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Mysterious triality and the exceptional symmetry of loop spaces 神秘的三重性和环空间的特殊对称性
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-09-09 DOI: 10.1007/s11005-025-01977-2
Hisham Sati, Alexander A. Voronov
{"title":"Mysterious triality and the exceptional symmetry of loop spaces","authors":"Hisham Sati,&nbsp;Alexander A. Voronov","doi":"10.1007/s11005-025-01977-2","DOIUrl":"10.1007/s11005-025-01977-2","url":null,"abstract":"<div><p>In previous work (Sati and Voronov in Commun Math Phys 400:1915–1960, 2023. https://doi.org/10.1007/s00220-023-04643-7, in Adv Theor Math Phys 28(8):2491–2601, 2024. https://doi.org/10.4310/atmp.241119034750), we introduced Mysterious Triality, extending the Mysterious Duality (Iqbal et al. in Adv Theor Math Phys 5:769–808, 2002. https://doi.org/10.4310/ATMP.2001.v5.n4.a5) between physics and algebraic geometry to include algebraic topology in the form of rational homotopy theory. Starting with the rational Sullivan minimal model of the 4-sphere <span>(S^4)</span>, capturing the dynamics of M-theory via Hypothesis H, this progresses to the dimensional reduction of M-theory on torus <span>(T^k)</span>, <span>(k ge 1)</span>, with its dynamics described via the iterated cyclic loop space <span>({mathcal {L}}_c^k S^4)</span> of the 4-sphere. From this, we also extracted data corresponding to the maximal torus/Cartan subalgebra and the Weyl group of the exceptional Lie group/algebra of type <span>(E_k)</span>. In this paper, we discover much richer symmetry by extending the action of the Cartan subalgebra by symmetries of the equations of motion of <span>((11-k))</span>d supergravity to a maximal parabolic subalgebra <span>(mathfrak {p}_k^{k(k)})</span> of the Lie algebra <span>(mathfrak {e}_{k(k)})</span> of the U-duality group. We do this by constructing the action on the rational homotopy model of the slightly more symmetric than <span>({mathcal {L}}_c^k S^4)</span> toroidification <span>({mathcal {T}}^k S^4)</span>, which is another bookkeeping device for the equations of motion. To justify these results, we identify the minimal model of the toroidification <span>({mathcal {T}}^k S^4)</span>, generalizing the results of Vigué-Poirrier, Sullivan, and Burghelea, and establish an algebraic toroidification/totalization adjunction.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 5","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145011964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic analysis for rarefaction problem of the focusing nonlinear Schrödinger equation with discrete spectrum 离散谱聚焦非线性Schrödinger方程稀疏问题的渐近分析
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-09-06 DOI: 10.1007/s11005-025-01985-2
Deng-Shan Wang, Dinghao Zhu
{"title":"Asymptotic analysis for rarefaction problem of the focusing nonlinear Schrödinger equation with discrete spectrum","authors":"Deng-Shan Wang,&nbsp;Dinghao Zhu","doi":"10.1007/s11005-025-01985-2","DOIUrl":"10.1007/s11005-025-01985-2","url":null,"abstract":"<div><p>The long-time asymptotic behaviors of the rarefaction problem for the focusing nonlinear Schrödinger equation with discrete spectrum are analyzed via the Riemann–Hilbert formulation. It is shown that for the rarefaction problem with pure step initial condition there are three asymptotic sectors in time–space: the plane wave sector, the 1-phase elliptic wave sector and the vacuum sector, while for the rarefaction problem with general initial data there are five asymptotic sectors in time–space: the plane wave sector, the sector of plane wave with soliton transmission, the sector of plane wave with phase shift, the sector of 1-phase elliptic wave with phase shift and the vacuum sector with phase shift. The leading-order term of each sector along with the corresponding error estimate is given by adopting the Deift–Zhou nonlinear steepest-descent method for Riemann–Hilbert problems. The asymptotic solutions match very well with the results from Whitham modulation theory and the direct numerical simulations.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 5","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145005504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Parabolic presentations of the modular super Yangian (Y_{M|N}) for arbitrary (0^{M}1^{N})-sequences 任意(0^{M}1^{N}) -序列的模超Yangian (Y_{M|N})的抛物表示
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-09-05 DOI: 10.1007/s11005-025-01980-7
Hongmei Hu
