Compactified Imaginary Liouville Theory

On a given Riemann surface, we construct a path integral based on the Liouville action functional with imaginary parameters. The construction relies on the compactified Gaussian Free Field (GFF), which we perturb with a curvature term and an exponential potential. In physics this path integral is conjectured to describe the scaling limit of critical loop models such as Potts and O(n) models. The potential term is defined by means of imaginary Gaussian Multiplicative Chaos theory. The curvature term involves integrated 1-forms, which are multivalued on the manifold, and requires a delicate regularisation in order to preserve diffeomorphism invariance. We prove that the probabilistic path integral satisfies the axioms of Conformal Field Theory (CFT) including Segal's gluing axioms. We construct the correlation functions for this CFT, involving electro-magnetic operators. This CFT has several exotic features: most importantly, it is non unitary and has the structure of a logarithmic CFT. This is the first mathematical construction of a logarithmic CFT and therefore the present paper provides a concrete mathematical setup for this concept

The timecourse of higher-level face aftereffects

AbstractPerceptual aftereffects for simple visual attributes processed early in the cortical hierarchy increase logarithmically with adapting duration and decay exponentially with test duration. This classic timecourse has been reported recently for a face identity aftereffect [Leopold, D. A., Rhodes, G., Müller, K.-M., & Jeffery, L. (2005). The dynamics of visual adaptation to faces. Proceedings of the Royal Society of London, Series B, 272, 897–904], suggesting that the dynamics of visual adaptation may be similar throughout the visual system. An alternative interpretation, however, is that the classic timecourse is a flow-on effect of adaptation of a low-level, retinotopic component of the face identity aftereffect. Here, we examined the timecourse of the higher-level (size-invariant) components of two face aftereffects, the face identity aftereffect and the figural face aftereffect. Both showed the classic pattern of logarithmic build-up and exponential decay. These results indicate that the classic timecourse of face aftereffects is not a flow-on effect of low-level retinotopic adaptation, and support the hypothesis that dynamics of visual adaptation are similar at higher and lower levels of the cortical visual hierarchy. They also reinforce the perceptual nature of face aftereffects, ruling out demand characteristics and other post-perceptual factors as plausible accounts