arXiv subjects

Daniel Roggenkamp

Publications and source records attributed to Daniel Roggenkamp.

At least 19 recordsLinked to original sources

arXiv2024

Defects and Phases of Higher Rank Abelian GLSMs

We construct defects describing the transition between different phases of gauged linear sigma models with higher rank abelian gauge groups, as well as defects embedding these phases into the GLSMs. Our construction refers entirely to the sector protected by B-type supersymmetry, decoupling the gauge sector. It relies on an abstract characterization of such transition defects and does not involve an actual perturbative analysis. It turns out that the choices that are required to characterize consistent transition defects match with the homotopy classes of paths between different phases. Our method applies to non-anomalous as well as anomalous GLSMs, and we illustrate both cases with examples. This includes the GLSM associated to the resolution of the $A_N$ singularity and one describing the entire parameter space of $N = 2$ minimal models, in particular, the relevant flows between them. Via fusion with boundary conditions, the defects we construct yield functors describing the transport of D-branes on parameter space. We find that our results match with known results on D-brane transport.

hep-th↗

arXiv2023

Truncated affine Rozansky--Witten models as extended defect TQFTs

We apply the cobordism hypothesis with singularities to the case of affine Rozansky--Witten models, providing a construction of extended TQFTs that includes all line and surface defects. On a technical level, this amounts to proving that the associated homotopy 2-category is pivotal, and to systematically employing its 3-dimensional graphical calculus. This in particular allows us to explicitly calculate state spaces for surfaces with arbitrary defect networks. As specific examples we discuss symmetry defects which can be used to model non-trivial background gauge fields, as well as boundary conditions.

math-ph↗

arXiv2022

Truncated affine Rozansky--Witten models as extended TQFTs

We construct extended TQFTs associated to Rozansky--Witten models with target manifolds $T^*\mathbb{C}^n$. The starting point of the construction is the 3-category whose objects are such Rozansky--Witten models, and whose morphisms are defects of all codimensions. By truncation, we obtain a (non-semisimple) 2-category $\mathcal{C}$ of bulk theories, surface defects, and isomorphism classes of line defects. Through a systematic application of the cobordism hypothesis we construct a unique extended oriented 2-dimensional TQFT valued in $\mathcal{C}$ for every affine Rozansky--Witten model. By evaluating this TQFT on closed surfaces we obtain the infinite-dimensional state spaces (graded by flavour and R-charges) of the initial 3-dimensional theory. Furthermore, we explicitly compute the commutative Frobenius algebras that classify the restrictions of the extended theories to circles and bordisms between them.

math-ph↗

arXiv2021

Defects and phase transitions to geometric phases of abelian GLSMs

We consider gauged linear sigma models with gauge group U(1) that exhibit a geometric as well as a Landau Ginzburg phase. We construct defects that implement the transport of D-branes from the Landau-Ginzburg phase to the geometric phase. Through their fusion with boundary conditions these defects in particular provide functors between the respective D-brane categories. The latter map (equivariant) matrix factorizations to coherent sheaves and can be formulated explicitly in terms of complexes of matrix factorizations.

hep-th↗

arXiv2021

Phase transitions in GLSMs and defects

In this paper, we construct defects (domain walls) that connect different phases of two-dimensional gauged linear sigma models (GLSMs), as well as defects that embed those phases into the GLSMs. Via their action on boundary conditions these defects give rise to functors between the D-brane categories, which respectively describe the transport of D-branes between different phases, and embed the D-brane categories of the phases into the category of D-branes of the GLSMs.

hep-th↗

arXiv2020

Complementary Projection Defects and Decompositions

As put forward in [arXiv:1907.12339] topological quantum field theories can be projected using so-called projection defects. The projected theory and its correlation functions can be completely realized within the unprojected one. An interesting example is the case of topological quantum field theories associated to IR fixed points of renormalization group flows, which by this method can be realized inside the theories associated to the UV. In this note we show that projection defects in triangulated defect categories (such as defects in 2d topologically twisted N=(2,2) theories) always come with complementary projection defects, and that the unprojected theory decomposes into the theories associated to the two projection defects. We demonstrate this in the context of Landau-Ginzburg orbifold theories.

hep-th↗

arXiv2019

Realizing IR theories by projections in the UV

We study bulk RG flows in the context of TQFTs and show how IR theories can be entirely represented within the respective UV theories by means of codimension-one projection defects. What is more, RG flows of the bulk theory can be described in terms of RG flows of the codimension-one identity defect in the fixed UV bulk theory. We illustrate this in the example of RG flows between Landau-Ginzburg orbifold models, for which the respective defects can be described in terms of matrix factorizations.

hep-th↗

arXiv2016

Junctions of surface operators and categorification of quantum groups

We show how networks of Wilson lines realize quantum groups U_q(sl(m)), for arbitrary m, in 3d SU(N) Chern-Simons theory. Lifting this construction to foams of surface operators in 4d theory we find that rich structure of junctions is encoded in combinatorics of planar diagrams. For a particular choice of surface operators we reproduce known mathematical constructions of categorical representations and categorified quantum groups.

