Relevant bibliographies by topics / Hermitian-Yang-Mills equations

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  2. Dissertations / Theses
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Academic literature on the topic 'Hermitian-Yang-Mills equations'

Author: Grafiati
Published: 6 September 2023

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

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Li, Zhen Yang, and Xi Zhang. "Dirichlet problem for Hermitian Yang–Mills–Higgs equations over Hermitian manifolds." Journal of Mathematical Analysis and Applications 310, no. 1 (October 2005): 68–80. http://dx.doi.org/10.1016/j.jmaa.2005.01.033.

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Zhang, Xi. "Hermitian Yang–Mills–Higgs Metrics on Complete Kähler Manifolds." Canadian Journal of Mathematics 57, no. 4 (August 1, 2005): 871–96. http://dx.doi.org/10.4153/cjm-2005-034-3.

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AbstractIn this paper, first, we will investigate the Dirichlet problem for one type of vortex equation, which generalizes the well-known Hermitian Einstein equation. Secondly, we will give existence results for solutions of these vortex equations over various complete noncompact Kähler manifolds.
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Zhou, Jundong, and Yawei Chu. "Hessian equations of Krylov type on compact Hermitian manifolds." Open Mathematics 20, no. 1 (January 1, 2022): 1126–44. http://dx.doi.org/10.1515/math-2022-0504.

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Abstract In this article, we are concerned with the equations of Krylov type on compact Hermitian manifolds, which are in the form of the linear combinations of the elementary symmetric functions of a Hermitian matrix. Under the assumption of the 𝒞-subsolution, we obtain a priori estimates in Γ k − 1 {\Gamma }_{k-1} cone. By using the method of continuity, we prove an existence theorem, which generalizes the relevant results. As an application, we give an alternative way to solve the deformed Hermitian Yang-Mills equation on compact Kähler threefold.
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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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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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IHL, MATTHIAS, and SEBASTIAN UHLMANN. "NONCOMMUTATIVE EXTENDED WAVES AND SOLITON-LIKE CONFIGURATIONS IN N = 2 STRING THEORY." International Journal of Modern Physics A 18, no. 26 (October 20, 2003): 4889–931. http://dx.doi.org/10.1142/s0217751x03016446.

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The Seiberg–Witten limit of fermionic N = 2 string theory with nonvanishing B-field is governed by noncommutative self-dual Yang–Mills theory (ncSDYM) in 2+2 dimensions. Conversely, the self-duality equations are contained in the equation of motion of N = 2 string field theory in a B-field background. Therefore finding solutions to noncommutative self-dual Yang–Mills theory on ℝ2,2 might help to improve our understanding of nonperturbative properties of string (field) theory. In this paper, we construct nonlinear soliton-like and multi-plane wave solutions of the ncSDYM equations corresponding to certain D-brane configurations by employing a solution generating technique, an extension of the so-called dressing approach. The underlying Lax pair is discussed in two different gauges, the unitary and the Hermitian gauge. Several examples and applications for both situations are considered, including Abelian solutions constructed from GMS-like projectors, noncommutative U(2) soliton-like configurations and interacting plane waves. We display a correspondence to earlier work on string field theory and argue that the solutions found here can serve as a guideline in the search for nonperturbative solutions of nonpolynomial string field theory.
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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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Sergeev, A. G., and A. B. Sukhov. "Hermitian Yang–Mills equations and their generalizations." International Journal of Modern Physics A, July 8, 2022. http://dx.doi.org/10.1142/s0217751x22430199.

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Ghosh, Kartick. "Coupled Kähler-Einstein and Hermitian-Yang-Mills equations." Bulletin des Sciences Mathématiques, January 2023, 103232. http://dx.doi.org/10.1016/j.bulsci.2023.103232.

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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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Dissertations / Theses on the topic "Hermitian-Yang-Mills equations"

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Mandolesi, André Luís Godinho. "Adiabatic limits of the Hermitian Yang-Mills equations on slicewise stable bundles." Thesis, 2002. http://hdl.handle.net/2152/754.

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Mandolesi, André Luís Godinho. "Adiabatic limits of the Hermitian Yang-Mills equations on slicewise stable bundles." 2002. http://wwwlib.umi.com/cr/utexas/fullcit?p3110649.

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(9132815), Kuang-Ru Wu. "Hermitian-Yang-Mills Metrics on Hilbert Bundles and in the Space of Kahler Potentials." Thesis, 2020.

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The two main results in this thesis have a common point: Hermitian--Yang--Mills (HYM) metrics. In the first result, we address a Dirichlet problem for the HYM equations in bundles of infinite rank over Riemann surfaces. The solvability has been known since the work of Donaldson \cite{Donaldson92} and Coifman--Semmes \cite{CoifmanSemmes93}, but only for bundles of finite rank. So the novelty of our first result is to show how to deal with infinite rank bundles. The key is an a priori estimate obtained from special feature of the HYM equation.
In the second result, we take on the topic of the so-called ``geometric quantization." This is a vast subject. In one of its instances the aim is to approximate the space of K\"ahler potentials by a sequence of finite dimensional spaces. The approximation of a point or a geodesic in the space of K\"ahler potentials is well-known, and it has many applications in K\"ahler geometry. Our second result concerns the approximation of a Wess--Zumino--Witten type equation in the space of K\"ahler potentials via HYM equations, and it is an extension of the point/geodesic approximation.
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Ghosh, Kartick. "On some canonical metrics on holomorphic vector bundles over Kahler manifolds." Thesis, 2023. https://etd.iisc.ac.in/handle/2005/6152.

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This thesis consists of two parts. In the first part, we introduce coupled Kähler- Einstein and Hermitian-Yang-Mills equations. It is shown that these equations have an interpretation in terms of a moment map. We identify a Futaki-type invariant as an obstruction to the existence of solutions of these equations. We also prove a Matsushima- Lichnerowicz-type theorem as another obstruction. Using the Calabi ansatz, we produce nontrivial examples of solutions of these equations on some projective bundles. Another class of nontrivial examples is produced using deformation. In the second part, we prove a priori estimates for vortex-type equations. We then apply these a priori estimates in some situations. One important application is the existence and uniqueness result concerning solutions of the Calabi-Yang-Mills equations. We recover a priori estimates of the J-vortex equation and the Monge-Ampère vortex equation. We establish a corre- spondence result between Gieseker stability and the existence of almost Hermitian-Yang- Mills metric in a particular case. We also investigate the Kählerity of the symplectic form which arises in the moment map interpretation of the Calabi-Yang-Mills equations.
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Book chapters on the topic "Hermitian-Yang-Mills equations"

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Collins, Tristan C., Dan Xie, and Shing-Tung Yau. "The Deformed Hermitian–Yang–Mills Equation in Geometry and Physics." In Geometry and Physics: Volume I, 69–90. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198802013.003.0004.

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This chapter provides an introduction to the mathematics and physics of the deformed Hermitian–Yang–Mills equation, a fully non-linear geometric PDE on Kähler manifolds, which plays an important role in mirror symmetry. The chapter discusses the physical origin of the equation, and some recent progress towards its solution. In addition, in dimension 3, it proves a new Chern number inequality and discusses the relationship with algebraic stability conditions.
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