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Refined, Motivic, and Quantum

Dimofte, Tudor and Gukov, Sergei (2010) Refined, Motivic, and Quantum. Letters in Mathematical Physics, 91 (1). pp. 1-27. ISSN 0377-9017. doi:10.1007/s11005-009-0357-9.

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It is well known that in string compactifications on toric Calabi–Yau manifolds one can introduce refined BPS invariants that carry information not only about the charge of the BPS state but also about the spin content. In this paper we study how these invariants behave under wall crossing. In particular, by applying a refined wall crossing formula, we obtain the refined BPS degeneracies for the conifold in different chambers. The result can be interpreted in terms of a new statistical model that counts “refined” pyramid partitions; the model provides a combinatorial realization of wall crossing and clarifies the relation between refined pyramid partitions and the refined topological vertex. We also compare the wall crossing behavior of the refined BPS invariants with that of the motivic Donaldson–Thomas invariants introduced by Kontsevich–Soibelman. In particular, we argue that, in the context of BPS state counting, the three adjectives in the title of this paper are essentially synonymous.

Item Type:Article
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URLURL TypeDescription Paper
Gukov, Sergei0000-0002-9486-1762
Additional Information:© 2009 Springer. Received: 17 June 2009; accepted: 16 September 2009; published online: 14 November 2009. We thank A. Gorsky, E. Gorsky, D. Jafferis, G. Moore, A. Neitzke, H. Ooguri, Y. Soibelman, and M. Yamazaki for useful discussions and comments. We are grateful to the KITP, Santa Barbara for warm hospitality during the program “Fundamental Aspects of Superstring Theory,” where part of this work was carried out. TD acknowledges support from a National Defense Science and Engineering Graduate Fellowship. Research of SG is supported in part by the Alfred P. Sloan Foundation, by DARPA under Grant No. HR0011-09-1-0015, and by the National Science Foundation under Grant No. PHY05-51164 and Grant No. PHY07-57647. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.
Group:Caltech Theory
Funding AgencyGrant Number
National Defense Science and Engineering Graduate (NDSEG) FellowshipUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Defense Advanced Research Projects Agency (DARPA)HR0011-09-1-0015
Subject Keywords:motivic Donaldson–Thomas invariants; D-branes, BPS invariants; wall-crossing; three-dimensional partitions
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Issue or Number:1
Classification Code:Mathematics Subject Classification (2000): 81T30 - 14N35 - 14E15 - 05A18
Record Number:CaltechAUTHORS:20100104-122110812
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:17050
Deposited On:06 Jan 2010 21:09
Last Modified:08 Nov 2021 23:32

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