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Scientific article
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English

ABJM on ellipsoid and topological strings

ContributorsHatsuda, Yasuyuki
Published inThe journal of high energy physics, vol. 1607, p. 026-056
Collection
  • Open Access - SCOAP3
Publication date2016
Abstract

It is known that the large N expansion of the partition function in ABJM theory on a three-sphere 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
Citation (ISO format)
HATSUDA, Yasuyuki. ABJM on ellipsoid and topological strings. In: The journal of high energy physics, 2016, vol. 1607, p. 026–056. doi: 10.1007/JHEP07(2016)026
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ISSN of the journal1029-8479
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