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A bstract We establish the elliptic blowup equations for E-strings and M-strings and solve elliptic genera and refined BPS invariants from them. Such elliptic blowup equations can be derived from a path integral interpretation. We...
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A bstract We establish the elliptic blowup equations for E-strings and M-strings and solve elliptic genera and refined BPS invariants from them. Such elliptic blowup equations can be derived from a path integral interpretation. We provide toric hypersurface construction for the Calabi-Yau geometries of M-strings and those of E-strings with up to three mass parameters turned on, as well as an approach to derive the perturbative prepotential directly from the local description of the Calabi-Yau threefolds. We also demonstrate how to systematically obtain blowup equations for all rank one 5d SCFTs from E-string by blow-down operations. Finally, we present blowup equations for E–M and M string chains.
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A bstract 4 d N \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \b...
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A bstract 4 d 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 super Yang-Mills (SYM) with simply connected gauge group G has h gapped vacua arising from the spontaneously broken discrete R -symmetry, where h is the dual Coxeter number of G . Therefore, the theory admits stable domain walls interpolating between any two vacua, but it is a nonperturbative problem to determine the low energy theory on the domain wall. We put forward an explicit answer to this question for all the domain walls for G = SU( N ) , Sp( N ) , Spin( N ) and G _(2), and for the minimal domain wall connecting neighboring vacua for arbitrary G . We propose that the domain wall theories support specific nontrivial topological quantum field theories (TQFTs), which include the Chern-Simons theory proposed long ago by Acharya-Vafa for SU( N ). We provide nontrivial evidence for our proposals by exactly matching renormalization group invariant partition functions twisted by global symmetries of SYM computed in the ultraviolet with those computed in our proposed infrared TQFTs. A crucial element in this matching is constructing the Hilbert space of spin TQFTs, that is, theories that depend on the spin structure of spacetime and admit fermionic states — a subject we delve into in some detail.
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A bstract We test recently proposed IR dualities and supersymmetry enhancement by studying the supersymmetry on domain walls. In the SU(3) Wess-Zumino model studied in [ 1 , 2 ], we show that domain walls exhibit supersymmetry enh...
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A bstract We test recently proposed IR dualities and supersymmetry enhancement by studying the supersymmetry on domain walls. In the SU(3) Wess-Zumino model studied in [ 1 , 2 ], we show that domain walls exhibit supersymmetry enhancement. This model was conjectured to be dual to an 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 abelian gauge theory. We show that domain walls on the gauge theory side are consistent with the proposed duality, as they are described by the same effective theory on the wall. In [ 3 ], a third model was conjectured to be dual to the same IR theory. We study the phases and domain walls of this model and we show that they also agree. We then consider the analogous SU(5) Wess-Zumino model, and study its mass deformations and phases. We argue that even though one might expect supersymmetry enhancement in this model as well, the analysis of its domain walls shows that there is none. Finally, we study the 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 model in [ 4 ] which was conjectured to have 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 supersymmetry in the IR. In this case we don't see the supersymmetry enhancement on the domain wall; however, we argue that half-BPS domain walls of the 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 algebra are quarter-BPS of the 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 algebra. This is then in agreement with the conjectured enhancement, even though it does not show that it takes place.
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We present a detailed study of a filtering method based upon Dirac quasi-zeromodes in the adjoint representation. The procedure induces no distortions on configurations which are solutions of the euclidean classical equations of m...
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We present a detailed study of a filtering method based upon Dirac quasi-zeromodes in the adjoint representation. The procedure induces no distortions on configurations which are solutions of the euclidean classical equations of motion. On the other hand, it is very effective in reducing the short-wavelength stochastic noise present in Monte-Carlo generated configurations. After testing the performance of the method in various situations, we apply it successfully to study the effect of Monte-Carlo dynamics on topological structures like instantons.
