How to add a boundary condition

Given a conformal QFT local net of von Neumann algebras B_2 on the two-dimensional Minkowski spacetime with irreducible subnet A\otimes\A, where A is a completely rational net on the left/right light-ray, we show how to consistently add a boundary to B_2: we provide a procedure to construct a Boundary CFT net B of von Neumann algebras on the half-plane x>0, associated with A, and locally isomorphic to B_2. All such locally isomorphic Boundary CFT nets arise in this way. There are only finitely many locally isomorphic Boundary CFT nets and we get them all together. In essence, we show how to directly redefine the C* representation of the restriction of B_2 to the half-plane by means of subfactors and local conformal nets of von Neumann algebras on S^1.Comment: 20 page

Group Cohomology, Modular Theory and Space-time Symmetries

The Bisognano-Wichmann property on the geometric behavior of the modular group of the von Neumann algebras of local observables associated to wedge regions in Quantum Field Theory is shown to provide an intrinsic sufficient criterion for the existence of a covariant action of the (universal covering of) the Poincar\'e group. In particular this gives, together with our previous results, an intrinsic characterization of positive-energy conformal pre-cosheaves of von Neumann algebras. To this end we adapt to our use Moore theory of central extensions of locally compact groups by polish groups, selecting and making an analysis of a wider class of extensions with natural measurable properties and showing henceforth that the universal covering of the Poincar\'e group has only trivial central extensions (vanishing of the first and second order cohomology) within our class.Comment: 18 pages, plain TeX, preprint Roma Tor vergata n. 20 dec. 9

A 2.5-D representation of the human hand

Primary somatosensory maps in the brain represent the body as a discontinuous, fragmented set of 2-D skin regions. We nevertheless experience our body as a coherent 3-D volumetric object. The links between these different aspects of body representation, however, remain poorly understood. Perceiving the body’s location in external space requires that immediate afferent signals from the periphery be combined with stored representations of body size and shape. At least for the back of the hand, this body representation is massively distorted, in a highly stereotyped manner. Here we test whether a common pattern of distortions applies to the entire hand as a 3-D object, or whether each 2-D skin surface has its own characteristic pattern of distortion. Participants judged the location in external space of landmark points on the dorsal and palmar surfaces of the hand. By analyzing the internal configuration of judgments, we produced implicit maps of each skin surface. Qualitatively similar distortions were observed in both cases. The distortions were correlated across participants, suggesting that the two surfaces are bound into a common underlying representation. The magnitude of distortion, however, was substantially smaller on the palmar surface, suggesting that this binding is incomplete. The implicit representation of the human hand may be a hybrid, intermediate between a 2-D representation of individual skin surfaces and a 3-D representation of the hand as a volumetric object

Nets of Subfactors

A subtheory of a quantum field theory specifies von~Neumann subalgebras \aa(\oo) (the `observables' in the space-time region \oo) of the von~Neumann algebras \bb(\oo) (the `fields' localized in \oo). Every local algebra being a (type \III_1) factor, the inclusion \aa(\oo) \subset \bb(\oo) is a subfactor. The assignment of these local subfactors to the space-time regions is called a `net of subfactors'. The theory of subfactors is applied to such nets. In order to characterize the `relative position' of the subtheory, and in particular to control the restriction and induction of superselection sectors, the canonical endomorphism is studied. The crucial observation is this: the canonical endomorphism of a local subfactor extends to an endomorphism of the field net, which in turn restricts to a localized endomorphism of the observable net. The method allows to characterize, and reconstruct, local extensions \bb of a given theory $\aa$ in terms of the observables. Various non-trivial examples are given.Comment: Plain TeX, 32 pages. Several unnecessarily restrictive assumptions have been relaxed. Proposition 4.10. has been reformulated in a more natural way. Sect. 3 has been rearranged and a too general statement has been adjusted. Some further minor change

Tool use induces complex and flexible plasticity of human body representations

Plasticity of body representation fundamentally underpins human tool use. Recent studies have demonstrated remarkably complex plasticity of body representation in humans, showing that such plasticity: (1) occurs flexibly across multiple time-scales, and (2) involves multiple body representations responding differently to tool use. Such findings reveal remarkable sophistication of body plasticity in humans, suggesting that Vaesen may overestimate the similarity of such mechanisms in humans and non-human primates

The classification of non-local chiral CFT with c<1

All non-local but relatively local irreducible extensions of Virasoro chiral CFTs with c<1 are classified. The classification, which is a prerequisite for the classification of local c<1 boundary CFTs on a two-dimensional half-space, turns out to be 1 to 1 with certain pairs of A-D-E graphs with distinguished vertices.Comment: 13 pages. v3: additional material (concerning the Hilbert spaces) adde

How to remove the boundary in CFT - an operator algebraic procedure

The relation between two-dimensional conformal quantum field theories with and without a timelike boundary is explored.Comment: 18 pages, 2 figures. v2: more precise title, reference correcte

More than skin deep: body representation beyond primary somatosensory cortex

The neural circuits underlying initial sensory processing of somatic information are relatively well understood. In contrast, the processes that go beyond primary somatosensation to create more abstract representations related to the body are less clear. In this review, we focus on two classes of higher-order processing beyond somatosensation. Somatoperception refers to the process of perceiving the body itself, and particularly of ensuring somatic perceptual constancy. We review three key elements of somatoperception: (a) remapping information from the body surface into an egocentric reference frame (b) exteroceptive perception of objects in the external world through their contact with the body and (c) interoceptive percepts about the nature and state of the body itself. Somatorepresentation, in contrast, refers to the essentially cognitive process of constructing semantic knowledge and attitudes about the body, including: (d) lexical-semantic knowledge about bodies generally and one’s own body specifically, (e) configural knowledge about the structure of bodies, (f) emotions and attitudes directed towards one’s own body, and (g) the link between physical body and psychological self. We review a wide range of neuropsychological, neuroimaging and neurophysiological data to explore the dissociation between these different aspects of higher somatosensory function

On local boundary CFT and non-local CFT on the boundary

The holographic relation between local boundary conformal quantum field theories (BCFT) and their non-local boundary restrictions is reviewed, and non-vacuum BCFT's, whose existence was conjectured previously, are constructed.Comment: 16 pages. Contribution to "Rigorous Quantum Field Theory", Symposium in honour of J. Bros, Paris, July 2004. Based on joint work math-ph/0405067 with R. Long