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Special Joyce structures and hyperkähler metrics 特殊乔伊斯结构和超卡勒度量
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-10-29 DOI: 10.1007/s11005-024-01871-3
Iván Tulli
{"title":"Special Joyce structures and hyperkähler metrics","authors":"Iván Tulli","doi":"10.1007/s11005-024-01871-3","DOIUrl":"10.1007/s11005-024-01871-3","url":null,"abstract":"<div><p>Joyce structures were introduced by T. Bridgeland in the context of the space of stability conditions of a three-dimensional Calabi–Yau category and its associated Donaldson–Thomas invariants. In subsequent work, T. Bridgeland and I. Strachan showed that Joyce structures satisfying a certain non-degeneracy condition encode a complex hyperkähler structure on the tangent bundle of the base of the Joyce structure. In this work we give a definition of an analogous structure over an affine special Kähler (ASK) manifold, which we call a special Joyce structure. Furthermore, we show that it encodes a real hyperkähler (HK) structure on the tangent bundle of the ASK manifold, possibly of indefinite signature. Particular examples include the semi-flat HK metric associated to an ASK manifold (also known as the rigid c-map metric) and the HK metrics associated to certain uncoupled variations of BPS structures over the ASK manifold. Finally, we relate the HK metrics coming from special Joyce structures to HK metrics on the total space of algebraic integrable systems.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01871-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142540741","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
Vortices on cylinders and warped exponential networks 圆柱体上的旋涡和扭曲指数网络
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-10-26 DOI: 10.1007/s11005-024-01873-1
Kunal Gupta, Pietro Longhi
{"title":"Vortices on cylinders and warped exponential networks","authors":"Kunal Gupta,&nbsp;Pietro Longhi","doi":"10.1007/s11005-024-01873-1","DOIUrl":"10.1007/s11005-024-01873-1","url":null,"abstract":"<div><p>We study 3d <span>(mathcal {N}=2)</span> <i>U</i>(1) Chern–Simons-Matter QFT on a cylinder <span>(Ctimes mathbb {R})</span>. The topology of <i>C</i> gives rise to BPS sectors of low-energy solitons known as kinky vortices, which interpolate between (possibly) different vacua at the ends of the cylinder and at the same time carry magnetic flux. We compute the spectrum of BPS vortices on the cylinder in an isolated Higgs vacuum, through the framework of warped exponential networks, which we introduce. We then conjecture a relation between these and standard vortices on <span>(mathbb {R}^2)</span>, which are related to genus-zero open Gromov–Witten invariants of toric branes. More specifically, we show that in the limit of large Fayet–Iliopoulos coupling, the spectrum of kinky vortices on <i>C</i> undergoes an infinite sequence of wall-crossing transitions and eventually stabilizes. We then propose an exact relation between a generating series of stabilized CFIV indices and the Gromov–Witten disk potential and discuss its consequences for the structure of moduli spaces of vortices.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01873-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142519123","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
The structure of the wave operator in four dimensions in the presence of resonances 存在共振的四维波算子结构
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-10-19 DOI: 10.1007/s11005-024-01868-y
Angus Alexander, Adam Rennie
{"title":"The structure of the wave operator in four dimensions in the presence of resonances","authors":"Angus Alexander,&nbsp;Adam Rennie","doi":"10.1007/s11005-024-01868-y","DOIUrl":"10.1007/s11005-024-01868-y","url":null,"abstract":"<div><p>We show that the wave operators for Schrödinger scattering in <span>(mathbb {R}^4)</span> have a particular form which depends on the existence of resonances. As a consequence of this form, we determine the contribution of resonances to the index of the wave operator.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01868-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142451028","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
Ergodic theory of diagonal orthogonal covariant quantum channels 对角正交协变量子信道的遍历理论
