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A bstract We establish the precise relation between the Nekrasov-Shatashvili (NS) quantization scheme and Grassi-Hatsuda-Mari?o conjecture for the mirror curve of arbitrary toric Calabi-Yau threefold. For a mirror curve of genus g...
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A bstract We establish the precise relation between the Nekrasov-Shatashvili (NS) quantization scheme and Grassi-Hatsuda-Mari?o conjecture for the mirror curve of arbitrary toric Calabi-Yau threefold. For a mirror curve of genus g , the NS quantization scheme leads to g quantization conditions for the corresponding integrable system. The exact NS quantization conditions enjoy a self S-duality with respect to Planck constant h and can be derived from the Lockhart-Vafa partition function of non-perturbative topological string. Based on a recent observation on the correspondence between spectral theory and topological string, another quantization scheme was proposed by Grassi-Hatsuda-Mari?o, in which there is a single quantization condition and the spectra are encoded in the vanishing of a quantum Riemann theta function. We demonstrate that there actually exist at least g nonequivalent quantum Riemann theta functions and the intersections of their theta divisors coincide with the spectra determined by the exact NS quantization conditions. This highly nontrivial coincidence between the two quantization schemes requires infinite constraints among the refined Gopakumar-Vafa invariants. The equivalence for mirror curves of genus one has been verified for some local del Pezzo surfaces. In this paper, we generalize the correspondence to higher genus, and analyze in detail the resolved ? 3 / ? 5 $$ {\mathbb{C}}^3/{\mathbb{Z}}_5 $$ orbifold and several SU( N ) geometries. We also give a proof for some models at ? = 2π /k .
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A bstract G?ttsche-Nakajima-Yoshioka K-theoretic blowup equations characterize the Nekrasov partition function of five dimensional N = 1 $$ \mathcal{N}=1 $$ supersymmetric gauge theories compactified on a circle, which via geometr...
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A bstract G?ttsche-Nakajima-Yoshioka K-theoretic blowup equations characterize the Nekrasov partition function of five dimensional N = 1 $$ \mathcal{N}=1 $$ supersymmetric gauge theories compactified on a circle, which via geometric engineering correspond to the refined topological string theory on SU( N ) geometries. In this paper, we study the K-theoretic blowup equations for general local Calabi-Yau threefolds. We find that both vanishing and unity blowup equations exist for the partition function of refined topological string, and the crucial ingredients are the r fields introduced in our previous paper. These blowup equations are in fact the functional equations for the partition function and each of them results in infinite identities among the refined free energies. Evidences show that they can be used to determine the full refined BPS invariants of local Calabi-Yau threefolds. This serves an independent and sometimes more powerful way to compute the partition function other than the refined topological vertex in the A-model and the refined holomorphic anomaly equations in the B-model. We study the modular properties of the blowup equations and provide a procedure to determine all the vanishing and unity r fields from the polynomial part of refined topological string at large radius point. We also find that certain form of blowup equations exist at generic loci of the moduli space.
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A bstract We systemically study the Hecke relations and the c = 8 k coset relations among 2d rational conformal field theories (RCFTs) with up to seven characters. We propose that the characters of any 2d RCFT — unitary or non-un...
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A bstract We systemically study the Hecke relations and the c = 8 k coset relations among 2d rational conformal field theories (RCFTs) with up to seven characters. We propose that the characters of any 2d RCFT — unitary or non-unitary — satisfying a holomorphic modular linear differential equation (MLDE) can be realized as either a Hecke image or the coset of a Hecke image with respect to a c = 8 k theory. Benefited from the recent results on holomorphic modular bootstrap, we check this proposal for all admissible theories with up to five characters. We also find many new interesting Hecke relations. For example, the characters of WZW models ( E _(6))_(2) , ( E _(7))_(2) , ( E 7 1 2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {E}_{7\frac{1}{2}} $$\end{document} )_(2)can be realized as the Hecke images T_(13) , T_(19) , T_(19)of Virasoro minimal models M _(sub)(7 , 6), M (5 , 4) , M _(eff)(13 , 2) respectively. Besides, we find the characters associated to the second largest Fisher group Fi _(23)and the Harada-Norton group HN can be realized as the Hecke images T_(23) , T_(19)of the product theories M _(eff)(5 , 2) ? M _(eff)(7 , 2) and M _(eff)(7 , 2)~(?2)respectively. Mathematically, our study provides a great many interesting examples of vector-valued modular functions up to rank seven.
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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 We propose novel functional equations for the BPS partition functions of 6d (1, 0) SCFTs, which can be regarded as an elliptic version of G?ttsche-Nakajima-Yoshioka’s K-theoretic blowup equations. From the viewpoint of ...
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A bstract We propose novel functional equations for the BPS partition functions of 6d (1, 0) SCFTs, which can be regarded as an elliptic version of G?ttsche-Nakajima-Yoshioka’s K-theoretic blowup equations. From the viewpoint of geometric engineering, these are the generalized blowup equations for refined topological strings on certain local elliptic CalabiYau threefolds. We derive recursion formulas for elliptic genera of self-dual strings on the tensor branch from these functional equations and in this way obtain a universal approach for determining refined BPS invariants. As examples, we study in detail the minimal 6d SCFTs with SU(3) and SO(8) gauge symmetry. In companion papers, we will study the elliptic blowup equations for all other non-Higgsable clusters.
