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Title 
ABJM on ellipsoid and topological strings 

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Published in  Journal of High Energy Physics. 2016, vol. 1607, p. 02656  
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Open Access  SCOAP3 

Abstract  It is known that the large N expansion of the partition function in ABJM theory on a threesphere is completely determined by the topological string on local Hirzebruch surface F 0 $$ {\mathbb{F}}_0 $$ . In this note, we investigate the ABJM partition function on an ellipsoid, which has a conventional deformation parameter b . Using 3d mirror symmetry, we find a remarkable relation between the ellipsoid partition function for b 2 = 3 (or b 2 = 1 / 3) in ABJM theory at k = 1 and a matrix model for the topological string on another CalabiYau threefold, known as local ℙ 2 $$ {\mathrm{\mathbb{P}}}^2 $$ . As in the case of b = 1, we can compute the full large N expansion of the partition function in this case. This is the first example of the complete large N solution in ABJM theory on the squashed sphere. Using the obtained results, we also analyze the supersymmetric Rényi entropy.  
Keywords  1/N Expansion — Matrix Models — Nonperturbative Effects — Topological Strings  
Identifiers  arXiv: 1601.02728  
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Citation (ISO format)  HATSUDA, Yasuyuki. ABJM on ellipsoid and topological strings. In: Journal of High Energy Physics, 2016, vol. 1607, p. 02656. https://archiveouverte.unige.ch/unige:85591 