From counting to construction of BPS states in N=4 SYM

We describe a universal element in the group algebra of symmetric groups, whose characters provides the counting of quarter and eighth BPS states at weak coupling in N=4 SYM, refined according to representations of the global symmetry group. A related projector acting on the Hilbert space of the free theory is used to construct the matrix of two-point functions of the states annihilated by the one-loop dilatation operator, at finite N or in the large N limit. The matrix is given simply in terms of Clebsch-Gordan coefficients of symmetric groups and dimensions of U(N) representations. It is expected, by non-renormalization theorems, to contain observables at strong coupling. Using the stringy exclusion principle, we interpret a class of its eigenvalues and eigenvectors in terms of giant gravitons. We also give a formula for the action of the one-loop dilatation operator on the orthogonal basis of the free theory, which is manifestly covariant under the global symmetry.Comment: 41 pages + Appendices, 4 figures; v2 - refs and acknowledgments adde

Object ownership and action: the influence of social context and choice on the physical manipulation of personal property

Understanding who owns what is important for guiding appropriate action in a social context. Previously, we demonstrated that ownership influences our kinematic patterns associated with hand-object interactions (Constable et al. in Cognition 119(3):430-437, 2011). Here, we present a series of experiments aimed at determining the underlying mechanisms associated with this effect. We asked participants to lift mugs that differed in terms of ownership status (Experiments 1 and 2) and personal preference (Experiment 3) while recording spatial and acceleration measures. In Experiment 1, participants lifted their own mug with greater acceleration and drew it closer to themselves than they did the experimenter's mug. They also lifted the experimenter's mug further to the right compared with other mugs. In Experiment 2, spatial trajectory effects were preserved, but the acceleration effect abolished, when the owner of the 'other-owned' mug was a known-but absent-confederate. Experiment 3 demonstrated that merely choosing to use a mug was not sufficient to elicit rightward drift or acceleration effects. We suggest that these findings reflect separate and distinct mechanisms associated with socially related visuomotor processing

Cues of control modulate the ascription of object ownership

Knowing whether an object is owned and by whom is essential to avoid costly conflicts. We hypothesize that everyday interactions around objects are influenced by a minimal sense of object ownership grounded on respect of possession. In particular, we hypothesize that tracking object ownership can be influenced by any cue that predicts the establishment of individual physical control over objects. To test this hypothesis we used an indirect method to determine whether visual cues of physical control like spatial proximity to an object, temporal priority in seeing it, and touching it influence this minimal sense of object ownership. In Experiment 1 participants were shown a neutral object located on a table, in the reaching space of one of two characters. In Experiment 2 one character found the object first; then another character appeared and saw the object. In Experiments 3 and 4, spatial proximity, temporal priority, and touch are pitted against each other to assess their relative weight. After having seen the scenes, participants were required to judge the sensibility of sen- tences in which ownership of the object was ascribed to one of the two characters. Responses were faster when the objects were located in the reaching space of the characterto whom ownership was ascribed in the sentence and when ownership was ascribed to the character who finds the object first. When contrasting the relevant cues, results indicate that touch is stronger than temporal priority in modulating the ascription of object ownership. However, all these effects were also influenced by contextual social cues like the gender of both characters and participants, the presence of a third-party observer, and the co-presence of characters. Consistent with our hypothesis, our results provide evidence that many different cues of physical control influence the ascription of ownership in daily social contexts

Cut-and-join operators and N=4 super Yang-Mills

We show which multi-trace structures are compatible with the symmetrisation of local operators in \cN=4 super Yang-Mills when they are organised into representations of the global symmetry group. Cut-and-join operators give the non-planar expansion of correlation functions of these operators in the free theory. Using these techniques we find the 1/N corrections to the quarter-BPS operators which remain protected at weak coupling. We also present a new way of counting these chiral ring operators using the Weyl group S_N.Comment: 44 pages, 3 figures; minor clarifications and typos fixe