1,355,966 research outputs found
Some remarks on Gopakumar-Vafa invariants
No full textWe show that Gopakumar-Vafa invariants can be expressed in terms of the cohomology
ring of moduli space of D-branes without reference to the sl_2 \times sl_2 action. We also
give a simple construction of this action
Unramified Gromov-Witten and Gopakumar-Vafa invariants
No full textKim, Kresch and Oh defined unramified Gromov-Witten invariants. For a
threefold, Pandharipande conjectured that they are equal to Gopakumar-Vafa
invariants (BPS invariants) in the case of Fano classes and primitive
Calabi-Yau classes. We prove the conjecture using a wall-crossing technique.
This provides an algebro-geometric construction of Gopakumar-Vafa invariants in
these cases.Comment: 61 page
Genus zero Gopakumar-Vafa invariants from open strings
No full textAbstract We propose a new way to compute the genus zero Gopakumar-Vafa invariants for two families of non-toric non-compact Calabi-Yau threefolds that admit simple flops: Reid’s Pagodas, and Laufer’s examples. We exploit the duality between M-theory on these threefolds, and IIA string theory with D6-branes and O6-planes. From this perspective, the GV invariants are detected as five-dimensional open string zero modes. We propose a definition for genus zero GV invariants for threefolds that do not admit small crepant resolutions. We find that in most cases, non-geometric T-brane data is required in order to fully specify the invariants
Learning approach among health sciences students in a medical college in Nepal: a cross-sectional study
No full textAji Gopakumar,1 Susirith Mendis,2 Jayakumary Muttappallymyalil,3 Jayadevan Sreedharan3 1Department of General Education, 2Continuing Medical Education, Continuing Professional Development and Center for Continuing Education and Community Outreach, 3Department of Community Medicine, Gulf Medical University, Ajman, United Arab Emirates Shah et al aimed to explore the learning approaches among medical, dental, and nursing students which were considered useful to transform the students to become better learners. While the generic objective of the study is appreciated, we have some concerns regarding the methodology and statistical analysis of the study. View the original paper by Author and colleagues. 
A note on BPS structures and Gopakumar–Vafa invariants
No full textWe regard the work of Maulik and Toda, proposing a sheaf-theoretic approach to Gopakumar–Vafa invariants, as defining a BPS structure, that is, a collection of BPS invariants together with a central charge. Assuming their conjectures, we show that a canonical flat section of the flat connection corresponding to this BPS structure, at the level of formal power series, reproduces the Gromov–Witten partition function for all genera, up to some error terms in genus 0 and 1. This generalises a result of Bridgeland and Iwaki for the contribution from genus 0 Gopakumar–Vafa invariants
Gopakumar-Vafa Invariants and Macdonald Formula
No full textIn this paper, we present an investigation of the Gopakumar-Vafa (GV)
invariant, a curve-counting integral invariant associated with Calabi-Yau
threefolds, as proposed by physicists. Building upon the conjectural definition
of the GV invariant in terms of perverse sheaves, as formulated by Maulik-Toda
in 2016, we focus on the total space of the canonical bundle of
and compute the relevant invariants. We establish a conjectural correspondence
between the Gopakumar-Vafa and Pandharipande-Thomas invariants at the level of
perverse sheaves, drawing inspiration from the work of Migliorini, Shende, and
Viviani. This work serves as a significant step towards validating the
conjecture and deepening our understanding of the GV invariant and its
connections to algebraic geometry and physics
Cohomological X-independence for Higgs bundles and Gopakumar–Vafa invariants
No full textThe aim of this paper is two-fold. Firstly, we prove Toda’s X-independence conjecture for Gopakumar–Vafa invariants of arbitrary local curves. Secondly, following Davison’s work, we introduce the BPS cohomology for moduli spaces of Higgs bundles of rank r and Euler characteristic X which are not necessary coprime, and show that it does not depend on X. This result extends the Hausel–Thaddeus conjecture on the X-independence of E-polynomials proved by Mellit, Groechenig–Wyss–Ziegler and Yu in two ways: We obtain an isomorphism of mixed Hodge modules on the Hitchin base rather than an equality of E-polynomials, and we do not need the coprime assumption. The proof of these results is based on a description of the moduli stack of one-dimensional coherent sheaves on a local curve as a global critical locus which is obtained in the companion paper by the first author and Naruki Masuda
Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds
No full textAs an analogy to Gopakumar-Vafa conjecture on Calabi-Yau 3-folds,
Klemm-Pandharipande defined Gopakumar-Vafa type invariants of a Calabi-Yau
4-fold using Gromov-Witten theory. When is holomorphic symplectic,
Gromov-Witten invariants vanish and one can consider the corresponding reduced
theory. In a companion work, we propose a definition of Gopakumar-Vafa type
invariants for such a reduced theory. In this paper, we give them a sheaf
theoretic interpretation via moduli spaces of stable pairs.Comment: 25 pages. Published version. arXiv admin note: text overlap with
arXiv:2201.1087
Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality
No full textWe consider aspects of Chern-Simons theory on L (p, q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-S U (2) cyclic quotients of the conifold. To this aim we find, on one hand, a useful matrix integral representation of the S U (N) C S partition function in a generic flat background for the whole L (p, q) family and provide a solution for its large N dynamics; on the other hand, we perform in full detail the construction of a family of would-be dual closed string backgrounds through conifold geometric transition from T* L (p, q). We can then explicitly prove the claim in [5] that Gopakumar-Vafa duality in a fixed vacuum fails in the case q > 1, and briefly discuss how it could be restored in a non-perturbative setting.</p
Gopakumar-Vafa Hierarchies in Winding Inflation and Uplifts
No full textWe propose a combined mechanism to realize both winding inflation and de Sitter uplifts. We realize the necessary structure of competing terms in the scalar potential not via tuning the vacuum expectation values of the complex structure moduli, but by a hierarchy of the Gopakumar-Vafa invariants of the underlying Calabi-Yau threefold. To show that Calabi-Yau threefolds with the prescribed hierarchy actually exist, we explicitly create a database of all the genus Gopakumar-Vafa invariants up to total degree for all the complete intersection Calabi-Yau's up to Picard number . As a side product, we also identify all the redundancies present in the CICY list, up to Picard number . Both databases can be accessed at this link: https://www.desy.de/~westphal/GV_CICY_webpage/GVInvariants.html
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