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Two homomorphisms from the affine Yangian associated with (widehat{mathfrak {sl}}(n)) to the affine Yangian associated with (widehat{mathfrak {sl}}(n+1)) 从与(widehat{mathfrak {sl}}(n)) 相关的仿射杨格到与(widehat{mathfrak {sl}}(n+1)) 相关的仿射杨格的两个同态关系
IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Pub Date : 2024-11-14 DOI: 10.1007/s11005-024-01879-9
Mamoru Ueda

We construct a homomorphism from the affine Yangian (Y_{hbar ,varepsilon +hbar }(widehat{mathfrak {sl}}(n))) to the affine Yangian (Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(n+1))) which is different from the one in Ueda (A homomorphism from the affine Yangian (Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(n))) to the affine Yangian (Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(n+1))), 2023. arXiv:2312.09933). By using this homomorphism, we give a homomorphism from (Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(n))otimes Y_{hbar ,varepsilon +nhbar }(widehat{mathfrak {sl}}(m))) to (Y_{hbar ,varepsilon }(widehat{mathfrak {sl}}(m+n))). As an application, we construct a homomorphism from the affine Yangian (Y_{hbar ,varepsilon +nhbar }(widehat{mathfrak {sl}}(m))) to the centralizer algebra of the pair of affine Lie algebras ((widehat{mathfrak {gl}}(m+n),widehat{mathfrak {sl}}(n))) and the coset vertex algebra of the pair of rectangular W-algebras (mathcal {W}^k(mathfrak {gl}(2m+2n),(2^{m+n}))) and (mathcal {W}^{k+m}(mathfrak {sl}(2n),(2^{n}))).

我们构建了一个从仿射杨式 (Y_hbar ,varepsilon +hbar }(widehatmathfrak {sl}}(n))) 到仿射杨式 (Y_{hbar 、(widehat/mathfrak{sl}}(n+1))的同构不同于上田(A homomorphism from the affine Yangian (Y_{hbar 、varepsilon }(widehatmathfrak {sl}}(n))) 到仿射杨式 (Y_{hbar ,varepsilon }(widehatmathfrak {sl}}(n+1))) 的同构, 2023.arXiv:2312.09933)。通过使用这个同态性,我们给出了一个同态性:从 (Y_{hbar ,varepsilon }(widehatmathfrak {sl}}(n))otimes Y_{hbar 、varepsilon +nhbar }(widehatmathfrak {sl}}(m))/) to(Y_{hbar ,varepsilon }(widehatmathfrak {sl}}(m+n))/).作为应用,我们构建了一个从仿射杨代数 (Y_hbar ,varepsilon +nhbar }(widehatmathfrak {sl}}(m))) 到一对仿射李代数 ((widehatmathfrak {gl}}(m+n)、)和一对矩形 W 算法的余集顶点代数((mathcal {W}^k(mathfrak {gl}(2m+2n)、(2^{m+n}))) and(mathcal {W}^{k+m}(mathfrak {sl}(2n),(2^{n}))).
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引用次数: 0
Ground states of fermionic nonlinear Schrödinger systems with Coulomb potential I: the (L^2)-subcritical case 具有库仑势的费米子非线性薛定谔系统的基态 I:(L^2)-次临界情况
IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Pub Date : 2024-11-14 DOI: 10.1007/s11005-024-01877-x
Bin Chen, Yujin Guo

We consider ground states of the N coupled fermionic nonlinear Schrödinger systems with the Coulomb potential V(x) in the (L^2)-subcritical case. By studying the associated constraint variational problem, we prove the existence of ground states for the system with any parameter (alpha >0), which represents the attractive strength of the non-relativistic quantum particles. The limiting behavior of ground states for the system is also analyzed as (alpha rightarrow infty ), where the mass concentrates at one of the singular points for the Coulomb potential V(x).

