Holomorphic anomaly in gauge theories and matrix models

Huang, Min–xin; Klemm, Albrecht

doi:10.1088/1126-6708/2007/09/054

Cited by 116 publications

(273 citation statements)

References 44 publications

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“…Here the role of G and G 2 is played by the one-point torus function with possible insertion of the Virasoro part of I 2 in (7.4). In other words, (7.14) is totally similar to (7.7) when written in the form Tr 15) where, see (7.3) and (7.5), …”

Section: Jhep05(2017)023mentioning

confidence: 80%

Chiral trace relations in Ω-deformed N = 2 $$ \mathcal{N}=2 $$ theories

Beccaria

Fachechi

Macorini

2017

J. High Energ. Phys.

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We consider N = 2 SU(2) gauge theories in four dimensions (pure or mass deformed) and discuss the properties of the simplest chiral observables in the presence of a generic Ω-deformation. We compute them by equivariant localization and analyze the structure of the exact instanton corrections to the classical chiral ring relations. We predict exact relations valid at all instanton number among the traces Trϕ n , where ϕ is the scalar field in the gauge multiplet. In the Nekrasov-Shatashvili limit, such relations may be explained in terms of the available quantized Seiberg-Witten curves. Instead, the full two-parameter deformation enjoys novel features and the ring relations require non trivial additional derivative terms with respect to the modular parameter. Higher rank groups are briefly discussed emphasizing non-factorization of correlators due to the Ω-deformation. Finally, the structure of the deformed ring relations in the N = 2 theory is analyzed from the point of view of the Alday-Gaiotto-Tachikawa correspondence proving consistency as well as some interesting universality properties.

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Section: Jhep05(2017)023mentioning

confidence: 80%

Chiral trace relations in Ω-deformed N = 2 $$ \mathcal{N}=2 $$ theories

Beccaria

Fachechi

Macorini

2017

J. High Energ. Phys.

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“…and of course the ABJM matrix model correlators (14) have the same type of expansion. The first term in this expansion corresponds to the genus zero or planar vev.…”

Section: Wilson Loops In the Geometric Descriptionmentioning

confidence: 97%

“…It is a standard result in matrix model theory that planar correlators of the form (14) are given by moments of the eigenvalue densities,…”

Section: Wilson Loops In the Geometric Descriptionmentioning

confidence: 99%

Aharony–Bergman–Jafferis–Maldacena Wilson Loops in the Fermi Gas Approach

Klemm

Mariño

Soroush

2013

Zeitschrift Für Naturforschung A

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159

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The matrix model of the Aharony-Bergman-Jafferis-Maldacena theory can be formulated in terms of an ideal Fermi gas with a non-trivial one-particle Hamiltonian. We show that, in this formalism, vacuum expectation values (vevs) of Wilson loops correspond to averages of operators in the statistical-mechanical problem. This makes it possible to calculate these vevs at all orders in 1/N, up to exponentially small corrections, and for arbitrary Chern-Simons coupling, by using the WentzelKramer-Brillouin expansion. We present explicit results for the vevs of 1/6 and the 1/2 BogomolnyiPrasad-Sommerfield Wilson loops, at any winding number, in terms of Airy functions. Our expressions are shown to reproduce the low genus results obtained previously in the 't Hooft expansion.

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“…In particular the leading singularity in (30) as well as the absence of subleading singular terms follows from the Schwinger loop computation of [15], which computes the effect of the extra massless hypermultiplet in the space-time theory [19]. The singular structure and the "gap" of subleading singular terms have been also observed in the dual matrix model [20] and were first used in [13,9] to fix the holomorphic ambiguity to very high genus. Note that the space-time derivation of [15] is not restricted to the conifold case and applies also to Calabi-Yau singularities which give rise to a different spectrum of extra massless vector and hypermultiplets in space-time.…”

Section: Holomorphic Ambiguity and Boundary Conditionsmentioning

confidence: 99%

Global properties of topological string amplitudes and orbifold invariants

Alim¹,

Länge²,

Mayr³

2010

J. High Energ. Phys.

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We derive topological string amplitudes on local Calabi-Yau manifolds in terms of polynomials in finitely many generators of special functions. These objects are defined globally in the moduli space and lead to a description of mirror symmetry at any point in the moduli space. Holomorphic ambiguities of the anomaly equations are fixed by global information obtained from boundary conditions at few special divisors in the moduli space. As an illustration we compute higher genus orbifold Gromov-Witten invariants for

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Holomorphic anomaly in gauge theories and matrix models

Cited by 116 publications

References 44 publications

Chiral trace relations in Ω-deformed N = 2 $$ \mathcal{N}=2 $$ theories

Chiral trace relations in Ω-deformed N = 2 $$ \mathcal{N}=2 $$ theories

Aharony–Bergman–Jafferis–Maldacena Wilson Loops in the Fermi Gas Approach

Global properties of topological string amplitudes and orbifold invariants

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