The refined BPS index from stable pair invariants
type: Item
instance of: scholarly article
title: The refined BPS index from stable pair invariants
zbMATH Open document ID: 1315.14070
author: Jinwon Choi
author: Sheldon Katz
author: Albrecht Klemm
published in: Communications in Mathematical Physics
publication date: 2014-06-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/1210.4403
review text: Refined BPS invariants can be defined in rigid \(N=2\) theories in \(4\) dimensions, the only known examples of which are type II string compactifications on non-compact Calabi-Yau. They record multiplicities of BPS particles in the lattice of \(K\)-theory charges of even \(D\)-branes with given spin quantum numbers labeling representations of the twisted off-shell Lorentz group \(\mathrm{SU}(2)\times \mathrm{SU}(2)\) . In this paper, the authors extend a B-model calculation from unrefined to refined invariants, and relate them conjecturally to refined stable pair invariants, confirming the correspondence by explicit evaluation for local \(\mathbb{P}^2\) and \(\mathbb{P}^1\times\mathbb{P}^1\). The refined stable pair invariants can be defined mathematically in terms of a virtual Bialynicki-Birula decomposition, and are expected to be related to BPS invariants via a \(5\)-dimensional BPS supertrace and the Schwinger loop calculation. The stable pair invariants are evaluated via the localization algorithm for the Pandharipande-Thomas invariants of toric Calabi-Yaus, and their partition function is expressed as an infinite product depending only on \(\mathrm{SU}(2)\times \mathrm{SU}(2)\) BPS invariants and related to wall-crossing.
reviewed by: Sergiy Koshkin
Mathematics Subject Classification ID: 14N35
Mathematics Subject Classification ID: 81T30
Mathematics Subject Classification ID: 14J32
zbMATH DE Number: 6309471
zbMATH Keywords: Pandharipande-Thomas invariants
zbMATH Keywords: toric Calabi-Yau
zbMATH Keywords: \(K\)-theory charges
zbMATH Keywords: twisted off-shell Lorentz group
zbMATH Keywords: BPS supertrace
zbMATH Keywords: virtual Bialynicki-Birula decomposition
zbMATH Keywords: Schwinger loop calculation
MaRDI profile type: Publication
OpenAlex ID: W2042300477
arXiv ID: 1210.4403
cites work: Quantum geometry of refined topological strings
cites work: Genus zero Gopakumar-Vafa invariants of contractible curves
cites work: Orientifolds and the refined topological string
cites work: Knot homology and refined Chern-Simons index
cites work: Donaldson-Thomas type invariants via microlocal geometry
cites work: Motivic degree zero Donaldson-Thomas invariants
cites work: Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes
cites work: Moduli spaces of \(\alpha\)-stable pairs and wall-crossing on \(\mathbb{P}^2\)
cites work: The Milnor fibre of the Pfaffian and the Hilbert scheme of four points on \(\mathbb{C}^3\)
cites work: From weak to strong coupling in ABJM theory
cites work: Riemann-Roch theorems and elliptic genus for virtually smooth schemes
cites work: Topological gravity as large \(N\) topological gauge theory
cites work: Refined curve counting on complex surfaces
cites work: Integrability of the holomorphic anomaly equations
cites work: ESPACES DE MODULES DE SYSTÈMES COHÉRENTS
cites work: Q4434432
cites work: The \(\Omega \) deformed \(B\)-model for rigid \(N=2\) theories
cites work: Holomorphicity and modularity in Seiberg-Witten theories with matter
cites work: Direct integration for general \(\Omega\) backgrounds
cites work: Topological String Theory on Compact Calabi–Yau: Modularity and Boundary Conditions
cites work: Link homologies and the refined topological vertex
cites work: Refined Hopf link revisited
cites work: Non-perturbative results on the point particle limit of \(N=2\) heterotic string compactifications
cites work: Q3636464
cites work: Geometric engineering of quantum field theories
cites work: M-theory, topological strings and spinning black holes
cites work: Extended holomorphic anomaly in gauge theory
cites work: ABCD of beta ensembles and topological strings
cites work: Exact results in ABJM theory from topological strings
cites work: Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants
cites work: Gromov–Witten theory and Donaldson–Thomas theory, I
cites work: Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex
cites work: Comments on worldsheet description of the Omega background
cites work: Seiberg-Witten prepotential from instanton counting
cites work: Q5482632
cites work: Darboux coordinates, Yang-Yang functional, and gauge theory
cites work: The omega deformation, branes, integrability and Liouville theory
cites work: Curve counting via stable pairs in the derived category
cites work: The 3-fold vertex via stable pairs
cites work: Stable pairs and BPS invariants
cites work: Phases of \(N=2\) theories in two dimensions
DOI: 10.1007/S00220-014-1978-0
description: scientific article