Communications in Number Theory and Physics最新文献_第4页

KP hierarchy for Hurwitz-type cohomological field theories hurwitz型上同场理论的KP层次

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2021-07-12 DOI: 10.4310/cntp.2023.v17.n2.a1

Reinier Kramer

引用次数: 2

Degeneracy and hidden symmetry for the asymmetric quantum Rabi model with integral bias 具有积分偏置的非对称量子Rabi模型的退化性和隐藏对称性

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2021-06-16 DOI: 10.4310/CNTP.2022.v16.n3.a4

Cid Reyes-Bustos, M. Wakayama

{"title":"Degeneracy and hidden symmetry for the asymmetric quantum Rabi model with integral bias","authors":"Cid Reyes-Bustos, M. Wakayama","doi":"10.4310/CNTP.2022.v16.n3.a4","DOIUrl":"https://doi.org/10.4310/CNTP.2022.v16.n3.a4","url":null,"abstract":"The hidden symmetry of the asymmetric quantum Rabi model (AQRM) with a half-integral bias (ibQRM (cid:96) ) was uncovered in recent studies by the explicit construction of operators J (cid:96) commuting with the Hamiltonian. The existence of such symmetry has been widely believed to cause the degeneration of the spectrum, that is, the crossings on the energy curves. In this paper we propose a conjectural relation between the symmetry and degeneracy for the ibQRM (cid:96) given explicitly in terms of two polynomials appearing independently in the respective investigations. Concretely, one of the polynomials appears as the quotient of the constraint polynomials that assure the existence of degenerate solutions while the other determines a quadratic relation (in general, it deﬁnes a curve of hyperelliptic type) between the ibQRM (cid:96) Hamiltonian and its basic commuting operator J (cid:96) . Following this conjecture, we derive several interesting structural insights of the whole spectrum. For instance, the energy curves are naturally shown to lie on a surface determined by the family of hyperelliptic curves by considering the coupling constant as a variable. This geometric picture contains the generalization of the parity decomposition of the symmetric quantum Rabi model. Moreover, it allows us to describe a remarkable approximation of the ﬁrst (cid:96) energy curves by the zero-section of the corresponding hyperelliptic curve. These investigations naturally lead to a geometric picture of the (hyper-)elliptic surfaces given by the Kodaira-N´eron type model for a family of curves over the projective line in connection with the energy curves, which may be expected to provide a complex analytic proof of the conjecture.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42334478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 9

Integrality of the LMOV invariants for framed unknot 框架unknot的LMOV不变量的可积性

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2021-06-05 DOI: 10.4310/CNTP.2019.V13.N1.A3

Wei Luo, Shengmao Zhu

引用次数: 7

On arithmetic Dijkgraaf–Witten theory 论算术Dijkgraaf–Witten理论

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2021-06-04 DOI: 10.4310/cntp.2023.v17.n1.a1

Hikaru Hirano, Junhyeong Kim, M. Morishita

引用次数: 0

Graphical functions in even dimensions 偶维的图形函数

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2021-05-11 DOI: 10.4310/CNTP.2022.v16.n3.a3

M. Borinsky, O. Schnetz

引用次数: 17

Elliptic threefolds with high Mordell–Weil rank 椭圆型三层，具有较高的莫德尔-韦尔秩

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2021-05-06 DOI: 10.4310/cntp.2022.v16.n4.a3

A. Grassi, T. Weigand

{"title":"Elliptic threefolds with high Mordell–Weil rank","authors":"A. Grassi, T. Weigand","doi":"10.4310/cntp.2022.v16.n4.a3","DOIUrl":"https://doi.org/10.4310/cntp.2022.v16.n4.a3","url":null,"abstract":"We present the first examples of smooth elliptic Calabi-Yau threefolds with Mordell-Weil rank 10, the highest currently known value. They are given by the Schoen threefolds introduced by Namikawa; there are six isolated fibers of Kodaira Type IV. We explicitly compute the Shioda homomorphism for the generators of the Mordell-Weil group and their induced height pairing. Compactification of F-theory on these threefolds gives an effective theory in six dimensions which contains ten abelian gauge group factors. We compute the massless matter spectrum. In particular, we show that the charged singlet matter need not reside at enhancement loci of Type $I_2$, as previously believed. We relate the multiplicities of the massless spectrum to genus-zero Gopakumar-Vafa invariants and other geometric quantities of the Calabi-Yau. We show that the gravitational and abelian anomaly cancellation conditions are satisfied. We prove a Geometric Anomaly Cancellation equation and we deduce birational equivalence for the quantities in the spectrum. We explicitly describe a Weierstrass model over $mathbb P^2$ of the Calabi-Yau threefolds as a log canonical model and compare it to a construction by Elkies and classical results of Burkhardt.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48654758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Berezin–Toeplitz quantization in real polarizations with toric singularities 复曲面奇异实极化中的Berezin–Toeplitz量子化

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2021-05-06 DOI: 10.4310/cntp.2022.v16.n4.a6

N. Leung, Y. Yau

引用次数: 1

Vertex operator algebras of rank $2$: The Mathur–Mukhi–Sen theorem revisited 秩$2$的顶点算子代数:对mathur1 - mukhi - sen定理的再考察

IF 1.9 3区数学

Communications in Number Theory and Physics Pub Date : 2021-01-01 DOI: 10.4310/cntp.2021.v15.n1.a2

G. Mason, K. Nagatomo, Yuichi Sakai

引用次数: 5

Wrońskian algebra and Broadhurst–Roberts quadratic relations Wrońskian代数与Broadhurst–Roberts二次关系