On 6d "Gauge" Theories with Irrational Theta Angle

A recent proposal for 6d "gauge" theories with rational theta angle is discussed. These theories were constructed from n_C coinciding (p,q) 5-branes of IIB in the limit of vanishing string constant. They have (1,1) supersymmetry and the low energy theory is 6d Yang-Mills with gauge group SU(n_C) and a rational theta angle theta_6/(2 pi)=f/q, where fp=1 (mod q). By changing the point of view, considering the (p,q) 5-branes to be D5-branes, the 6d theta angle is identified with a 10d theta angle. This point of view together with some assumptions suggests a generalization of the previous limit to arbitrary theta. This limit seems to define a decoupled 6d theory even though the 10d theory does not become free in general.Comment: 8 pages, latex, 1 figur

Theory of Two-Photon Interactions with Broadband Down-Converted Light and Entangled Photons

When two-photon interactions are induced by down-converted light with a bandwidth that exceeds the pump bandwidth, they can obtain a behavior that is pulse-like temporally, yet spectrally narrow. At low photon fluxes this behavior reflects the time and energy entanglement between the down-converted photons. However, two-photon interactions such as two-photon absorption (TPA) and sum-frequency generation (SFG) can exhibit such a behavior even at high power levels, as long as the final state (i.e. the atomic level in TPA, or the generated light in SFG) is narrowband enough. This behavior does not depend on the squeezing properties of the light, is insensitive to linear losses, and has potential applications. In this paper we describe analytically this behavior for travelling-wave down-conversion with continuous or pulsed pumping, both for high- and low-power regimes. For this we derive a quantum-mechanical expression for the down-converted amplitude generated by an arbitrary pump, and formulate operators that represent various two-photon interactions induced by broadband light. This model is in excellent agreement with experimental results of TPA and SFG with high power down-converted light and with entangled photons [Dayan et al., Phys. Rev. Lett. 93, 023005 (2004), Dayan et al., Phys. Rev. Lett. 94, 043602, (2005), Pe'er et al., Phys. Rev. Lett. 94, 073601 (2005)].Comment: 23 pages, 4 figures, submitted to Phys. Rev.