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We present all charge one monopole solutions of the Bogomolny equation with k prescribed Dirac singularities for the gauge groups U(2) , SO(3) , or SU(2) . We analyze these solutions comparing them to the previously known expressi...
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We present all charge one monopole solutions of the Bogomolny equation with k prescribed Dirac singularities for the gauge groups U(2) , SO(3) , or SU(2) . We analyze these solutions comparing them to the previously known expressions for the cases of one or two singularities.
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We present all charge one monopole solutions of the Bogomolny equation with k prescribed Dirac singularities for the gauge groups U(2), SO(3), or SU(2). We analyze these solutions comparing them to the previously known expressions...
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We present all charge one monopole solutions of the Bogomolny equation with k prescribed Dirac singularities for the gauge groups U(2), SO(3), or SU(2). We analyze these solutions comparing them to the previously known expressions for the cases of one or two singularities.
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The sphaleron rate is defined as the diffusion constant for topological number \( {N_{\text{CS}}} \equiv \int {\frac{{{g^2}F\tilde{F}}}{{32{\pi^2}}}} \). It establishes the rate of equilibration of axial light quark number in QCD ...
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The sphaleron rate is defined as the diffusion constant for topological number \( {N_{\text{CS}}} \equiv \int {\frac{{{g^2}F\tilde{F}}}{{32{\pi^2}}}} \). It establishes the rate of equilibration of axial light quark number in QCD and is of interest both in electroweak baryogenesis and possibly in heavy ion collisions. We calculate the weak-coupling behavior of the SU(3) sphaleron rate, as well as making the most sensible extrapolation towards intermediate coupling which we can. We also study the behavior of the sphaleron rate at weak coupling at large N c .
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We define a class of supersymmetric defect loop operators in \( \mathcal{N} \) = 2 gauge theories in 2 + 1 dimensions. We give a prescription for computing the expectation value of such operators in a generic \( \mathcal{N} \) = 2...
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We define a class of supersymmetric defect loop operators in \( \mathcal{N} \) = 2 gauge theories in 2 + 1 dimensions. We give a prescription for computing the expectation value of such operators in a generic \( \mathcal{N} \) = 2 theory on the three-sphere using localization. We elucidate the role of defect loop operators in IR dualities of supersymmetric gauge theories, and write down their transformation properties under the SL(2, \( \mathbb{Z} \)) action on conformal theories with abelian global symmetries.
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We reconsider string and domain wall central charges in \( \mathcal{N} \) = 2 supersymmetric gauge theories in four dimensions in presence of the Omega background in the Nekrasov-Shatashvili (NS) limit. Existence of these charges ...
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We reconsider string and domain wall central charges in \( \mathcal{N} \) = 2 supersymmetric gauge theories in four dimensions in presence of the Omega background in the Nekrasov-Shatashvili (NS) limit. Existence of these charges entails presence of the corresponding topological defects in the theory — vortices and domain walls. In spirit of the 4d/2d duality we discuss the worldsheet low energy effective theory living on the BPS vortex in \( \mathcal{N} \) =2 Supersymmetric Quantum Chromodynamics (SQCD). We discuss some aspects of the brane realization of the dualities between various quantum integrable models. A chain of such dualities enables us to check the AGT correspondence in the NS limit.
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There have been two distinct schemes studied in the literature for instanton counting in A p−1 asymptotically locally Euclidean (ALE) spaces. We point out that the two schemes — namely the counting of orbifolded instantons and ...
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There have been two distinct schemes studied in the literature for instanton counting in A p−1 asymptotically locally Euclidean (ALE) spaces. We point out that the two schemes — namely the counting of orbifolded instantons and instanton counting in the resolved space — lead in general to different results for partition functions. We illustrate this observation in the case of \( \mathcal{N}=2 \) U(N) gauge theory with 2N flavors on the A p−1 ALE space. We propose simple relations between the instanton partition functions given by the two schemes and test them by explicit calculations.
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