hep-th↗

arXiv2013

A worldsheet extension of O(d,d;Z)

We study superconformal interfaces between N=(1,1) supersymmetric sigma models on tori, which preserve a u(1)^{2d} 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 O(d,d;Q), 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.

hep-th↗

arXiv2013

Fusion of Critical Defect Lines in the 2D Ising Model

Two defect lines separated by a distance delta look from much larger distances like a single defect. In the critical theory, when all scales are large compared to the cutoff scale, this fusion of defect lines is universal. We calculate the universal fusion rule in the critical 2D Ising model and show that it is given by the Verlinde algebra of primary fields, combined with group multiplication in O(1,1)/Z_2. Fusion is in general singular and requires the subtraction of a divergent Casimir energy.

cond-mat.stat-mech↗

arXiv2010

Attractor Flows from Defect Lines

Deforming a two dimensional conformal field theory on one side of a trivial defect line gives rise to a defect separating the original theory from its deformation. The Casimir force between these defects and other defect lines or boundaries is used to construct flows on bulk moduli spaces of CFTs. It turns out, that these flows are constant reparametrizations of gradient flows of the g-functions of the chosen defect or boundary condition. The special flows associated to supersymmetric boundary conditions in N=(2,2) superconformal field theories agree with the attractor flows studied in the context of black holes in N=2 supergravity.

hep-th↗

arXiv2009

Defect Perturbations in Landau-Ginzburg Models

Perturbations of B-type defects in Landau-Ginzburg models are considered. In particular, the effect of perturbations of defects on their fusion is analyzed in the framework of matrix factorizations. As an application, it is discussed how fusion with perturbed defects induces perturbations on boundary conditions. It is shown that in some classes of models all boundary perturbations can be obtained in this way. Moreover, a universal class of perturbed defects is constructed, whose fusion under certain conditions obey braid relations. The functors obtained by fusing these defects with boundary conditions are twist functors as introduced in the work of Seidel and Thomas.

hep-th↗

arXiv2008

Defects and D-Brane Monodromies

In this paper D-brane monodromies are studied from a world-sheet point of view. More precisely, defect lines are used to describe the parallel transport of D-branes along deformations of the underlying bulk conformal field theories. This method is used to derive B-brane monodromies in Kahler moduli spaces of non-linear sigma models on projective hypersurfaces. The corresponding defects are constructed at Landau-Ginzburg points in these moduli spaces where matrix factorisation techniques can be used. Transporting them to the large volume phase by means of the gauged linear sigma model we find that their action on B-branes at large volume can be described by certain Fourier-Mukai transformations which are known from target space geometric considerations to represent the corresponding monodromies.

hep-th↗

arXiv2008

Defects and Bulk Perturbations of Boundary Landau-Ginzburg Orbifolds

We propose defect lines as a useful tool to study bulk perturbations of conformal field theories, in particular to analyse the induced renormalisation group flows of boundary conditions. As a concrete example we investigate bulk perturbations of N=2 supersymmetric minimal models. To these perturbations we associate a special class of defects between the respective UV and IR theories, whose fusion with boundary conditions indeed reproduces the behaviour of the latter under the corresponding RG flows. v2: Some explanations added in section 4, minor changes.

hep-th↗

arXiv2008

Decoding the geometry of conformal field theories

To certain geometries, string theory associates conformal field theories. We discuss techniques to perform the reverse procedure: To recover geometrical data from abstractly defined conformal field theories. This is done by introducing appropriate notions of limits of conformal field theories and their degenerations, and by applying techniques from noncommutative geometry. This note is a summary of our work hep-th/0308143 , aimed to be less technical than the original paper, along with some new calculations confirming our interpretation of the rescaled limiting zero mode of the Virasoro field.

hep-th↗

arXiv2007

B-type defects in Landau-Ginzburg models

We consider Landau-Ginzburg models with possibly different superpotentials glued together along one-dimensional defect lines. Defects preserving B-type supersymmetry can be represented by matrix factorisations of the difference of the superpotentials. The composition of these defects and their action on B-type boundary conditions is described in this framework. The cases of Landau-Ginzburg models with superpotential W=X^d and W=X^d+Z^2 are analysed in detail, and the results are compared to the CFT treatment of defects in N=2 superconformal minimal models to which these Landau-Ginzburg models flow in the IR.

hep-th↗

arXiv2005

Permutation branes and linear matrix factorisations

All the known rational boundary states for Gepner models can be regarded as permutation branes. On general grounds, one expects that topological branes in Gepner models can be encoded as matrix factorisations of the corresponding Landau-Ginzburg potentials. In this paper we identify the matrix factorisations associated to arbitrary B-type permutation branes.

hep-th↗

arXiv2004

The coset D-branes of SU(n)

Using a nested coset construction a collection of D-branes that appear to generate all the K-theory charges of string theory on SU(n) are constructed and their charges are determined.

hep-th↗