# Equivalences Between GIT Quotients of Landau-Ginzburg B-Models

@article{Segal2011EquivalencesBG, title={Equivalences Between GIT Quotients of Landau-Ginzburg B-Models}, author={Ed Segal}, journal={Communications in Mathematical Physics}, year={2011}, volume={304}, pages={411-432} }

We define the category of B-branes in a (not necessarily affine) Landau-Ginzburg B-model, incorporating the notion of R-charge. Our definition is a direct generalization of the category of perfect complexes. We then consider pairs of Landau-Ginzburg B-models that arise as different GIT quotients of a vector space by a one-dimensional torus, and show that for each such pair the two categories of B-branes are quasi-equivalent. In fact we produce a whole set of quasi-equivalences indexed by the…

## 77 Citations

The closed state space of affine Landau-Ginzburg B-models

- Mathematics
- 2009

We study the category of perfect cdg-modules over a curved algebra, and in particular the category of B-branes in an affine Landau-Ginzburg model. We construct an explicit chain map from the…

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

- Mathematics
- 2012

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,…

The closed state space of affine

- Mathematics
- 2011

We study the category of perfect cdg-modules over a curved algebra, and in particular the category of B-branes in an affine Landau-Ginzburg model. We construct an explicit chain map from the…

Landau–Ginzburg/Calabi–Yau Correspondence for a Complete Intersection via Matrix Factorizations

- Mathematics
- 2019

By generalizing the Landau-Ginzburg/Calabi-Yau correspondence for hypersurfaces, we can relate a Calabi-Yau complete intersection to a hybrid Landau-Ginzburg model: a family of isolated singularities…

Derived Knörrer periodicity and Orlov’s theorem for gauged Landau–Ginzburg models

- MathematicsCompositio Mathematica
- 2017

We prove a Knörrer-periodicity-type equivalence between derived factorization categories of gauged Landau–Ginzburg models, which is an analogy of a theorem proved by Shipman and Isik independently.…

Grassmannian twists, derived equivalences and brane transport

- Mathematics
- 2013

This note is based on a talk given at String-Math 2012 in Bonn, on a joint paper with Ed Segal. We exhibit derived equivalences corresponding to certain Grassmannian flops. The construction of these…

THE DERIVED CATEGORY OF A GIT QUOTIENT ( DRAFT )

- Mathematics
- 2012

Given a quasiprojective algebraic variety with a reductive group action, we describe a relationship between its equivariant derived category and the derived category of its geometric invariant theory…

## References

SHOWING 1-10 OF 18 REFERENCES

Triangulated categories of singularities and D-branes in Landau-Ginzburg models

- Mathematics
- 2003

In spite of physics terms in the title, this paper is purely mathematical. Its purpose is to introduce triangulated categories related to singularities of algebraic varieties and establish a…

Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities

- Mathematics
- 2005

In this paper we establish an equivalence between the category of graded D-branes of type B in Landau–Ginzburg models with homogeneous superpotential W and the triangulated category of singularities…

Phases Of N=2 Theories In 1+1 Dimensions With Boundary

- Mathematics
- 2008

We study B-type D-branes in linear sigma models with Abelian gauge groups. The most important finding is the grade restriction rule. It classifies representations of the gauge group on the Chan-Paton…

On the unipotence of autoequivalences of toric complete intersection Calabi–Yau categories

- Mathematics
- 2009

Consider the derived category of coherent sheaves, Db(X), on a compact Calabi–Yau complete intersection X in a toric variety. The scope of this work is to establish the (quasi-)unipotence of a class…

Localization and traces in open-closed topological Landau-Ginzburg models

- Mathematics
- 2005

We reconsider the issue of localization in open-closed B-twisted Lan- dau-Ginzburg models with arbitrary Calabi-Yau target. Through careful analsysis of zero-mode reduction, we show that the closed…

Braid group actions on derived categories of coherent sheaves

- Mathematics
- 2000

This paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety $X$. The motivation for this is Kontsevich's homological mirror conjecture, together…

The homotopy theory of dg-categories and derived Morita theory

- Mathematics
- 2004

The main purpose of this work is to study the homotopy theory of dg-categories up to quasi-equivalences. Our main result is a description of the mapping spaces between two dg-categories C and D in…

Cohomology ring of crepant resolutions of orbifolds

- Mathematics
- 2001

Motivated by physics, we propose two conjectures regarding the cohomology ring of the crepant resolutions of orbifolds and cohomological invariants of K-equivalent manifolds.