical E-string theory in R^4 x T^2. We clarify how the amplitudes are written as polynomials in a finite number of generators expressed in terms of the Seiberg-Witten curve. We determine the coefficients of the polynomials by solving the holomorphic anomaly equation and the gap condition, and construct the amplitudes explicitly up to genus three. The results encompass topological string amplitudes for all local del Pezzo surfaces.Comment: 35 pages, v2: several clarifications made, an equation and references added, v3: published versio