Default Values in Verb Frames: Cognitive Biases for Learning Verb Meanings

Two experiments investigated children's and adults' initial mapping of verb meanings.In Experiment 1, subjects were asked to use a newly learned verb to label events in which the instrument, action, or result was different from the events used to teach the verbs. All subjects showed a bias to interpret the result as the most important component of the novel verbs' meanings, and this bias increased with age. In Experiment 2, either the instrument, action, or result of events was varied during training to test subjects' ability to override their default biases. When results were varied in training, 5-year-olds and adults, but not 3-year-olds, were more likely to use the novel verb to label an event in which the result was changed again.When results were varied in training, all subjects were less likely to use the novel verb to label an event in which the action was changed. These findings suggest that there is a default rule hierarchy for learning novel verbs, and that both default rules and the ability to override these rules when presented with conflicting information about the meaning of a verb are still developing during preschool

Wall-Crossing from Boltzmann Black Hole Halos

A key question in the study of N=2 supersymmetric string or field theories is to understand the decay of BPS bound states across walls of marginal stability in the space of parameters or vacua. By representing the potentially unstable bound states as multi-centered black hole solutions in N=2 supergravity, we provide two fully general and explicit formulae for the change in the (refined) index across the wall. The first, "Higgs branch" formula relies on Reineke's results for invariants of quivers without oriented loops, specialized to the Abelian case. The second, "Coulomb branch" formula results from evaluating the symplectic volume of the classical phase space of multi-centered solutions by localization. We provide extensive evidence that these new formulae agree with each other and with the mathematical results of Kontsevich and Soibelman (KS) and Joyce and Song (JS). The main physical insight behind our results is that the Bose-Fermi statistics of individual black holes participating in the bound state can be traded for Maxwell-Boltzmann statistics, provided the (integer) index \Omega(\gamma) of the internal degrees of freedom carried by each black hole is replaced by an effective (rational) index \bar\Omega(\gamma)= \sum_{m|\gamma} \Omega(\gamma/m)/m^2. A similar map also exists for the refined index. This observation provides a physical rationale for the appearance of the rational Donaldson-Thomas invariant \bar\Omega(\gamma) in the works of KS and JS. The simplicity of the wall crossing formula for rational invariants allows us to generalize the "semi-primitive wall-crossing formula" to arbitrary decays of the type \gamma\to M\gamma_1+N\gamma_2 with M=2,3.Comment: 71 pages, 1 figure; v3: changed normalisation of symplectic form 3.22, corrected 3.35, other cosmetic change

Permutation Branes

N-fold tensor products of a rational CFT carry an action of the permutation group S_N. These automorphisms can be used as gluing conditions in the study of boundary conditions for tensor product theories. We present an ansatz for such permutation boundary states and check that it satisfies the cluster condition and Cardy's constraints. For a particularly simple case, we also investigate associativity of the boundary OPE, and find an intriguing connection with the bulk OPE. In the second part of the paper, the constructions are slightly extended for application to Gepner models. We give permutation branes for the quintic, together with some formulae for their intersections.Comment: 27 page

Charged and Uncharged D-branes in various String Theories

We describe how the D-brane spectra of the various ten-dimensional string theories can be related to general properties of the open-closed duality, encoded in the $S$ and $P$ matrices of the conformal field theory. We also complete the classification and the description of non-BPS branes in these string theories, elucidating their non-Abelian structures and the nature of the corresponding super-Higgs mechanisms. We find that the type 0 theories and their orientifolds have two types of uncharged branes, distinguished by their couplings to the closed string tachyon. We also find that the 0A orientifold has the unusual feature of having charged and uncharged branes with identical world-volume dimensions. We conclude with some comments on fractional branes, elucidating their role in connection with the boundary states of $D_{odd}$ SU(2) WZW models.Comment: 4 extra references and acknowledgment of previous work by Felder, Fuchs, Frohlich and Schweigert on WZW Dodd branes. Final version to appear in Nucl. Phys. B. 55 pages, LaTe

ARTICLE Word learning in the absence of a speaker

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