Symmetry breaking patterns and collective modes of spin-one color superconductors

Spin-one color superconductor is a viable candidate phase of dense matter in the interiors of compact stars. Its low-energy excitations will influence the transport properties of such matter and thus have impact on late-stage evolution of neutron stars. It also provides a good example of spontaneous symmetry breaking with rich breaking patterns. In this contribution, we reanalyze the phase diagram of a spin-one color superconductor and point out that a part of it is occupied by noninert states, which have been neglected in literature so far. We classify the collective Nambu--Goldstone modes, which are essential to the transport phenomena.Comment: 6 pages, 1 figure, invited talk on the 4th International Symposium on Symmetries in Subatomic Physics, June 2-5,2009, Taipe

Energy shift of the three-particle system in a finite volume

Using the three-particle quantization condition recently obtained in the particle-dimer framework, the finite-volume energy shift of the two lowest three-particle scattering states is derived up to and including order $L^{-6}$. Furthermore, assuming that a stable dimer exists in the infinite volume, the shift for the lowest particle-dimer scattering state is obtained up to and including order $L^{-3}$. The result for the lowest three-particle state agrees with the results from the literature, and the result for the lowest particle-dimer state reproduces the one obtained by using the Luescher equation.Comment: Final version published in Phys. Rev. D. Corrected typos: factor of 2 in Eq. (115) [previously Eq. (114)] and factor 6 in Eq. (120) [previously Eq. (119)

Entanglement Entropy and Quantum Phase Transition in the O(N)O(N) σ\sigma-model

We investigate how entanglement entropy behaves in a system with a quantum phase transition. We study the $\sigma$-model which has an $O(N)$ symmetry when the mass squared parameter $\mu^2$ is positive, and when $\mu^2$ is negative, this symmetry is broken spontaneously. The area law and the leading divergence of entanglement entropy are preserved in both the symmetric and the broken phases. In 3+1 dimensions, the spontaneous symmetry breaking changes the subleading divergence from a log to log squared, while in 2+1 dimensions the subleading divergent structure is unchanged. At the leading order of the coupling constant expansion, the entanglement entropy reaches its local maximum with a cusp at the quantum phase transition point $\mu^2=0$ and decreases while $|\mu^2|$ is increased. We also find novel scaling behavior of the entanglement entropy near the transition point.Comment: 32 pp., 6 figures. v2. scaling behavior revised, 3 references added, submitted to JHE

Some recent progress on quark pairings in dense quark and nuclear matter

We give a brief overview on some recent progress in quark pairings in dense quark/nuclear matter mostly developed in the past five years. We focus on following aspects in particular: the BCS-BEC crossover in the CSC phase, the baryon formation and dissociation in dense quark/nuclear matter, the Ginzburg-Landau theory for three-flavor dense matter with $U_{A}$(1) anomaly, and the collective and Nambu-Goldstone modes for the spin-one CSC.Comment: RevTex 4, 25 pages, 9 figures, presented for the KITPC (Kavli Institute for Theoretical Physics China) program "AdS/CFT and Novel Approaches to Hadron and Heavy Ion Physics' in Oct. 11- Dec. 3, 201

Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data

We derive the three-body quantization condition in a finite volume using an effective field theory in the particle-dimer picture. Moreover, we consider the extraction of physical observables from the lattice spectrum using the quantization condition. To illustrate the general framework, we calculate the volume-dependent three-particle spectrum in a simple model both below and above the three-particle threshold. The relation to existing approaches is discussed in detail