我们考虑了在(L^2)-次临界情况下具有库仑势V(x)的N个耦合费米子非线性薛定谔系统的基态。通过研究相关的约束变分问题,我们证明了任意参数(α >0)下系统基态的存在,该参数代表了非相对论量子粒子的吸引力强度。我们还分析了该系统基态的极限行为((alpha rightarrow infty ),其中质量集中在库仑势 V(x) 的奇异点之一。
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引用次数: 0
Quantum intersection numbers and the Gromov–Witten invariants of ({{{mathbb {C}}}{{mathbb {P}}}}^1) 量子交集数和({{mathbb {C}}}{{mathbb {P}}}}^1) )的格罗莫夫-维滕不变式
IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Pub Date : 2024-11-13 DOI: 10.1007/s11005-024-01869-x
Xavier Blot, Alexandr Buryak

The notion of a quantum tau-function for a natural quantization of the KdV hierarchy was introduced in a work of Dubrovin, Guéré, Rossi, and the second author. A certain natural choice of a quantum tau-function was then described by the first author, the coefficients of the logarithm of this series are called the quantum intersection numbers. Because of the Kontsevich–Witten theorem, a part of the quantum intersection numbers coincides with the classical intersection numbers of psi-classes on the moduli spaces of stable algebraic curves. In this paper, we relate the quantum intersection numbers to the stationary relative Gromov–Witten invariants of (({{{mathbb {C}}}{{mathbb {P}}}}^1,0,infty )) with an insertion of a Hodge class. Using the Okounkov–Pandharipande approach to such invariants (with the trivial Hodge class) through the infinite wedge formalism, we then give a short proof of an explicit formula for the “purely quantum” part of the quantum intersection numbers, found by the first author, which in particular relates these numbers to the one-part double Hurwitz numbers.

杜布罗文、盖雷、罗西和第二位作者的著作中引入了量子陶函数的概念,用于 KdV 层次的自然量子化。随后,第一作者描述了量子陶函数的某种自然选择,该数列的对数系数被称为量子交集数。由于康采维奇-维滕定理,量子交点数的一部分与稳定代数曲线模空间上的经典交点数重合。在本文中,我们将量子交点数与插入霍奇类的 (({{mathbb {C}}}{{mathbb {P}}}}^1,0,infty )) 的静态相对格罗莫夫-维滕不变式联系起来。利用奥孔科夫-潘达里潘德方法,通过无限楔形式主义来处理这种不变量(有微不足道的霍奇类),然后我们给出了第一作者发现的量子交集数的 "纯量子 "部分的明确公式的简短证明,特别是把这些数与单部分双赫尔维茨数联系起来。
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引用次数: 0
The semiclassical limit of a quantum Zeno dynamics 量子芝诺动力学的半经典极限
IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Pub Date : 2023-11-06 DOI: 10.1007/s11005-023-01730-7
Fabio Deelan Cunden, Paolo Facchi, Marilena Ligabò

Motivated by a quantum Zeno dynamics in a cavity quantum electrodynamics setting, we study the asymptotics of a family of symbols corresponding to a truncated momentum operator, in the semiclassical limit of vanishing Planck constant (hbar rightarrow 0) and large quantum number (Nrightarrow infty ), with (hbar N) kept fixed. In a suitable topology, the limit is the discontinuous symbol (pchi _D(x,p)) where (chi _D) is the characteristic function of the classically permitted region D in phase space. A refined analysis shows that the symbol is asymptotically close to the function (pchi _D^{(N)}(x,p)), where (chi _D^{(N)}) is a smooth version of (chi _D) related to the integrated Airy function. We also discuss the limit from a dynamical point of view.

在腔量子电动力学环境中的量子Zeno动力学的激励下,我们研究了在消失普朗克常数(hbarrightarrow0)和大量子数(Nrightarrowinfty)的半经典极限下,与截断动量算子相对应的符号族的渐近性,其中(hparN)保持不变。在合适的拓扑中,极限是不连续符号(pchi_D(x,p)),其中(chi_D)是相空间中经典允许区域D的特征函数。一个精细的分析表明,符号渐近接近函数(pchi_D^{(N)}(x,p)),其中(chi_D^{(N)})是与积分Airy函数相关的(chi _D)的光滑版本。我们还从动力学的角度讨论了极限。
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引用次数: 0
Rigorous derivation of the Efimov effect in a simple model Efimov效应在一个简单模型中的严格推导
IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Pub Date : 2023-11-03 DOI: 10.1007/s11005-023-01734-3
Davide Fermi, Daniele Ferretti, Alessandro Teta