{"title":"Parabolic presentations of the modular super Yangian (Y_{M|N}) for arbitrary (0^{M}1^{N})-sequences","authors":"Hongmei Hu","doi":"10.1007/s11005-025-01980-7","DOIUrl":"10.1007/s11005-025-01980-7","url":null,"abstract":"<div><p>Let <span>(mu )</span> be an arbitrary composition of <span>(M+N)</span> and let <span>(mathfrak {s})</span> be an arbitrary <span>(0^{M}1^{N})</span>-sequence. The present paper is devoted to extending parabolic presentations, depending on <span>(mu )</span> and <span>(mathfrak {s})</span>, of the super Yangian <span>(Y_{M|N})</span> associated with the general linear Lie superalgebra <span>({mathfrak gmathfrak l}_{M|N})</span>, to a field of positive characteristic.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 5","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144990558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Affine super Yangians and non-rectangular W-superalgebras 仿射超杨子与非矩形w -超代数
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-09-02 DOI: 10.1007/s11005-025-01987-0
Mamoru Ueda
{"title":"Affine super Yangians and non-rectangular W-superalgebras","authors":"Mamoru Ueda","doi":"10.1007/s11005-025-01987-0","DOIUrl":"10.1007/s11005-025-01987-0","url":null,"abstract":"<div><p>We construct four edge contractions for the affine super Yangian of type <i>A</i>. As an application, by using these edge contractions, we give a homomorphism from the affine super Yangian of type <i>A</i> to the universal enveloping algebra of the non-rectangular <i>W</i>-superalgebra of type <i>A</i>.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 5","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-025-01987-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
perturbation of the nonlinear Schrödinger equation by a localized nonlinearity 局域非线性对非线性Schrödinger方程的扰动
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-08-28 DOI: 10.1007/s11005-025-01984-3
Gong Chen, Jiaqi Liu, Yuanhong Tian
{"title":"perturbation of the nonlinear Schrödinger equation by a localized nonlinearity","authors":"Gong Chen,&nbsp;Jiaqi Liu,&nbsp;Yuanhong Tian","doi":"10.1007/s11005-025-01984-3","DOIUrl":"10.1007/s11005-025-01984-3","url":null,"abstract":"<div><p>We revisit the perturbative theory of infinite dimensional integrable systems developed by P. Deift and X. Zhou [8], aiming to provide new and simpler proofs of some key <span>(L^infty )</span> bounds and <span>(L^p)</span> <i>a priori</i> estimates. Our proofs emphasizes a further step towards understanding focussing problems and extends the applicability to other integrable models. As a concrete application, we examine the perturbation of the one-dimensional defocussing cubic nonlinear Schrödinger equation by a localized higher-order term. We introduce improved estimates to control the power of the perturbative term and demonstrate that the perturbed equation exhibits the same long-time behavior as the completely integrable nonlinear Schrödinger equation.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 5","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144914812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The large N factorization does not hold for arbitrary multi-trace observables in random tensors 对于随机张量中的任意多迹观测量，大N分解不成立
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-08-26 DOI: 10.1007/s11005-025-01983-4
Razvan Gurau, Felix Joos, Benjamin Sudakov
{"title":"The large N factorization does not hold for arbitrary multi-trace observables in random tensors","authors":"Razvan Gurau,&nbsp;Felix Joos,&nbsp;Benjamin Sudakov","doi":"10.1007/s11005-025-01983-4","DOIUrl":"10.1007/s11005-025-01983-4","url":null,"abstract":"<div><p>We consider real tensors of order <i>D</i>, that is <i>D</i>-dimensional arrays of real numbers <span>(T_{a^1a^2 dots a^D})</span>, where each index <span>(a^c)</span> can take <i>N</i> values. The tensor entries <span>(T_{a^1a^2 dots a^D})</span> have no symmetry properties under permutations of the indices. The invariant polynomials built out of the tensor entries are called trace invariants. We prove that for a Gaussian random tensor with <span>(Dge 3)</span> indices (that is such that the entries <span>(T_{a^1a^2 dots a^D})</span> are independent identically distributed Gaussian random variables) the cumulant, or connected expectation, of a product of trace invariants is <i>not always</i> suppressed in scaling in <i>N</i> with respect to the product of the expectations of the individual invariants. Said otherwise, <i>not all</i> the multi-trace expectations factor at large <i>N</i> in terms of the single-trace ones and the Gaussian scaling is <i>not</i> subadditive on the connected components. This is in stark contrast to the <span>(D=2)</span> case of random matrices in which the multi-trace expectations always factor at large <i>N</i>. The best one can do for <span>(Dge 3)</span> is to identify restricted families of invariants for which the large <i>N</i> factorization holds and we check that this indeed happens when restricting to the family of melonic observables, the dominant family in the large <i>N</i> limit.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hirota, Fay and geometry Hirota， Fay和几何
