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A bstract We propose the refined topological string correspondence to the expectation values of half-BPS Wilson loop operators in 5d N \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \...
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A bstract We propose the refined topological string correspondence to the expectation values of half-BPS Wilson loop operators in 5d N \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 1 gauge theory partition function on the Omega-deformed background ? ? 1 , 2 4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathbb{R}}_{\upepsilon_{1,2}}^4 $$\end{document} × S ~(1). We provide the refined topological vertex method and the refined holomorphic anomaly equation method in the topological string theory, from which we have exact computations on the 5d Wilson loops partition functions in both A- and B-models. Finally, with the exact results we have in B-model, we recover the quantum periods of local ?~(1)× ?~(1)model and local ?~(2)model in the study of quantum geometry and we further give a refined generalization of A-period.
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A bstract We discuss a phenomenon in supersymmetric field theory and string theory whereby compactifying one of the dimensions of spacetime on an arbitrarily large circle can cause BPS states to become unstable. We exemplify this ...
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A bstract We discuss a phenomenon in supersymmetric field theory and string theory whereby compactifying one of the dimensions of spacetime on an arbitrarily large circle can cause BPS states to become unstable. We exemplify this by considering 5d N \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 1 theories on a circle and their embeddings into M-theory via geometric engineering. This implicates a subtle relationship between the BPS states of M-theory on a Calabi-Yau threefold, X , and those of type IIA on X with an arbitrary value of the coupling constant. Intuition for this phenomenon is provided by considering F-theory on a complex K3 surface in a limit where it degenerates to a real K3 surface.
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A bstract We initiate a systematic study of 2 d (0 , 2) quiver gauge theories on the world-volume of D1-branes probing singular toric Calabi-Yau 4-folds. We present an algorithm for efficiently calculating the classical mesonic mo...
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A bstract We initiate a systematic study of 2 d (0 , 2) quiver gauge theories on the world-volume of D1-branes probing singular toric Calabi-Yau 4-folds. We present an algorithm for efficiently calculating the classical mesonic moduli spaces of these theories, which correspond to the probed geometries. We also introduce a systematic procedure for constructing the gauge theories for arbitrary toric singularities by means of partial resolution, which translates to higgsing in the field theory. Finally, we introduce Brane Brick Models, a novel class of brane configurations that consist of D4-branes suspended from an NS5-brane wrapping a holomorphic surface, tessellating a 3-torus. Brane Brick Models are the 2 d analogues of Brane Tilings and allow a direct connection between geometry and gauge theory.
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A bstract It is widely considered that the classical Higgs branch of 4d N \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
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A bstract It is widely considered that the classical Higgs branch of 4d N \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 2 SQCD is a well understood object. However there is no satisfactory understanding of its structure. There are two complications: (1) the Higgs branch chiral ring contains nilpotent elements, as can easily be checked in the case of SU( N ) with 1 flavour. (2) the Higgs branch as a geometric space can in general be decomposed into two cones with nontrivial intersection, the baryonic and mesonic branches. To study the second point in detail we use the recently developed tool of magnetic quivers for five-brane webs, using the fact that the classical Higgs branch for theories with 8 supercharges does not change through dimensional reduction. We compare this approach with the computation of the hyper-K?hler quotient using Hilbert series techniques, finding perfect agreement if nilpotent operators are eliminated by the computation of a so called radical . We study the nature of the nilpotent operators and give conjectures for the Hilbert series of the full Higgs branch, giving new insights into the vacuum structure of 4d N \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 2 SQCD. In addition we demonstrate the power of the magnetic quiver technique, as it allows us to identify the decomposition into cones, and provides us with the global symmetries of the theory, as a simple alternative to the techniques that were used to date.
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A bstract We propose a string theory realization of three-dimensional N \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \...
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A bstract We propose a string theory realization of three-dimensional N \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 4 quiver gauge theories with special unitary gauge groups. This is most easily understood in type IIA string theory with D4-branes wrapped on holomorphic curves in local K3’s, by invoking the Stückelberg mechanism. From the type IIB perspective, this is understood as simply compactifying the familiar Hanany-Witten (HW) constructions on a T ~(3). The mirror symmetry duals are easily derived. We illustrate this with various examples of mirror pairs.
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A bstract We study the full moduli space of vacua of 6d worldvolume SCFTs on M5 branes probing an A -type singularity, focusing on the geometric incarnation of the discrete gauging mechanism which acts as a discrete quotient on th...