We consider a system of three identical bosons in (mathbb {R}^3) with two-body zero-range interactions and a three-body hard-core repulsion of a given radius ( a > 0). Using a quadratic form approach, we prove that the corresponding Hamiltonian is self-adjoint and bounded from below for any value of a. In particular, this means that the hard-core repulsion is sufficient to prevent the fall to the center phenomenon found by Minlos and Faddeev in their seminal work on the three-body problem in 1961. Furthermore, in the case of infinite two-body scattering length, also known as unitary limit, we prove the Efimov effect, i.e., we show that the Hamiltonian has an infinite sequence of negative eigenvalues (E_n) accumulating at zero and fulfilling the asymptotic geometrical law (;E_{n+1} / E_n ; rightarrow ; e^{-frac{2pi }{s_0}},; ,text {for} ,; nrightarrow +infty ) holds, where (s_0approx 1.00624).

我们考虑了一个在(mathbb{R}^3)中由三个相同玻色子组成的系统,该系统具有两个零程相互作用和给定半径的三体硬核排斥(a>;0)。使用二次型方法,我们证明了对应的哈密顿量是自伴随的,并且对于a的任何值都是从下有界的。特别地,这意味着硬核排斥足以防止Minlos和Faddeev在1961年关于三体问题的开创性工作中发现的中心落下现象。此外,在无穷长的两体散射长度(也称为酉极限)的情况下,我们证明了Efimov效应,即我们证明了哈密顿量有一个无穷多的负本征值序列(e_n)在零处积累并满足渐近几何定律(;e_{n+1}/e_n;rightarrow;e^{-frac{2pi}{s_0}},;,text{for};;nrightarrow+infty)成立,其中(s_0约1.00624)。
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引用次数: 0
Fundamental weight systems are quantum states 基本重量系统是量子态
IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Pub Date : 2023-10-30 DOI: 10.1007/s11005-023-01725-4
David Corfield, Hisham Sati, Urs Schreiber

Weight systems on chord diagrams play a central role in knot theory and Chern–Simons theory; and more recently in stringy quantum gravity. We highlight that the noncommutative algebra of horizontal chord diagrams is canonically a star-algebra and ask which weight systems are positive with respect to this structure; hence, we ask: Which weight systems are quantum states, if horizontal chord diagrams are quantum observables? We observe that the fundamental ({mathfrak {g}}{mathfrak {l}}(n))-weight systems on horizontal chord diagrams with N strands may be identified with the Cayley distance kernel at inverse temperature (beta = textrm{ln}(n)) on the symmetric group on N elements. In contrast to related kernels like the Mallows kernel, the positivity of the Cayley distance kernel had remained open. We characterize its phases of indefinite, semi-definite and definite positivity, in dependence of the inverse temperature (beta ); and we prove that the Cayley distance kernel is positive (semi-)definite at (beta = text {ln}(n)) for all (n = 1,2,3, ldots ). In particular, this proves that all fundamental ({mathfrak {g}}{mathfrak {l}}(n))-weight systems are quantum states, and hence, so are all their convex combinations. We close with briefly recalling how, under our “Hypothesis H”, this result impacts on the identification of bound states of multiple M5-branes.

弦图上的权重系统在结理论和Chern-Simons理论中起着核心作用;以及最近的弦量子引力。我们强调了水平弦图的非对易代数在规范上是一个星形代数,并询问了哪些权重系统相对于这个结构是正的;因此,我们要问:如果水平弦图是量子可观察性的,那么哪些权重系统是量子态?我们观察到,在具有n条弦的水平弦图上,基本的({mathfrak{g}}{math Frak{l}(n)})-权系统可以用n元素上对称群上逆温度下的Cayley距离核来识别。与Mallows核等相关核相比,Cayley距离核的正性仍然是开放的。我们描述了它的不定、半定和定正相,这与反温度(β)有关;并且我们证明了对于所有的(n=1,2,3,ldots),Cayley距离核在(β=text{ln}(n))处是正(半)定的。特别地,这证明了所有基本的({mathfrak{g}}{math frak{l}(n)})-权系统都是量子态,因此,它们的所有凸组合也是量子态。最后,我们简要回顾一下,在我们的“假设H”下,这一结果如何影响多个M5膜结合态的识别。
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引用次数: 3
Gravity from holomorphic discs and celestial (Lw_{1+infty }) symmetries 全纯圆盘引力与天体对称性
IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Pub Date : 2023-10-28 DOI: 10.1007/s11005-023-01735-2
Lionel Mason

