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181
$\mathcal{N}$ = 1 supersymmetric indices and the four-dimensional A-model
Published 2017“…<p>We compute the supersymmetric partition function of $\mathcal{N}$ = 1 supersymmetric gauge theories with an R-symmetry on $\mathcal{M}$<sub>4</sub> ≅ $\mathcal{M}$<sub><em>g,p</em></sub> × <em>S</em><sup>1</sup>, a principal elliptic fiber bundle of degree <em>p</em> over a genus-<em>g</em> Riemann surface, Σ<sub><em>g</em></sub> . Equivalently, we compute the generalized supersymmetric index <em>I</em><sub>$\mathcal{M}$<sub><em>g,p</em></sub></sub> , with the supersymmetric three-manifold $\mathcal{M}$<sub><em>g,p</em></sub> as the spatial slice. …”
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182
The ASD equations in split signature and hypersymplectic geometry
Published 2012“…</p> <p>Hitchin's harmonic map equations are the split signature analogue of the self-duality equations on a Riemann surface, in which case it is known that there is a smooth hyperkähler moduli space. …”
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183
Symplectic quotients of unstable Morse strata for normsquares of moment maps
Published 2020“…There is an analogous infinite-dimensional picture for the Yang–Mills functional over a Riemann surface with strata determined by Harder–Narasimhan type. …”
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184
A Method of the Riemann–Hilbert Problem for Zhang’s Conjecture 2 in a Ferromagnetic 3D Ising Model: Topological Phases
Published 2021-11-01“…Following the procedures of realizing the representation of knots on the Riemann surface and formulating the Riemann–Hilbert problem in our preceding paper [O. …”
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185
Consistent truncations to 3-dimensional supergravity
Published 2022-09-01“…We also show how to construct consistent truncations of IIB supergravity on S 5 fibred over a Riemann surface. These result in 3-dimensional N $$ \mathcal{N} $$ = 4 gauged supergravities with scalar manifold M = SO 6 4 SO 6 × SO 4 × SU 2 1 S U 1 × U 2 $$ \mathcal{M}=\frac{\mathrm{S}\mathrm{O}\left(6,4\right)}{\mathrm{S}\mathrm{O}(6)\times \mathrm{SO}(4)}\times \frac{\mathrm{S}\mathrm{U}\left(2,1\right)}{\mathrm{S}\left(\mathrm{U}(1)\times \mathrm{U}(2)\right)} $$ with a ISO(3) × U(1)4 gauging and for hyperboloidal Riemann surfaces contain N $$ \mathcal{N} $$ = (2, 2) AdS3 vacua.…”
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186
Analysis of contact Cauchy–Riemann maps III: Energy, bubbling and Fredholm theory
Published 2023-04-01“…The asymptotic limit of a contact instanton is a ‘spiraling’ instanton along a ‘rotating’ Reeb orbit near each puncture on a punctured Riemann surface [Formula: see text]. Each limiting Reeb orbit carries a ‘charge’ arising from the integral of [Formula: see text]. …”
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187
Topological semimetals with helicoid surface states
Published 2017“…Each helicoid or multi-helicoid is shown to be the non-compact Riemann surface representing a multi-valued holomorphic function (generating function). …”
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188
Isotropic to anisotropic transition in a fractional quantum Hall state
Published 2011“…Nevertheless, there are chiral edge modes when the theory is placed on a space with boundary and a nontrivial ground-state degeneracy kg when it is placed on a finite-size Riemann surface of genus g. The coefficient of ei2 is the only relevant coupling; it tunes the system through a quantum phase transition between an isotropic fractional quantum Hall state and an anisotropic fractional quantum Hall state. …”
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189
G2 geometry and integrable systems
Published 2009“…We study the Hitchin component in the space of representations of the fundamental group of a Riemann surface into a split real Lie group in the rank 2 case. …”
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190
Coherent-resonance enhancement of sensing at the exceptional points
Published 2024“…The branch point singularities in the Riemann surface of the parameter space are known as the exceptional points (EPs), at which two or more eigenvalues and their associated eigenvectors simultaneously coalesce. …”
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191
Prime Geodesic Theorems for Compact Locally Symmetric Spaces of Real Rank One
Published 2020-10-01“…First, following classical Randol’s appraoch in the compact Riemann surface case, we improve the error term in the corresponding result. …”
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192
Higgs bundles, Lagrangians and mirror symmetry
Published 2017“…<p>Let Σ be a compact Riemann surface of genus <em>g</em> ≥ 2. This thesis is dedicated to the study of certain loci of the Higgs bundle moduli space. …”
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193
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194
Dynamics of Fricke–Painlevé VI Surfaces
Published 2024-01-01“…The symmetries of a Riemann surface <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">Σ</mi><mo>∖</mo><mo>{</mo><msub><mi>a</mi><mi>i</mi></msub><mo>}</mo></mrow></semantics></math></inline-formula> with <i>n</i> punctures <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>a</mi><mi>i</mi></msub></semantics></math></inline-formula> are encoded in its fundamental group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>π</mi><mn>1</mn></msub><mrow><mo>(</mo><mi mathvariant="sans-serif">Σ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. …”
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195
Algebraic Construction of the Sigma Function for General Weierstrass Curves
Published 2022-08-01“…It is known that every compact Riemann surface has a Weierstrass curve <i>X</i>, which is birational to the surface. …”
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196
Discriminant and Root Trajectories of Characteristic Equation of Fractional Vibration Equation and Their Effects on Solution Components
Published 2022-09-01“…It is proved that for any <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>c</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo><mo>∪</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>, the characteristic equation always has a pair of conjugated simple complex roots with a negative real part on the principal Riemann surface. Particular attention is paid to the problem as to how the couple conjugated complex roots approach the two roots of the integer case <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, especially to the two different real roots in the case of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>c</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>. …”
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197
A study of horizontally weakly conformal maps and their distributions
Published 2023-05-01“…Corollary 2.8. [3] A smooth map from Riemannian manifold $ (M,g) $ into a Riemann surface $ \overline{M}^2 $, is a horizontally weakly conformal map if and only if for any local complex coordinate $ z $ on $ \overline{M}^2 $, $ \nabla z $ is isotropic. …”
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198
Large genus bounds for the distribution of triangulated surfaces in moduli space
Published 2022“…Triangulated surfaces are compact Riemann surfaces equipped with a conformal triangulation by equilateral triangles. …”
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199
Supermoduli and PCOs at genus two
Published 2023-01-01“…Abstract We illustrate the relation between supermoduli integration and picture changing operators (PCOs) particularly concerning the role of vertical integration, in the context of superstring vacuum amplitudes, by an explicit comparison of different parameterizations of the supermoduli space of genus two super Riemann surfaces.…”
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200
A metal-free photoactive nitrogen-doped carbon nanosolenoid with broad absorption in visible region for efficient photocatalysis
Published 2023-09-01“…Abstract Riemann surfaces inspired chemists to design and synthesize such multidimensional curved carbon architectures. …”
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