Ilka Brunner

A worldsheet extension of \( O\left( {d,d\left| \mathbb{Z} \right.} \right) \)

A bstractWe study superconformal interfaces between

Orbifolds and Topological Defects

\mathcal{N}=\left( {1,1} \right)

D-brane superpotentials: Geometric and worldsheet approaches

supersymmetric sigma models on tori, which preserve a

Discrete Torsion Defects

\widehat{u}{(1)^{2d }}

Entanglement entropy through conformal interfaces in the 2D Ising model

current algebra. Their fusion is non-singular and, using parallel transport on CFT deformation space, it can be reduced to fusion of defect lines in a single torus model. We show that the latter is described by a semi-group extension of

Defect perturbations in Landau-Ginzburg models

O\left( {d,d\left| \mathbb{Q} \right.} \right)

Entanglement and topological interfaces

), and that (on the level of Ramond charges) fusion of interfaces agrees with composition of associated geometric integral transformations. This generalizes the well-known fact that T-duality can be geometrically represented by Fourier-Mukai transformations.Interestingly, we find that the topological interfaces between torus models form the same semi-group upon fusion. We argue that this semi-group of orbifold equivalences can be regarded as the α′ deformation of the continuous O(d, d) symmetry of classical supergravity.

Calabi’s diastasis as interface entropy

AbstractWe study orbifolds of two-dimensional topological field theories using defects. If the TFT arises as the twist of a superconformal field theory, we recover results on the Neveu–Schwarz and Ramond sectors of the orbifold theory, as well as bulk-boundary correlators from a novel, universal perspective. This entails a structure somewhat weaker than ordinary TFT, which however still describes a sector of the underlying conformal theory. The case of B-twisted Landau–Ginzburg models is discussed in detail, where we compute charge vectors and superpotential terms for B-type branes. Our construction also works in the absence of supersymmetry and for generalised “orbifolds” that need not arise from symmetry groups. In general, this involves a natural appearance of Hochschild (co)homology in a 2-categorical setting, in which among other things we provide simple presentations of Serre functors and a further generalisation of the Cardy condition.

Attractor flows from defect lines

Abstract From the worldsheet perspective, the superpotential on a D-brane wrapping internal cycles of a Calabi–Yau manifold is given as a generating functional for disk correlation functions. On the other hand, from the geometric point of view, D-brane superpotentials are captured by certain chain integrals. In this work, we explicitly show for branes wrapping internal two-cycles how these two different approaches are related. More specifically, from the worldsheet point of view, D-branes at the Landau–Ginzburg point have a convenient description in terms of matrix factorizations. We use a formula derived by Kapustin and Li to explicitly evaluate disk correlators for families of D2-branes. On the geometry side, we then construct a three-chain whose period gives rise to the effective superpotential and show that the two expressions coincide. Finally, as an explicit example, we choose a particular compact Calabi–Yau hypersurface and compute the effective D2-brane superpotential in different branches of the open moduli space, in both geometric and worldsheet approaches.

Obstructions and lines of marginal stability from the world-sheet

Orbifolding two-dimensional quantum field theories by a symmetry group can involve a choice of discrete torsion. We apply the general formalism of ‘orbifolding defects’ to study and elucidate discrete torsion for topological field theories. In the case of Landau–Ginzburg models only the bulk sector had been studied previously, and we re-derive all known results. We also introduce the notion of ‘projective matrix factorisations’, show how they naturally describe boundary and defect sectors, and we further illustrate the efficiency of the defect-based approach by explicitly computing RR charges.Roughly half of our results are not restricted to Landau–Ginzburg models but hold more generally, for any topological field theory. In particular we prove that for a pivotal bicategory, any two objects of its orbifold completion that have the same base are orbifold equivalent. Equivalently, from any orbifold theory (including those based on nonabelian groups) the original unorbifolded theory can be obtained by orbifolding via the ‘quantum symmetry defect’.