The study of physical theories in various signatures has been important for uncovering structures not easily visible or definable in Lorentz signature. In split signature, global twistor constructions for conformally self-dual (SD) gravity and Yang–Mills construct solutions from twistor data that can be expressed in terms of free data without gauge freedom. This is developed for asymptotically flat SD gravity to give a fully nonlinear encoding of the asymptotic gravitational data in terms of a real homogeneous generating function h on the real twistor space. The recently discovered (Lw_{1+infty }) celestial symmetries, when real, act locally as passive Poisson diffeomorphisms on the real twistor space. The twistor data, h, generates an imaginary such Poisson transformation that then generates the gravitational field by shifting the real slice of the twistor space. The twistor chiral sigma models, whose correlators yield the Einstein gravity tree-level S-matrix, are reformulated as theories of holomorphic discs in twistor space whose boundaries lie on the deformed real slice determined by h. The real (Lw_{1+infty }) symmetries act on the corresponding formula for the S-matrix geometrically with vanishing Noether currents, but imaginary generators yield graviton vertex operators that generate gravitons in the perturbative expansion. A generating function for the all plus 1-loop amplitude, the analogous framework for Yang–Mills, possible interpretations in Lorentz signature and similar open string formulations of twistor and ambitwistor strings in 4d in split signature, are briefly discussed.

对各种特征中的物理理论的研究对于揭示洛伦兹特征中不容易看到或定义的结构具有重要意义。在分裂签名中,共形自对偶(SD)重力的全局扭曲器结构和Yang-Mills从扭曲器数据中构建了解,这些解可以用自由数据表示,而没有规范自由。这是为渐近平坦的SD引力而发展的,用实扭曲空间上的实齐次生成函数h给出渐近引力数据的完全非线性编码。最近发现的(Lw_{1+infty})天体对称性,当为实时,在实扭曲空间上局部充当被动泊松微分同胚。扭曲器数据h生成一个假想的泊松变换,然后通过移动扭曲器空间的真实切片来生成引力场。扭曲器手性西格玛模型的相关器产生了爱因斯坦重力树级S矩阵,该模型被重新表述为扭曲器空间中的全纯圆盘理论,其边界位于由h确定的变形实切片上,但虚生成器产生了在微扰展开中生成引力子的引力子顶点算子。简要讨论了全加1环振幅的生成函数、Yang-Mills的类似框架、Lorentz签名中的可能解释以及分裂签名中4d中扭曲器和双扭曲器串的类似开弦公式。
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引用次数: 0
Framed cohomological Hall algebras and cohomological stable envelopes 框架上同调霍尔代数与上同调稳定包络。
IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Pub Date : 2023-09-11 DOI: 10.1007/s11005-023-01716-5
Tommaso Maria Botta

There are multiple conjectures relating the cohomological Hall algebras (CoHAs) of certain substacks of the moduli stack of representations of a quiver Q to the Yangian (Y^{Q}_textrm{MO}) by Maulik–Okounkov, whose construction is based on the notion of stable envelopes of Nakajima varieties. In this article, we introduce the cohomological Hall algebra of the moduli stack of framed representations of a quiver Q (framed CoHA), and we show that the equivariant cohomology of the disjoint union of the Nakajima varieties ({mathcal {M}}_Q(text {v},text {w})) for all dimension vectors (text {v}) and framing vectors (text {w}) has a canonical structure of subalgebra of the framed CoHA. Restricted to this subalgebra, the algebra multiplication is identified with the stable envelope map. As a corollary, we deduce an explicit inductive formula to compute stable envelopes in terms of tautological classes.