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-08-21 DOI: 10.1007/s11005-025-01978-1
B. Eynard, S. Oukassi
{"title":"Hirota, Fay and geometry","authors":"B. Eynard,&nbsp;S. Oukassi","doi":"10.1007/s11005-025-01978-1","DOIUrl":"10.1007/s11005-025-01978-1","url":null,"abstract":"<div><p>This is a review of the relationship between Fay identities and Hirota equations in integrable systems, reformulated in a geometric language compatible with recent Topological Recursion formalism. We write Hirota equations as trans-series and Fay identities as spinor functional relations. We also recall several constructions of how some solutions to Fay/Hirota equations can be built from Riemann surface geometry.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-025-01978-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144880883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exponential control of excitations for trapped BEC in the Gross–Pitaevskii regime Gross-Pitaevskii区被困BEC激发的指数控制
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-08-21 DOI: 10.1007/s11005-025-01986-1
Nils Behrmann, Christian Brennecke, Simone Rademacher
{"title":"Exponential control of excitations for trapped BEC in the Gross–Pitaevskii regime","authors":"Nils Behrmann,&nbsp;Christian Brennecke,&nbsp;Simone Rademacher","doi":"10.1007/s11005-025-01986-1","DOIUrl":"10.1007/s11005-025-01986-1","url":null,"abstract":"<div><p>We consider trapped Bose gases in three dimensions in the Gross–Pitaevskii regime whose low energy states are well known to exhibit Bose–Einstein condensation. That is, the majority of the particles occupies the same condensate state. We prove exponential control of the number of particles orthogonal to the condensate state, generalizing recent results from Nam and Rademacher (Trans Am Math Soc, 2023, arXiv:2307.10622) for translation invariant systems.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-025-01986-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144880884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Self-adjointness of unbounded time operators 无界时间算子的自伴性
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-08-20 DOI: 10.1007/s11005-025-01981-6
Fumio Hiroshima, Noriaki Teranishi
{"title":"Self-adjointness of unbounded time operators","authors":"Fumio Hiroshima,&nbsp;Noriaki Teranishi","doi":"10.1007/s11005-025-01981-6","DOIUrl":"10.1007/s11005-025-01981-6","url":null,"abstract":"<div><p>Time operators associated with an abstract semi-bounded self-adjoint operator <i>H</i> possessing a purely discrete spectrum are considered. The existence of a bounded self-adjoint time operator <i>T</i> for such an operator <i>H</i> is known as the Galapon time operator. In this paper, we construct a self-adjoint but <i>unbounded</i> time operator <i>T</i> for <i>H</i> with a dense CCR-domain, thereby extending the framework beyond the bounded setting.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144868999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Teukolsky equations, twistor functions, and conformally self-dual spaces Teukolsky方程、扭函数与共形自对偶空间
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-08-12 DOI: 10.1007/s11005-025-01979-0
Bernardo Araneda
{"title":"Teukolsky equations, twistor functions, and conformally self-dual spaces","authors":"Bernardo Araneda","doi":"10.1007/s11005-025-01979-0","DOIUrl":"10.1007/s11005-025-01979-0","url":null,"abstract":"<div><p>We prove a correspondence, for Riemannian manifolds with self-dual Weyl tensor, between twistor functions and solutions to the Teukolsky equations for any conformal and spin weights. In particular, we give a contour integral formula for solutions to the Teukolsky equations, and we find a recursion operator that generates an infinite family of solutions and leads to the construction of Čech representatives and sheaf cohomology classes on twistor space. Apart from the general conformally self-dual case, examples include self-dual black holes, scalar-flat Kähler surfaces, and quaternionic-Kähler metrics, where we map the Teukolsky equation to the conformal wave equation, establish new relations to the linearised Przanowski equation, and find new classes of quaternionic deformations.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-025-01979-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144814553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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