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A bstract We study the full moduli space of vacua of 6d worldvolume SCFTs on M5 branes probing an A -type singularity, focusing on the geometric incarnation of the discrete gauging mechanism which acts as a discrete quotient on the Higgs branch fibered over the tensor branch. We combine insights from brane constructions and magnetic quiver techniques, in which discrete gauging is implemented through the concept of decoration introduced in [ 1 ]. We discover and characterize new transverse slices between phases of 6d SCFTs, identifying some of them with a family of isolated symplectic singularities recently discovered in [ 2 ], and conjecturing the existence of two new isolated symplectic singularities.
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A bstract In this paper, we study 5d N \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\o...
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A bstract In this paper, we study 5d N \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 1 Sp( N ) gauge theory with N _( f )( ≤ 2 N + 3) flavors based on 5-brane web diagram with O 5-plane. On the one hand, we discuss Seiberg-Witten curve based on the dual graph of the 5-brane web with O 5-plane. On the other hand, we compute the Nekrasov partition function based on the topological vertex formalism with O 5-plane. Rewriting it in terms of profile functions, we obtain the saddle point equation for the profile function after taking thermodynamic limit. By introducing the resolvent, we derive the Seiberg-Witten curve and its boundary conditions as well as its relation to the prepotential in terms of the cycle integrals. They coincide with those directly obtained from the dual graph of the 5-brane web with O 5-plane. This agreement gives further evidence for mirror symmetry which relates Nekrasov partition function with Seiberg-Witten curve in the case with orientifold plane and shed light on the non-toric Calabi-Yau 3-folds including D-type singularities.
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A bstract We solve a long standing problem on the computation of the Higgs branch H \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage...
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A bstract We solve a long standing problem on the computation of the Higgs branch H \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{H} $$\end{document} of linear quivers with 8 supercharges and with both unitary and special unitary gauge nodes. The solution uses the concept of magnetic quivers, where components of H \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{H} $$\end{document} are described as 3d N \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 4 Coulomb branches. When the starting quiver is good, there is a single component in H \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{H} $$\end{document} and the magnetic quiver is a 3d mirror. The magnetic quivers are obtained from studying the brane web for an auxiliary 5d theory (with only special unitary gauge groups), constrained by a new notion called brane locking , where some branes are required to move together. We view this as a computational tool rather than an operation in 5d. A detailed algorithm is provided.
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In this paper we discuss the dynamics of conformal field theories on anti-de Sitter space, focussing on the special case of the $ \mathcal{N} = 4 $ supersymmetric Yang-Mills theory on AdS~(4). We argue that the choice of boundary ...
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In this paper we discuss the dynamics of conformal field theories on anti-de Sitter space, focussing on the special case of the $ \mathcal{N} = 4 $ supersymmetric Yang-Mills theory on AdS~(4). We argue that the choice of boundary conditions, in particular for the gauge field, has a large effect on the dynamics. For example, for weak coupling, one of two natural choices of boundary conditions for the gauge field leads to a large N deconfinement phase transition as a function of the temperature, while the other does not. For boundary conditions that preserve supersymmetry, the strong coupling dynamics can be analyzed using S-duality (relevant for g ~(YM)? 1), utilizing results of Gaiotto and Witten, as well as by using the AdS/CFT correspondence (relevant for large N and large ’t Hooft coupling). We argue that some very specific choices of boundary conditions lead to a simple dual gravitational description for this theory, while for most choices the gravitational dual is not known. In the cases where the gravitational dual is known, we discuss the phase structure at large ’t Hooft coupling.
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A bstract N M5-branes probing the intersection between the orbifold ?~(2) / Γ_(ADE)and an E _(8)wall give rise to 6d (1 , 0) SCFTs known as ADE-type orbi-instantons. At fixed N and order of the orbifold, each element of Hom(Γ_(A...
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A bstract N M5-branes probing the intersection between the orbifold ?~(2) / Γ_(ADE)and an E _(8)wall give rise to 6d (1 , 0) SCFTs known as ADE-type orbi-instantons. At fixed N and order of the orbifold, each element of Hom(Γ_(ADE) , E _(8)) defines a different SCFT. The SCFTs are connected by Higgs branch RG flows, which generically reduce the flavor symmetry of the UV fixed point. We determine the full hierarchy of these RG flows for type A, i.e. ?~(2) / ?_( k ), for any value of N and k . The hierarchy takes the form of an intricate Hasse diagram: each node represents an IR orbi-instanton (homomorphism), and each edge an allowed flow, compatibly with the 6d a -theorem. The partial order is defined via quiver subtraction of the 3d magnetic quivers associated with the 6d SCFTs, which is equivalent to performing a so-called Kraft-Procesi transition between homomorphisms.
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