ID: 1006.2113

Wall Crossing, Quivers and Crystals

June 10, 2010

View on ArXiv

Similar papers 3

Wall-crossing, free fermions and crystal melting

October 29, 2009

85% Match
Piotr Sułkowski
Algebraic Geometry
Combinatorics

We describe wall-crossing for local, toric Calabi-Yau manifolds without compact four-cycles, in terms of free fermions, vertex operators, and crystal melting. Firstly, to each such manifold we associate two states in the free fermion Hilbert space. The overlap of these states reproduces the BPS partition function corresponding to the non-commutative Donaldson-Thomas invariants, given by the modulus square of the topological string partition function. Secondly, we introduce th...

Find SimilarView on arXiv

Wall-Crossing Effects on Quiver BPS Algebras

March 21, 2024

85% Match
Dmitry Galakhov, Alexei Morozov, Nikita Tselousov
Algebraic Geometry
Mathematical Physics
Quantum Algebra
Representation Theory

BPS states in supersymmetric theories can admit additional algebro-geometric structures in their spectra, described as quiver Yangian algebras. Equivariant fixed points on the quiver variety are interpreted as vectors populating a representation module, and matrix elements for the generators are then defined as Duistermaat-Heckman integrals in the vicinity of these points. The well-known wall-crossing phenomena are that the fixed point spectrum establishes a dependence on the...

Find SimilarView on arXiv

The Non-commutative Topological Vertex and Wall Crossing Phenomena

October 28, 2009

85% Match
Kentaro Nagao, Masahito Yamazaki
Algebraic Geometry
Combinatorics

We propose a generalization of the topological vertex, which we call the "non-commutative topological vertex". This gives open BPS invariants for a toric Calabi-Yau manifold without compact 4-cycles, where we have D0/D2/D6-branes wrapping holomorphic 0/2/6-cycles, as well as D2-branes wrapping disks whose boundaries are on D4-branes wrapping non-compact Lagrangian 3-cycles. The vertex is defined combinatorially using the crystal melting model proposed recently, and depends on...

Find SimilarView on arXiv

Brane Dimers and Quiver Gauge Theories

April 13, 2005

85% Match
Sebastian Franco, Amihay Hanany, Kristian D. Kennaway, ... , Wecht Brian
High Energy Physics - Theory

We describe a technique which enables one to quickly compute an infinite number of toric geometries and their dual quiver gauge theories. The central object in this construction is a ``brane tiling,'' which is a collection of D5-branes ending on an NS5-brane wrapping a holomorphic curve that can be represented as a periodic tiling of the plane. This construction solves the longstanding problem of computing superpotentials for D-branes probing a singular non-compact toric Cala...

Find SimilarView on arXiv

5D BPS Quivers and KK Towers

November 9, 2020

85% Match
Zhihao Duan, Dongwook Ghim, Piljin Yi
High Energy Physics - Theory

We explore BPS quivers for D=5 theories, compactified on a circle and geometrically engineered over local Calabi-Yau 3-folds, for which many of known machineries leading to (refined) indices fail due to the fine-tuning of the superpotential. For Abelian quivers, the counting reduces to a geometric one, but the technically challenging $L^2$ cohomology proved to be essential for sensible BPS spectra. We offer a mathematical theorem to remedy the difficulty, but for non-Abelian ...

Find SimilarView on arXiv

Open BPS Wall Crossing and M-theory

November 30, 2009

85% Match
Mina Aganagic, Masahito Yamazaki
High Energy Physics - Theory

Consider the degeneracies of BPS bound states of one D6 brane wrapping Calabi-Yau X with D0 branes and D2 branes. When we include D4-branes wrapping Lagrangian cycle L in addition, D2-branes can end on them. These give rise to new bound states in the d=2, N=(2,2) theory of the D4 branes. We call these "open" BPS states, in contrast to closed BPS states that arise from D-branes without boundaries. Lifting this to M-theory, we show that the generating function is captured by fr...

Find SimilarView on arXiv

Graded quivers and B-branes at Calabi-Yau singularities

November 16, 2018

85% Match
Cyril Closset, Sebastian Franco, ... , Hasan Azeem
High Energy Physics - Theory

A graded quiver with superpotential is a quiver whose arrows are assigned degrees $c\in \{0, 1, \cdots, m\}$, for some integer $m \geq 0$, with relations generated by a superpotential of degree $m-1$. Ordinary quivers ($m=1)$ often describe the open string sector of D-brane systems; in particular, they capture the physics of D3-branes at local Calabi-Yau (CY) 3-fold singularities in type IIB string theory, in the guise of 4d $\mathcal{N}=1$ supersymmetric quiver gauge theorie...

Find SimilarView on arXiv

Quiver Asymptotics and Amoeba: Instantons on Toric Divisors of Calabi-Yau Threefolds

June 24, 2020

85% Match
Ali Zahabi
Mathematical Physics

The BPS bound states of D4-D2-D0 branes on the non-compact divisors of Calabi-Yau threefolds and the instantons in the dual quiver gauge theories are previously studied using two-dimensional crystal melting model and dimer model. Using the tropical geometry associated with the toric quiver, we study the asymptotic of the quiver gauge theory to compute some of their thermodynamic observables and extract the phase structure. We obtain that the thermodynamic observables such as ...

Find SimilarView on arXiv

Crystals and intersecting branes

July 5, 2006

85% Match
Daniel Jafferis
High Energy Physics - Theory

We show that the index of BPS bound states of D4, D2 and D0 branes in IIA theory compactified on a toric Calabi Yau are encoded in the combinatoric counting of restricted three dimensional partitions. Using the torus symmetry, we demonstrate that the Euler character of the moduli space of bound states localizes to the number of invariant configurations that can be obtained by gluing D0 bound states in the C^3 vertex along the D2 brane wrapped P^1 legs of the toric diagram. We...

Find SimilarView on arXiv

D-Branes on Calabi-Yau Manifolds

March 16, 2004

85% Match
Paul S. Aspinwall
High Energy Physics - Theory

In this review we study BPS D-branes on Calabi-Yau threefolds. Such D-branes naturally divide into two sets called A-branes and B-branes which are most easily understood from topological field theory. The main aim of this paper is to provide a self-contained guide to the derived category approach to B-branes and the idea of Pi-stability. We argue that this mathematical machinery is hard to avoid for a proper understanding of B-branes. A-branes and B-branes are related in a ve...

Find SimilarView on arXiv