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-10-17 DOI: 10.1007/s11005-024-01864-2
Satvik Singh, Nilanjana Datta, Ion Nechita
{"title":"Ergodic theory of diagonal orthogonal covariant quantum channels","authors":"Satvik Singh,&nbsp;Nilanjana Datta,&nbsp;Ion Nechita","doi":"10.1007/s11005-024-01864-2","DOIUrl":"10.1007/s11005-024-01864-2","url":null,"abstract":"<div><p>We analyse the ergodic properties of quantum channels that are covariant with respect to diagonal orthogonal transformations. We prove that the ergodic behaviour of a channel in this class is essentially governed by a classical stochastic matrix. This allows us to exploit tools from classical ergodic theory to study quantum ergodicity of such channels. As an application of our analysis, we study dual unitary brickwork circuits which have recently been proposed as minimal models of quantum chaos in many-body systems. Upon imposing a local diagonal orthogonal invariance symmetry on these circuits, the long-term behaviour of spatio-temporal correlations between local observables in such circuits is completely determined by the ergodic properties of a channel that is covariant under diagonal orthogonal transformations. We utilize this fact to show that such symmetric dual unitary circuits exhibit a rich variety of ergodic behaviours, thus emphasizing their importance.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01864-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142447420","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
On B-type family of Dubrovin–Frobenius manifolds and their integrable systems 论 Dubrovin-Frobenius 流形的 B 型族及其可积分系统
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-10-13 DOI: 10.1007/s11005-024-01867-z
Alexey Basalaev
{"title":"On B-type family of Dubrovin–Frobenius manifolds and their integrable systems","authors":"Alexey Basalaev","doi":"10.1007/s11005-024-01867-z","DOIUrl":"10.1007/s11005-024-01867-z","url":null,"abstract":"<div><p>According to Zuo and an unpublished work of Bertola, there is a two-index series of Dubrovin–Frobenius manifold structures associated to a B-type Coxeter group. We study the relations between these structures for the different values of these indices. We show that part of the data of such Dubrovin–Frobenius manifold indexed by (<i>k</i>, <i>l</i>) can be recovered by the <span>((k+r,l+r))</span> Dubrovin–Frobenius manifold.Continuing the program of Basalaev et al. (J Phys A: Math Theor 54:115201, 2021) we associate an infinite system of commuting PDEs to these Dubrovin–Frobenius manifolds and show that these PDEs extend the dispersionless BKP hierarchy.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431053","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
Hadamard property of the Unruh state for massless fermions on Kerr spacetime: the large a case 克尔时空中无质量费米子的乌恩鲁状态的哈达玛特性：大a情况
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-10-10 DOI: 10.1007/s11005-024-01862-4
Dietrich Häfner, Christiane Klein
{"title":"Hadamard property of the Unruh state for massless fermions on Kerr spacetime: the large a case","authors":"Dietrich Häfner,&nbsp;Christiane Klein","doi":"10.1007/s11005-024-01862-4","DOIUrl":"10.1007/s11005-024-01862-4","url":null,"abstract":"<div><p>In Gérard et al. (Ann Sci Ecole Norm Sup 56:127–196, 2023), the Unruh state for massless fermions on a Kerr spacetime was constructed and the authors showed its Hadmard property in the case of very slowly rotating black holes <span>({left| a right| }ll M)</span>. In this note, we extend this result to the full non extreme case <span>({left| a right| }&lt;M)</span>.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411151","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
On absolutely continuous spectrum for one-channel unitary operators 论单信道单元算子的绝对连续谱
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-10-10 DOI: 10.1007/s11005-024-01866-0
Olivier Bourget, Gregorio Moreno, Christian Sadel, Amal Taarabt