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Abstract Heteroatom doping can endow MXenes with various new or improved electromagnetic, physicochemical, optical, and structural properties. This greatly extends the arsenal of MXenes materials and their potential for a spectrum...
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Abstract Heteroatom doping can endow MXenes with various new or improved electromagnetic, physicochemical, optical, and structural properties. This greatly extends the arsenal of MXenes materials and their potential for a spectrum of applications. This article comprehensively and critically discusses the syntheses, properties, and emerging applications of the growing family of heteroatom‐doped MXenes materials. First, the doping strategies, synthesis methods, and theoretical simulations of high‐performance MXenes materials are summarized. In order to achieve high‐performance MXenes materials, the mechanism of atomic element doping from three aspects of lattice optimization, functional substitution, and interface modification is analyzed and summarized, aiming to provide clues for developing new and controllable synthetic routes. The mechanisms underlying their advantageous uses for energy storage, catalysis, sensors, environmental purification and biomedicine are highlighted. Finally, future opportunities and challenges for the study and application of multifunctional high‐performance MXenes are presented. This work could open up new prospects for the development of high‐performance MXenes.
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A bstract A precise formula for the elliptic genus of three E-strings is presented. The related refined free energy coincides with the result calculated from topological string on local half K3 Calabi-Yau threefold up to genus twe...
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A bstract A precise formula for the elliptic genus of three E-strings is presented. The related refined free energy coincides with the result calculated from topological string on local half K3 Calabi-Yau threefold up to genus twelve. The elliptic genus of three heterotic strings computed from M9 domain walls matches with the result from orbifold formula to high orders. This confirms the n = 3 case of the recent conjecture that n pairs of E-strings can recombine into n heterotic strings.
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A precise formula for the elliptic genus of three E-strings is presented. The related refined free energy coincides with the result calculated from topological string on local half K3 Calabi-Yau threefold up to genus twelve. The e...
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A precise formula for the elliptic genus of three E-strings is presented. The related refined free energy coincides with the result calculated from topological string on local half K3 Calabi-Yau threefold up to genus twelve. The elliptic genus of three heterotic strings computed from M9 domain walls matches with the result from orbifold formula to high orders. This confirms the n = 3 case of the recent conjecture that n pairs of E-strings can recombine into n heterotic strings
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Abstract As an emerging solar energy utilization technology, solar redox batteries (SPRBs) combine the superior advantages of photoelectrochemical (PEC) devices and redox batteries and are considered as alternative candidates for ...
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Abstract As an emerging solar energy utilization technology, solar redox batteries (SPRBs) combine the superior advantages of photoelectrochemical (PEC) devices and redox batteries and are considered as alternative candidates for large‐scale solar energy capture, conversion, and storage. In this review, a systematic summary from three aspects, including: dye sensitizers, PEC properties, and photoelectronic integrated systems, based on the characteristics of rechargeable batteries and the advantages of photovoltaic technology, is presented. The matching problem of high‐performance dye sensitizers, strategies to improve the performance of photoelectrode PEC, and the working mechanism and structure design of multienergy photoelectronic integrated devices are mainly introduced and analyzed. In particular, the devices and improvement strategies of high‐performance electrode materials are analyzed from the perspective of different photoelectronic integrated devices (liquid‐based and solid‐state‐based). Finally, future perspectives are provided for further improving the performance of SPRBs. This work will open up new prospects for the development of high‐efficiency photoelectronic integrated batteries.
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Kesterite Cu_2ZnSn(S,Se)_4 (CZTSSe) with earth-abundant and environmentalbenign
constituents has been regarded as a promising solar energy harvesting
material for green and cost-effective photovoltaic applications. The
record e...
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Kesterite Cu_2ZnSn(S,Se)_4 (CZTSSe) with earth-abundant and environmentalbenign
constituents has been regarded as a promising solar energy harvesting
material for green and cost-effective photovoltaic applications. The
record efficiency of CZTSSe solar cells has recently been refreshed twice
after years-long stagnation, keeping it in the spotlight. Nevertheless, the
champion efficiency of 13.6% is still far behind its counterpart Cu(In,Ga)Se2
(CIGS) (23.35%) despite being endowed with a similar electronic structure
and nearly-identical device architecture. In fact, CZTSSe solar cells are more
susceptible to non-radiative recombination at bulk and interfaces, which must
be improved for further efficiency advancement. In this review, the state-ofart
strategies to enhance the power conversion efficiency of CZTSSe solar
cells are summarized and discussed, with focus given to three critical device
regions ⅰ) kesterite absorber, ⅱ) buffer/kesterite interface, and ⅲ) kesterite/
back contact interface. With the further elucidation of the latest progress and
disclosure of fundamental mechanisms, novel insights toward high-efficiency
kesterite solar cells are proposed.
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