scholarly journals On Framed Quivers, BPS Invariants and Defects

2017 ◽  
Vol 9 (2) ◽  
pp. 71-99 ◽  
Author(s):  
Michele Cirafici
Keyword(s):  
Bps Invariants

scholarly journals Genus Zero BPS Invariants for Local ℙ1

2012 ◽  
Vol 2014 (2) ◽  
pp. 418-450 ◽  
Author(s):  
Jinwon Choi
Keyword(s):  
Genus Zero ◽  
Bps Invariants

scholarly journals Local BPS Invariants: Enumerative Aspects and Wall-Crossing

2018 ◽  
Vol 2020 (17) ◽  
pp. 5450-5475 ◽  
Author(s):  
Jinwon Choi ◽  
Michel van Garrel ◽  
Sheldon Katz ◽  
Nobuyoshi Takahashi
Keyword(s):  
Projective Space ◽  
Euler Characteristic ◽  
Moduli Spaces ◽  
Del Pezzo Surfaces ◽  
Arithmetic Genus ◽  
One Dimensional ◽  
Wall Crossing ◽  
Bps Invariants ◽  
Del Pezzo ◽  
Dimensional Projective Space

Abstract We study the BPS invariants for local del Pezzo surfaces, which can be obtained as the signed Euler characteristic of the moduli spaces of stable one-dimensional sheaves on the surface $S$. We calculate the Poincaré polynomials of the moduli spaces for the curve classes $\beta $ having arithmetic genus at most 2. We formulate a conjecture that these Poincaré polynomials are divisible by the Poincaré polynomials of $((-K_S).\beta -1)$-dimensional projective space. This conjecture motivates the upcoming work on log BPS numbers [8].

scholarly journals Quantum black holes, elliptic genera and spectral partition functions

2014 ◽  
Vol 11 (05) ◽  
pp. 1450048 ◽  
Author(s):  
A. A. Bytsenko ◽  
M. Chaichian ◽  
R. J. Szabo ◽  
A. Tureanu
Keyword(s):  
Black Hole ◽  
Lie Algebras ◽  
Modular Forms ◽  
Partition Functions ◽  
Affine Lie Algebras ◽  
Hilbert Schemes ◽  
Spectral Functions ◽  
Infinite Dimensional ◽  
Elliptic Genera ◽  
Bps Invariants

We study M-theory and D-brane quantum partition functions for microscopic black hole ensembles within the context of the AdS/CFT correspondence in terms of highest weight representations of infinite-dimensional Lie algebras, elliptic genera, and Hilbert schemes, and describe their relations to elliptic modular forms. The common feature in our examples lies in the modular properties of the characters of certain representations of the pertinent affine Lie algebras, and in the role of spectral functions of hyperbolic three-geometry associated with q-series in the calculation of elliptic genera. We present new calculations of supergravity elliptic genera on local Calabi–Yau threefolds in terms of BPS invariants and spectral functions, and also of equivariant D-brane elliptic genera on generic toric singularities. We use these examples to conjecture a link between the black hole partition functions and elliptic cohomology.

scholarly journals Refined large N duality for knots

2020 ◽  
pp. 2041001
Author(s):  
Masaya Kameyama ◽  
Satoshi Nawata
Keyword(s):  
Moduli Spaces ◽  
Bound States ◽  
Simons Theory ◽  
Global Symmetry ◽  
Torus Knots ◽  
Torus Knot ◽  
Large N ◽  
Bps Invariants ◽  
Bps States ◽  
Chern Simons

We formulate large [Formula: see text] duality of [Formula: see text] refined Chern–Simons theory with a torus knot/link in [Formula: see text]. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the [Formula: see text]-background. This form enables us to relate refined Chern–Simons invariants of a torus knot/link in [Formula: see text] to refined BPS invariants in the resolved conifold. Assuming that the extra [Formula: see text] global symmetry acts on BPS states trivially, the duality predicts graded dimensions of cohomology groups of moduli spaces of M2–M5 bound states associated to a torus knot/link in the resolved conifold. Thus, this formulation can be also interpreted as a positivity conjecture of refined Chern–Simons invariants of torus knots/links. We also discuss about an extension to non-torus knots.