Maulik Okounkov的Yangian YMOQ与箭袋Q表示的模堆栈的某些子堆栈的上同调Hall代数(CoHA)有多种猜想,其构造基于Nakajima变种的稳定包络的概念。在本文中,我们引入了箭袋Q(framework CoHA)的框架表示的模栈的上同调Hall代数,并证明了所有维向量v和框架向量w的Nakajima变种MQ(v,w)的不相交并集的等变上同调具有框架CoHA的子代数的正则结构。受限于此子代数,代数乘法用稳定包络映射来识别。作为推论,我们推导了一个显式归纳公式,以计算重言类的稳定包络。
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引用次数: 0
Automata and one-dimensional TQFTs with defects 自动机与有缺陷的一维TQFT
IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Pub Date : 2023-09-05 DOI: 10.1007/s11005-023-01701-y
Paul Gustafson, Mee Seong Im, Remy Kaldawy, Mikhail Khovanov, Zachary Lihn

This paper explains how any nondeterministic automaton for a regular language L gives rise to a one-dimensional oriented topological quantum field theory (TQFT) with inner endpoints and zero-dimensional defects labeled by letters of the alphabet for L. The TQFT is defined over the Boolean semiring (mathbb {B}). Different automata for a fixed language L produce TQFTs that differ by their values on decorated circles, while the values on decorated intervals are described by the language L. The language L and the TQFT associated with an automaton can be given a path integral interpretation. In this TQFT, the state space of a one-point 0-manifold is a free module over (mathbb {B}) with the basis of states of the automaton. Replacing a free module by a finite projective (mathbb {B})-module P allows to generalize automata and this type of TQFT to a structure where defects act on open subsets of a finite topological space. Intersection of open subsets induces a multiplication on P allowing to extend the TQFT to a TQFT for one-dimensional foams (oriented graphs with defects modulo a suitable equivalence relation). A linear version of these constructions is also explained, with the Boolean semiring replaced by a commutative ring.

本文解释了正则语言L的任何不确定性自动机如何产生具有L的内端点和零维缺陷的一维定向拓扑量子场论(TQFT)。TQFT在布尔半环(mathbb {B})上定义。固定语言L的不同自动机产生的TQFT在装饰圆上的值不同,而装饰区间上的值由语言L描述。语言L和与自动机相关的TQFT可以给出路径积分解释。在这个TQFT中,零点流形的状态空间是(mathbb {B})上的一个自由模,具有自动机的状态基。用有限射影(mathbb {B}) -模P代替自由模,允许将自动机和这种类型的TQFT推广到缺陷作用于有限拓扑空间的开放子集的结构。开放子集的交集引起P上的乘法,允许将TQFT扩展到一维泡沫(具有缺陷的定向图模一个合适的等价关系)的TQFT。还解释了这些结构的线性版本,用交换环代替布尔半环。
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引用次数: 1
(C_2) generalization of the van Diejen model from the minimal ((D_5,D_5)) conformal matter 最小(D5,D5)共形物质对van Diejen模型的C2推广。
IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Pub Date : 2023-09-05 DOI: 10.1007/s11005-023-01714-7
Belal Nazzal, Anton Nedelin

We study superconformal indices of 4d compactifications of the 6d minimal ((D_{N+3},D_{N+3})) conformal matter theories on a punctured Riemann surface. Introduction of supersymmetric surface defect in these theories is done at the level of the index by the action of the finite difference operators on the corresponding indices. There exist at least three different types of such operators according to three types of punctures with (A_N, C_N) and (left( A_1right) ^N) global symmetries. We mainly concentrate on (C_2) case and derive explicit expression for an infinite tower of difference operators generalizing the van Diejen model. We check various properties of these operators originating from the geometry of compactifications. We also provide an expression for the kernel function of both our (C_2) operator and previously derived (A_2) generalization of van Diejen model. Finally, we also consider compactifications with (A_N)-type punctures and derive the full tower of commuting difference operators corresponding to this root system generalizing the result of our previous paper.

我们研究了穿孔黎曼表面上6d极小(DN+3,DN+3)共形物质理论的4d压缩的超共形指数。在这些理论中引入超对称表面缺陷是通过有限差分算子对相应指数的作用在指数水平上完成的。根据具有AN、CN和A1N全局对称性的三种类型的打孔,存在至少三种不同类型的这种算子。我们主要关注C2情况,并推广van Diejen模型,导出了差分算子的无穷塔的显式表达式。我们检查了这些算子的各种性质,这些性质源于紧致化的几何。我们还提供了我们的C2算子和先前导出的范迪扬模型的A2推广的核函数的表达式。最后,我们还考虑了具有AN型删截的紧致化,并推广了我们先前论文的结果,导出了与该根系统相对应的交换差算子的全塔。
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引用次数: 3
期刊
Letters in Mathematical Physics
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