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Academic literature on the topic 'Calabi-Yang-Mills equations'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Calabi-Yang-Mills equations"

1

Yang, Hyun Seok, and Sangheon Yun. "Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons, and Mirror Symmetry." Advances in High Energy Physics 2017 (2017): 1–27. http://dx.doi.org/10.1155/2017/7962426.

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We address the issue of why Calabi-Yau manifolds exist with a mirror pair. We observe that the irreducible spinor representation of the Lorentz group Spin(6) requires us to consider the vector spaces of two forms and four forms on an equal footing. The doubling of the two-form vector space due to the Hodge duality doubles the variety of six-dimensional spin manifolds. We explore how the doubling is related to the mirror symmetry of Calabi-Yau manifolds. Via the gauge theory formulation of six-dimensional Riemannian manifolds, we show that the curvature tensor of a Calabi-Yau manifold satisfies the Hermitian Yang-Mills equations on the Calabi-Yau manifold. Therefore, the mirror symmetry of Calabi-Yau manifolds can be recast as the mirror pair of Hermitian Yang-Mills instantons. We discuss the mirror symmetry from the gauge theory perspective.
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2

Bonelli, Giulio, Fabrizio Del Monte, and Alessandro Tanzini. "BPS Quivers of Five-Dimensional SCFTs, Topological Strings and q-Painlevé Equations." Annales Henri Poincaré 22, no. 8 (March 31, 2021): 2721–73. http://dx.doi.org/10.1007/s00023-021-01034-3.

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AbstractWe study the discrete flows generated by the symmetry group of the BPS quivers for Calabi–Yau geometries describing five-dimensional superconformal quantum field theories on a circle. These flows naturally describe the BPS particle spectrum of such theories and at the same time generate bilinear equations of q-difference type which, in the rank one case, are q-Painlevé equations. The solutions of these equations are shown to be given by grand canonical topological string partition functions which we identify with $$\tau $$ τ -functions of the cluster algebra associated to the quiver. We exemplify our construction in the case corresponding to five-dimensional SU(2) pure super Yang–Mills and $$N_f=2$$ N f = 2 on a circle.
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3

Papoulias, Vasileios Ektor. "Spin(7) Instantons and Hermitian Yang–Mills Connections for the Stenzel Metric." Communications in Mathematical Physics 384, no. 3 (May 17, 2021): 2009–66. http://dx.doi.org/10.1007/s00220-021-04055-5.

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AbstractWe use the highly symmetric Stenzel Calabi–Yau structure on $$T^{\star }S^{4}$$ T ⋆ S 4 as a testing ground for the relationship between the Spin(7) instanton and Hermitian–Yang–Mills (HYM) equations. We reduce both problems to tractable ODEs and look for invariant solutions. In the abelian case, we establish local equivalence and prove a global nonexistence result. We analyze the nonabelian equations with structure group SO(3) and construct the moduli space of invariant Spin(7) instantons in this setting. This is comprised of two 1-parameter families—one of them explicit—of irreducible Spin(7) instantons. Each carries a unique HYM connection. We thus negatively resolve the question regarding the equivalence of the two gauge theoretic PDEs. The HYM connections play a role in the compactification of this moduli space, exhibiting a removable singularity phenomenon that we aim to further examine in future work.
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4

Popov, Alexander D. "Hermitian Yang–Mills equations and pseudo-holomorphic bundles on nearly Kähler and nearly Calabi–Yau twistor 6-manifolds." Nuclear Physics B 828, no. 3 (April 2010): 594–624. http://dx.doi.org/10.1016/j.nuclphysb.2009.11.011.

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5

Acharya, Bobby Samir, Alex Kinsella, and Eirik Eik Svanes. "T 3-invariant heterotic Hull-Strominger solutions." Journal of High Energy Physics 2021, no. 1 (January 2021). http://dx.doi.org/10.1007/jhep01(2021)197.

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Abstract We consider the heterotic string on Calabi-Yau manifolds admitting a Strominger-Yau-Zaslow fibration. Upon reducing the system in the T3-directions, the Hermitian Yang-Mills conditions can then be reinterpreted as a complex flat connection on ℝ3 satisfying a certain co-closure condition. We give a number of abelian and non-abelian examples, and also compute the back-reaction on the geometry through the non-trivial α′-corrected heterotic Bianchi identity, which includes an important correction to the equations for the complex flat connection. These are all new local solutions to the Hull-Strominger system on T3× ℝ3. We also propose a method for computing the spectrum of certain non-abelian models, in close analogy with the Morse-Witten complex of the abelian models.
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6

Brini, Andrea, and Kento Osuga. "Five-dimensional gauge theories and the local B-model." Letters in Mathematical Physics 112, no. 3 (May 9, 2022). http://dx.doi.org/10.1007/s11005-022-01538-x.

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AbstractWe propose an effective framework for computing the prepotential of the topological B-model on a class of local Calabi–Yau geometries related to the circle compactification of five-dimensional $$\mathcal {N}=1$$ N = 1 super Yang–Mills theory with simple gauge group. In the simply laced case, we construct Picard–Fuchs operators from the Dubrovin connection on the Frobenius manifolds associated with the extended affine Weyl groups of type $$\mathrm {ADE}$$ ADE . In general, we propose a purely algebraic construction of Picard–Fuchs ideals from a canonical subring of the space of regular functions on the ramification locus of the Seiberg–Witten curve, encompassing non-simply laced cases as well. We offer several precision tests of our proposal for simply laced cases by comparing with the gauge theory prepotentials obtained from the K-theoretic blow-up equations, finding perfect agreement. Whenever there is more than one candidate Seiberg-Witten curve for non-simply laced gauge groups in the literature, we employ our framework to verify which one agrees with the K-theoretic blow-up equations.
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