A-twisted correlators and Hori dualities

Closset, Cyril; Mekareeya, Noppadol; Park, Daniel

doi:10.1007/jhep08(2017)101

Cited by 15 publications

(27 citation statements)

References 42 publications

(187 reference statements)

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“…The argument that the twisted superpotential (and effective dilaton) of the 3d theory reduces to that of the 2d theory then directly implies that these ingredients reduce to those of the 2d reduction, and so the τ → 0 limit of the Σ g × S 1 τ partition function is the Σ g partition function of the 2d theory. This was recently checked to match for the 2d dualities of Hori-Tong and Hori in [25], and we expect that the identities found there can be obtained from the limit of identities of the Σ g × S 1 τ partition function for appropriate 3d dualities. More precisely, one generally finds (after appropriately rescaling the dynamical twisted chiral fields) that contributions from multiple terms in the direct sum will appear in the sum over vacua above, and one of these terms is typically dominant in the τ → 0 limit, as discussed for the S 2 × S 1 τ index above.…”

Section: )mentioning

confidence: 77%

From 3d duality to 2d duality

Aharony

Razamat

Willett

2017

J. High Energ. Phys.

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In this paper we discuss 3d N = 2 supersymmetric gauge theories and their IR dualities when they are compactified on a circle of radius r, and when we take the 2d limit in which r → 0. The 2d limit depends on how the mass parameters are scaled as r → 0, and often vacua become infinitely distant in the 2d limit, leading to a direct sum of different 2d theories. For generic mass parameters, when we take the same limit on both sides of a duality, we obtain 2d dualities (between gauge theories and/or Landau-Ginzburg theories) that pass all the usual tests. However, when there are non-compact branches the discussion is subtle because the metric on the moduli space, which is not controlled by supersymmetry, plays an important role in the low-energy dynamics after compactification. Generally speaking, for IR dualities of gauge theories, we conjecture that dualities involving non-compact Higgs branches survive. On the other hand when there is a non-compact Coulomb branch on at least one side of the duality, the duality fails already when the 3d theories are compactified on a circle. Using the valid reductions we reproduce many known 2d IR dualities, giving further evidence for their validity, and we also find new 2d dualities.

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Section: )mentioning

confidence: 77%

From 3d duality to 2d duality

Aharony

Razamat

Willett

2017

J. High Energ. Phys.

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“…Furthermore, comparing correlator relations among dual N = (2, 2) gauge theories -as considered for instance in refs. [47,57,58] -can provide a non-trivial duality check. The derived universal forms of Picard-Fuchs operators in terms of correlators together with the exhibited differential-algebraic relations among their coefficient functions may serve as a starting point to classify differential operators for classes of Calabi-Yau geometries -as already performed for Calabi-Yau threefolds with a single Kähler modulus by Almkvist, van Enckevort, van Straten, and Zudilin [59].…”

Section: Discussionmentioning

confidence: 99%

The geometry of gauged linear sigma model correlation functions

Gerhardus¹,

Jockers²,

Ninad³

2018

Nuclear Physics B

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Applying advances in exact computations of supersymmetric gauge theories, we study the structure of correlation functions in two-dimensional N = (2, 2) Abelian and non-Abelian gauge theories. We determine universal relations among correlation functions, which yield differential equations governing the dependence of the gauge theory ground state on the Fayet-Iliopoulos parameters of the gauge theory. For gauge theories with a non-trivial infrared N = (2, 2) superconformal fixed point, these differential equations become the Picard-Fuchs operators governing the moduli-dependent vacuum ground state in a Hilbert space interpretation. For gauge theories with geometric target spaces, a quadratic expression in the Givental I-function generates the analyzed correlators. This gives a geometric interpretation for the correlators, their relations, and the differential equations. For classes of Calabi-Yau target spaces, such as threefolds with up to two Kähler moduli and fourfolds with a single Kähler modulus, we give general and universally applicable expressions for Picard-Fuchs operators in terms of correlators. We illustrate our results with representative examples of two-dimensional N = (2, 2) gauge theories.March, 2018

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“…(See e.g. [30][31][32] for more discussions on localization.) We describe this method in detail in section 2.2.…”

Section: Introductionmentioning

confidence: 99%

Quantum Sheaf Cohomology and Duality of Flag Manifolds

Guo

2019

Commun. Math. Phys.

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We study the quantum sheaf cohomology of flag manifolds with deformations of the tangent bundle and use the ring structure to derive how the deformation transforms under the biholomorphic duality of flag manifolds. Realized as the OPE ring of A/2-twisted twodimensional theories with (0,2) supersymmetry, quantum sheaf cohomology generalizes the notion of quantum cohomology. Complete descriptions of quantum sheaf cohomology have been obtained for abelian gauged linear sigma models (GLSMs) and for nonabelian GLSMs describing Grassmannians. In this paper we continue to explore the quantum sheaf cohomology of nonabelian theories. We first propose a method to compute the generating relations for (0,2) GLSMs with (2,2) locus. We apply this method to derive the quantum sheaf cohomology of products of Grassmannians and flag manifolds. The dual deformation associated with the biholomorphic duality gives rise to an explicit IR duality of two A/2-twisted (0,2) gauge theories.

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A-twisted correlators and Hori dualities

Cited by 15 publications

References 42 publications

From 3d duality to 2d duality

From 3d duality to 2d duality

The geometry of gauged linear sigma model correlation functions

Quantum Sheaf Cohomology and Duality of Flag Manifolds

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