On c-theorems in arbitrary dimensions

The dilaton action in 3+1 dimensions plays a crucial role in the proof of the a-theorem. This action arises using Wess-Zumino consistency conditions and crucially relies on the existence of the trace anomaly. Since there are no anomalies in odd dimensions, it is interesting to ask how such an action could arise otherwise. Motivated by this we use the AdS/CFT correspondence to examine both even and odd dimensional CFTs. We find that in even dimensions, by promoting the cut-off to a field, one can get an action for this field which coincides with the WZ action in flat space. In three dimensions, we observe that by finding an exact Hamilton-Jacobi counterterm, one can find a non-polynomial action which is invariant under global Weyl rescalings. We comment on how this finding is tied up with the F-theorem conjectures.Comment: 25 pages, v3: reference added, Cotton tensor dependence of counterterm at eight-derivative order shown, v4: published versio

CW-pumped telecom band polarization entangled photon pair generation in a Sagnac interferometer

A polarization entangled photon pair source is widely used in many quantum information processing applications such as teleportation, quantum swapping, quantum computation and high precision quantum metrology. Here, we report on the generation of a continuous-wave pumped degenerated 1550 nm polarization entangled photon pair source at telecom wavelength using a type-II phase-matched periodically poled KTiOPO4 crystal in a Sagnac interferometer. Hong-Ou-Mandel-type interference measurement shows the photon bandwidth of 2.4 nm. High quality of entanglement is verified by various kinds of measurements, for example two-photon interference fringes, Bell inequality and quantum states tomography. The wavelength of photons can be tuned over a broad range by changing the temperature of crystal or pump power without losing the quality of entanglement. This source will be useful for building up long-distance quantum networks