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19
Nonperturbative effects and the refined topological string
, 2013
"... The partition function of ABJM theory on the threesphere has nonperturbative corrections due to membrane instantons in the Mtheory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi–Yau manifold known as lo ..."
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Cited by 23 (7 self)
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The partition function of ABJM theory on the threesphere has nonperturbative corrections due to membrane instantons in the Mtheory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi–Yau manifold known as local P1 × P1, in the Nekrasov–Shatashvili limit. Our result can be interpreted as a firstprinciples derivation of the full series of nonperturbative effects for the closed topological string on this Calabi–Yau background. Based on this, we make a proposal for the nonperturbative free energy of topological strings on general, local Calabi–Yau manifolds.
Topological strings and 5d TN partition functions
"... We evaluate the Nekrasov partition function of 5d gauge theories engineered by webs of 5branes, using the refined topological vertex on the dual CalabiYau threefolds. The theories include certain nonLagrangian theories such as the TN theory. The refined topological vertex computation generically ..."
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Cited by 8 (1 self)
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We evaluate the Nekrasov partition function of 5d gauge theories engineered by webs of 5branes, using the refined topological vertex on the dual CalabiYau threefolds. The theories include certain nonLagrangian theories such as the TN theory. The refined topological vertex computation generically contains contributions from decoupled M2branes which are not charged under the 5d gauge symmetry engineered. We argue that, after eliminating them, the refined topological string partition function agrees with the 5d Nekrasov partition function. We explicitly check this for the T3 theory as well as Sp(1) gauge theories with Nf = 2, 3, 4 flavors. In particular, our method leads to a new expression of the Sp(1) Nekrasov partition functions without any contour integrals. We also develop prescriptions to calculate the partition functions of theories obtained by Higgsing the TN theory. We compute the partition function of the E7 theory via this prescription, and find the E7 global symmetry enhancement. We finally discuss a potential application of the refined topological vertex to nontoric web diagrams. ar X iv
REFINED CURVE COUNTING ON COMPLEX SURFACES
, 2012
"... We define refined invariants which “count” nodal curves in sufficiently ample linear systems on surfaces, conjecture that their generating function is multiplicative, and conjecture explicit formulas in the case of K3 and abelian surfaces. We also give a refinement of the CaporasoHarris recursion ..."
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Cited by 5 (3 self)
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We define refined invariants which “count” nodal curves in sufficiently ample linear systems on surfaces, conjecture that their generating function is multiplicative, and conjecture explicit formulas in the case of K3 and abelian surfaces. We also give a refinement of the CaporasoHarris recursion, and conjecture that it produces the same invariants in the sufficiently ample setting. The refined recursion specializes at y = −1 to the ItenbergKharlamovShustin recursion for Welschinger invariants. We find similar interactions between refined invariants of individual curves and real invariants of their versal families.
Lectures on Mirror Symmetry and Topological String Theory
 Open Problems and Surveys of Contemporary Mathematics
"... These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N = 2 superconformal algebra, its deformations and its chiral ring are reviewed. A topological field theory can be constructed whose observab ..."
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Cited by 5 (2 self)
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These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N = 2 superconformal algebra, its deformations and its chiral ring are reviewed. A topological field theory can be constructed whose observables are only the elements of the chiral ring. When coupled to gravity, this leads to topological string theory. The identification of the topological string A and Bmodels by mirror symmetry leads to surprising connections in mathematics and provides tools for exact computations as well as new insights in physics. A recursive construction of the higher genus amplitudes of topological string theory expressed as polynomials is reviewed. 1 ar
Instanton Effects in ABJM Theory from Fermi Gas Approach, JHEP 1301 (2013) 158, [arXiv:1211.1251
 Instanton Bound States in ABJM Theory, JHEP 1305 (2013) 054, [arXiv:1301.5184
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Special polynomial rings, quasi modular forms and duality of topological strings
 arXiv:1306.0002[hepth], 2013. 118 TOM COATES AND HIROSHI IRITANI
"... We study the differential polynomial rings which are defined using the special geometry of the moduli spaces of CalabiYau threefolds. The higher genus topological string amplitudes are expressed as polynomials in the generators of these rings, giving them a global description in the moduli space. A ..."
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We study the differential polynomial rings which are defined using the special geometry of the moduli spaces of CalabiYau threefolds. The higher genus topological string amplitudes are expressed as polynomials in the generators of these rings, giving them a global description in the moduli space. At particular loci, the amplitudes yield the generating functions of GromovWitten invariants. We show that these rings are isomorphic to the rings of quasi modular forms for threefolds with duality groups for which these are known. For the other cases, they provide generalizations thereof. We furthermore study an involution which acts on the quasi modular forms. We interpret it as a duality which exchanges two distinguished expansion loci of the topological string amplitudes in the moduli space. We construct these special polynomial rings and match them with known quasi modular forms for noncompact CalabiYau geometries and their mirrors including local P2 and local del Pezzo geometries with E5, E6, E7 and E8 type singularities. We provide the analogous special polynomial ring for the quintic.
On the geometry of the moduli space of onedimensional sheaves. ArXiv eprints
, 1311
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