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

Cardy states as idempotents of fusion ring in string field theory

With some assumptions, the algebra between Ishibashi states in string field theory can be reduced to a commutative ring. From this viewpoint, Cardy states can be identified with its idempotents. The algebra can be identified with a fusion ring for the rational conformal field theory and a group ring for the orbifold. This observation supports our previous observation that boundary states satisfy a universal idempotency relation under closed string star product.Comment: 8 page

Open Strings in Simple Current Orbifolds

We study branes and open strings in a large class of orbifolds of a curved background using microscopic techniques of boundary conformal field theory. In particular, we obtain factorizing operator product expansions of open string vertex operators for such branes. Applications include branes in Z2 orbifolds of the SU(2) WZW model and in the D-series of unitary minimal models considered previously by Runkel.Comment: Latex, 1 figur

The classifying algebra for defects

We demonstrate that topological defects in a rational conformal field theory can be described by a classifying algebra for defects - a finite-dimensional semisimple unital commutative associative algebra whose irreducible representations give the defect transmission coefficients. We show in particular that the structure constants of the classifying algebra are traces of operators on spaces of conformal blocks and that the defect transmission coefficients determine the defect partition functions.Comment: 47 pages, several figures. v2: ref. [13] added; comparison of results with those of ref. [18] added (pages 15 and 34) v3: comment on the folding trick added at the end of section 2, typos correcte

Sharp lower bounds on the fractional matching number

A fractional matching of a graph G is a function f from E(G) to the interval [0,1] such that \sum_{e\in\Gamma(v)}f(e) \le 1 for each v\in V(G), where \Gamma(v) is the set of edges incident to v. The fractional matching number of G, written \alpha'_*(G), is the maximum of \sum_{e\in E(G)}f(e) over all fractional matchings f. For G with n vertices, m edges, positive minimum degree d, and maximum degree D, we prove \alpha'_*(G) \ge \max\{m/D, n-m/d, d n/(D+d)\}. For the first two bounds, equality holds if and only if each component of G is r-regular or is bipartite with all vertices in one part having degree r, where r=D for the first bound and r=d for the second. Equality holds in the third bound if and only if G is regular or is (d,D)-biregular

Polynomial Bridgeland stability conditions and the large volume limit

and the large volume limi

D-Branes on ALE Spaces and the ADE Classification of Conformal Field Theories

The spectrum of D2-branes wrapped on an ALE space of general ADE type is determined, by representing them as boundary states of N=2 superconformal minimal models. The stable quantum states have RR charges which precisely represent the gauge fields of the corresponding Lie algebra. This provides a simple and direct physical link between the ADE classification of N=2 superconformal field theories, and the corresponding root systems. An affine extension of this structure is also considered, whose boundary states represent the D2-branes plus additional D0-branes.Comment: 12p, harvmac, minor corrrections and ref adde

Abelian and non-Abelian branes in WZW models and gerbes

We discuss how gerbes may be used to set up a consistent Lagrangian approach to the WZW models with boundary. The approach permits to study in detail possible boundary conditions that restrict the values of the fields on the worldsheet boundary to brane submanifolds in the target group. Such submanifolds are equipped with an additional geometric structure that is summarized in the notion of a gerbe module and includes a twisted Chan-Paton gauge field. Using the geometric approach, we present a complete classification of the branes that conserve the diagonal current-algebra symmetry in the WZW models with simple, compact but not necessarily simply connected target groups. Such symmetric branes are supported by a discrete series of conjugacy classes in the target group and may carry Abelian or non-Abelian twisted gauge fields. The latter situation occurs for the conjugacy classes with fundamental group Z_2\times Z_2 in SO(4n)/Z_2. The branes supported by such conjugacy classes have to be equipped with a projectively flat twisted U(2) gauge field in one of the two possible WZW models differing by discrete torsion. We show how the geometric description of branes leads to explicit formulae for the boundary partition functions and boundary operator product coefficients in the WZW models with non-simply connected target groups.Comment: 59 pages, latex, 1 incorporated figur

Level-rank duality of D-branes on the SU(N) group manifold

The consequences of level-rank duality for untwisted D-branes on an SU(N) group manifold are explored. Relations are found between the charges of D-branes (which are classified by twisted K-theory) belonging to su(N)_K and su(K)_N WZW theories, in the case of odd N+K. An isomorphism between the charge algebras is also demonstrated in this case.Comment: 15 pages. v2 and v3: references added. v4: proof clarified and minor typos fixe

Notes on D-branes and dualities in (p,q) minimal superstring theory

We study boundary states in (p,q) minimal superstring theory, combining the explicit form of matter wave functions. Within the modular bootstrap framework, Cardy states of (p,q) minimal superconformal field theory are completely determined in both cases of the different supercharge combinations, and the remaining consistency checks in the super-Liouville case are also performed. Using these boundary states, we determine the explicit form of FZZT- and ZZ-brane boundary states both in type 0A and 0B GSO projections. Annulus mplitudes of FZZT branes are evaluated and principal FZZT branes are identified. In particular, we found that these principal FZZT branes do not satisfy Cardy's consistency conditions for each other and play a role of order/disorder parameters of the Kramers-Wannier duality in spacetime of this superstring theory.Comment: 34 pages; v2: Grammatical errors corrected, minor change; v3: references adde