Rigidity and defect actions in Landau-Ginzburg models

Studying two-dimensional field theories in the presence of defect lines naturally gives rise to monoidal categories: their objects are the different (topological) defect conditions, their morphisms are junction fields, and their tensor product describes the fusion of defects. These categories should be equipped with a duality operation corresponding to reversing the orientation of the defect line, providing a rigid and pivotal structure. We make this structure explicit in topological Landau-Ginzburg models with potential x^d, where defects are described by matrix factorisations of x^d-y^d. The duality allows to compute an action of defects on bulk fields, which we compare to the corresponding N=2 conformal field theories. We find that the two actions differ by phases.Comment: 53 pages; v2: clarified exposition of pivotal structures, corrected proof of theorem 2.13, added remark 3.9; version to appear in CM

Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence

We show that the Gromov-Witten theory of Calabi-Yau hypersurfaces matches, in genus zero and after an analytic continuation, the quantum singularity theory (FJRW theory) recently introduced by Fan, Jarvis and Ruan following ideas of Witten. Moreover, on both sides, we highlight two remarkable integral local systems arising from the common formalism of Gamma-integral structures applied to the derived category of the hypersurface {W=0} and to the category of graded matrix factorizations of W. In this setup, we prove that the analytic continuation matches Orlov equivalence between the two above categories.Comment: 72pages, v2: Appendix B and references added. Typos corrected, v3: several mistakes corrected, final versio

Women on boards of Malaysian firms: Impact on market and accounting performance

We seek to offer some reconciliation for the conflicting theoretical arguments and empirical findings regarding the impact of women’s participation in boards on firms’ performance.We suggest that this impact differs in relation to market- and accounting-performance, and it is firm-specific, and varies by firms’ ownership type and the composition of their boards.These arguments find theoretical underpinnings in agency and resource-dependency theories, combined with behavioral and discrimination theories that articulate women behavior in the workplace and market perception of gender equality.The empirical analysis is based on a dataset of 841 publicly-listed firms in Malaysia.The results show positive impact of women’s participation on accounting-performance and negative impact on market-performance, suggesting that women directors create economic value, which is undervalued by the market. We interpret the findings with reference to the perception of women’s role in society and business in Malaysia, and the nature of corporate governance and ownership types prevalent among Malaysian firms.We suggest that the relationships might be context-specific, and hence the desired level of women’s participation varies across countries.We discuss the normative implications of the findings for government authorities considering legislation of gender-quota on boards, and for firms