scholarly journals Exponential BPS Graphs and D Brane Counting on Toric Calabi-Yau Threefolds: Part I

2021 ◽  
Author(s):  
Sibasish Banerjee ◽  
Pietro Longhi ◽  
Mauricio Romo
Keyword(s):  
Wall Crossing ◽  
Bps Invariants ◽  
Bps States ◽  
Exponential Networks

AbstractWe study BPS spectra of D-branes on local Calabi-Yau threefolds $$\mathcal {O}(-p)\oplus \mathcal {O}(p-2)\rightarrow \mathbb {P}^1$$ O ( - p ) ⊕ O ( p - 2 ) → P 1 with $$p=0,1$$ p = 0 , 1 , corresponding to $$\mathbb {C}^3/\mathbb {Z}_{2}$$ C 3 / Z 2 and the resolved conifold. Nonabelianization for exponential networks is applied to compute directly unframed BPS indices counting states with D2 and D0 brane charges. Known results on these BPS spectra are correctly reproduced by computing new types of BPS invariants of 3d-5d BPS states, encoded by nonabelianization, through their wall-crossing. We also develop the notion of exponential BPS graphs for the simplest toric examples, and show that they encode both the quiver and the potential associated to the Calabi-Yau via geometric engineering.

scholarly journals Refined BPS invariants of 6d SCFTs from anomalies and modularity

2017 ◽  
Vol 2017 (5) ◽  
Author(s):  
Jie Gu ◽  
Min-xin Huang ◽  
Amir-Kian Kashani-Poor ◽  
Albrecht Klemm
Keyword(s):  
Bps Invariants

scholarly journals BPS Invariants of Semi-Stable Sheaves on Rational Surfaces

2013 ◽  
Vol 103 (8) ◽  
pp. 895-918 ◽  
Author(s):  
Jan Manschot
Keyword(s):  
Rational Surfaces ◽  
Bps Invariants ◽  
Stable Sheaves

scholarly journals BPS invariants for Seifert manifolds

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
Hee-Joong Chung
Keyword(s):  
Seifert Manifolds ◽  
Bps Invariants

scholarly journals Hilbert schemes of points on a locally planar curve and the Severi strata of its versal deformation

2012 ◽  
Vol 148 (2) ◽  
pp. 531-547 ◽  
Author(s):  
Vivek Shende
Keyword(s):  
Singular Point ◽  
Present Author ◽  
Central Point ◽  
Versal Deformation ◽  
Hilbert Schemes ◽  
Euler Numbers ◽  
Planar Curve ◽  
Bps Invariants

AbstractLet C be a locally planar curve. Its versal deformation admits a stratification by the genera of the fibres. The strata are singular; we show that their multiplicities at the central point are determined by the Euler numbers of the Hilbert schemes of points on C. These Euler numbers have made two prior appearances. First, in certain simple cases, they control the contribution of C to the Pandharipande–Thomas curve counting invariants of three-folds. In this context, our result identifies the strata multiplicities as the local contributions to the Gopakumar–Vafa BPS invariants. Second, when C is smooth away from a unique singular point, a conjecture of Oblomkov and the present author identifies the Euler numbers of the Hilbert schemes with the ‘U(∞)’ invariant of the link of the singularity. We make contact with combinatorial ideas of Jaeger, and suggest an approach to the conjecture.

scholarly journals BPS invariants for resolutions of polyhedral singularities

2009 ◽  
Vol 15 (4) ◽  
pp. 521-533 ◽  
Author(s):  
Jim Bryan ◽  
Amin Gholampour
Keyword(s):  
Bps Invariants
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