Large-N analysis of (2+1)-dimensional Thirring model

We analyze $(2+1)$-dimensional vector-vector type four-Fermi interaction (Thirring) model in the framework of the $1/N$ expansion. By solving the Dyson-Schwinger equation in the large-$N$ limit, we show that in the two-component formalism the fermions acquire parity-violating mass dynamically in the range of the dimensionless coupling $\alpha$, $0 \leq \alpha \leq \alpha_c \equiv {1\over16} {\rm exp} (- {N \pi^2 \over 16})$. The symmetry breaking pattern is, however, in a way to conserve the overall parity of the theory such that the Chern-Simons term is not induced at any orders in $1/N$. $\alpha_c$ turns out to be a non-perturbative UV-fixed point in $1/N$. The $\beta$ function is calculated to be $\beta (\alpha) = -2 (\alpha - \alpha_c)$ near the fixed point, and the UV-fixed point and the $\beta$ function are shown exact in the $1/N$ expansion.Comment: 14 pages Latex. (Revised version: some changes have been made and references added.) To appear in Phys. Rev. D, SNUTP 93-4

Eta invariants with spectral boundary conditions

We study the asymptotics of the heat trace \Tr\{fPe^{-tP^2}\} where $P$ is an operator of Dirac type, where $f$ is an auxiliary smooth smearing function which is used to localize the problem, and where we impose spectral boundary conditions. Using functorial techniques and special case calculations, the boundary part of the leading coefficients in the asymptotic expansion is found.Comment: 19 pages, LaTeX, extended Introductio

Comment on "Spectroscopic Evidence for Multiple Order Parameter Components in the Heavy Fermion Superconductor CeCoIn5_5"

Recently, Rourke et al. reported point-contact spectroscopy results on the heavy-fermion superconductor CeCoIn$_5$ [1]. They obtained conductance spectra on the c-axis surfaces of CeCoIn$_5$ single crystals. Their major claims are two-fold: CeCoIn$_5$ has i) d-wave pairing symmetry and ii) two coexisting order parameter components. In this Comment, we show that these claims are not warranted by the data presented. [1] Rourke et al., Phys. Rev. Lett. 94, 107005 (2005).Comment: accepted for publication in Phys. Rev. Lett., final for

Universal curvature identities

We study scalar and symmetric 2-form valued universal curvature identities. We use this to establish the Gauss-Bonnet theorem using heat equation methods, to give a new proof of a result of Kuz'mina and Labbi concerning the Euler-Lagrange equations of the Gauss-Bonnet integral, and to give a new derivation of the Euh-Park-Sekigawa identity.Comment: 11 page