{"title":"On absolutely continuous spectrum for one-channel unitary operators","authors":"Olivier Bourget,&nbsp;Gregorio Moreno,&nbsp;Christian Sadel,&nbsp;Amal Taarabt","doi":"10.1007/s11005-024-01866-0","DOIUrl":"10.1007/s11005-024-01866-0","url":null,"abstract":"<div><p>In this paper, we develop the radial transfer matrix formalism for unitary one-channel operators. This generalizes previous formalisms for CMV matrices and scattering zippers. We establish an analog of Carmona’s formula and deduce criteria for absolutely continuous spectrum which we apply to random Hilbert Schmidt perturbations of periodic scattering zippers.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411179","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
Young wall models for the level 1 highest weight and Fock space crystals of (U_q(E_6^{(2)})) and (U_q(F_4^{(1)})) U_q(E_6^{(2)}) 和 U_q(F_4^{(1)})的第 1 层最高权重和 Fock 空间晶体的杨墙模型
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-09-30 DOI: 10.1007/s11005-024-01845-5
Shaolong Han, Yuanfeng Jin, Seok-Jin Kang, Duncan Laurie
{"title":"Young wall models for the level 1 highest weight and Fock space crystals of (U_q(E_6^{(2)})) and (U_q(F_4^{(1)}))","authors":"Shaolong Han,&nbsp;Yuanfeng Jin,&nbsp;Seok-Jin Kang,&nbsp;Duncan Laurie","doi":"10.1007/s11005-024-01845-5","DOIUrl":"10.1007/s11005-024-01845-5","url":null,"abstract":"<div><p>In this paper, we construct Young wall models for the level 1 highest weight and Fock space crystals of quantum affine algebras in types <span>(E_6^{(2)})</span> and <span>(F_4^{(1)})</span>. Our starting point in each case is a combinatorial realization for a certain level 1 perfect crystal in terms of Young columns. Then, using energy functions and affine energy functions we define the notions of reduced and proper Young walls, which model the highest weight and Fock space crystals, respectively.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142415284","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
Entanglement bounds for single-excitation energy eigenstates of quantum oscillator systems 量子振荡器系统单激发能量特征状态的纠缠边界
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-09-25 DOI: 10.1007/s11005-024-01863-3
Houssam Abdul-Rahman, Robert Sims, Günter Stolz
{"title":"Entanglement bounds for single-excitation energy eigenstates of quantum oscillator systems","authors":"Houssam Abdul-Rahman,&nbsp;Robert Sims,&nbsp;Günter Stolz","doi":"10.1007/s11005-024-01863-3","DOIUrl":"10.1007/s11005-024-01863-3","url":null,"abstract":"<div><p>We provide an analytic method for estimating the entanglement of the non-Gaussian energy eigenstates of disordered harmonic oscillator systems. We invoke the explicit formulas of the eigenstates of the oscillator systems to establish bounds for their <span>(epsilon )</span>-Rényi entanglement entropy <span>(epsilon in (0,1))</span>. Our methods result in a logarithmically corrected area law for the entanglement of eigenstates, corresponding to one excitation, of the disordered harmonic oscillator systems.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413663","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
Non-stationary difference equation for q-Virasoro conformal blocks q-Virasoro 保角块的非稳态差分方程
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2024-09-25 DOI: 10.1007/s11005-024-01856-2
Sh. Shakirov
{"title":"Non-stationary difference equation for q-Virasoro conformal blocks","authors":"Sh. Shakirov","doi":"10.1007/s11005-024-01856-2","DOIUrl":"10.1007/s11005-024-01856-2","url":null,"abstract":"<div><p>Conformal blocks of <i>q</i>, <i>t</i>-deformed Virasoro and <span>({mathcal {W}})</span>-algebras are important special functions in representation theory with applications in geometry and physics. In the Nekrasov–Shatashvili limit <span>(t rightarrow 1)</span>, whenever one of the representations is degenerate then conformal block satisfies a difference equation with respect to the coordinate associated with that degenerate representation. This is a stationary Schrodinger equation for an appropriate relativistic quantum integrable system. It is expected that generalization to generic <span>(t ne 1)</span> is a non-stationary Schrodinger equation where <i>t</i> parametrizes shift in time. In this paper we make the non-stationary equation explicit for the <i>q</i>, <i>t</i>-Virasoro block with one degenerate and four generic Verma modules and prove it when three modules out of five are degenerate, using occasional relation to Macdonald polynomials.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413695","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
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