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Refined open topological strings revisited

Cheng, Shi and Sułkowski, Piotr (2021) Refined open topological strings revisited. Physical Review D, 104 (10). Art. No. 106012. ISSN 2470-0010. doi:10.1103/PhysRevD.104.106012.

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In this work we verify consistency of refined topological string theory from several perspectives. First, we advance the method of computing refined open amplitudes by means of geometric transitions. Based on such computations we show that refined open BPS (Bogomol’nyi–Prasad–Sommerfield) invariants are non-negative integers for a large class of toric Calabi-Yau threefolds: an infinite class of strip geometries, closed topological vertex geometry, and some threefolds with compact four-cycles. Furthermore, for an infinite class of toric geometries without compact four-cycles we show that refined open string amplitudes take form of quiver generating series. This generalizes the relation to quivers found earlier in the unrefined case, implies that refined open BPS states are made of a finite number of elementary BPS states, and asserts that all refined open BPS invariants associated to a given brane are non-negative integers in consequence of their relation to (integer and non-negative) motivic Donaldson-Thomas invariants. Non-negativity of motivic Donaldson-Thomas invariants of a symmetric quiver is therefore crucial in the context of refined open topological strings. Furthermore, reinterpreting these results in terms of webs of five-branes, we analyze Hanany-Witten transitions in novel configurations involving Lagrangian branes.

Item Type:Article
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URLURL TypeDescription Paper
Cheng, Shi0000-0002-4481-3287
Sułkowski, Piotr0000-0002-6176-6240
Additional Information:© 2021 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. Received 15 April 2021; accepted 11 October 2021; published 17 November 2021. We thank Andrea Brini, Sung-Soo Kim, Hélder Larraguível, Miłosz Panfil, and Xin Wang for valuable discussions and comments on the manuscript. S. C. thanks DESY and ICTP for hospitality at different stages of this work. This work has been supported by the TEAM programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund (POIR.04.04.00-00-5C55/17-00).
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Foundation for Polish ScienceUNSPECIFIED
European Regional Development FundPOIR.04.04.00-00-5C55/17-00
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Issue or Number:10
Record Number:CaltechAUTHORS:20210409-081915926
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108669
Deposited By: Tony Diaz
Deposited On:11 Apr 2021 23:14
Last Modified:18 Nov 2021 17:35

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