发布求助
文献互助 智能选刊 最新文献

Communications in Number Theory and Physics最新文献

筛选
英文 中文
Bhabha scattering and a special pencil of K3 surfaces Bhabha散射和K3表面的特殊铅笔
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-09-13 DOI: 10.4310/CNTP.2019.V13.N2.A4
Dino Festi, D. Straten
{"title":"Bhabha scattering and a special pencil of K3 surfaces","authors":"Dino Festi, D. Straten","doi":"10.4310/CNTP.2019.V13.N2.A4","DOIUrl":"https://doi.org/10.4310/CNTP.2019.V13.N2.A4","url":null,"abstract":"We study a pencil of K3 surfaces that appeared in the $2$-loop diagrams in Bhabha scattering. By analysing in detail the Picard lattice of the general and special members of the pencil, we identify the pencil with the celebrated Apery--Fermi pencil, that was related to Apery's proof of the irrationality of $zeta(3)$ through the work of F. Beukers, C. Peters and J. Stienstra. The same pencil appears miraculously in different and seemingly unrelated physical contexts.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":"1 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41781992","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: 20
From Möbius inversion to renormalisation 从Möbius反转到重整化
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-09-04 DOI: 10.4310/CNTP.2020.v14.n1.a3
Joachim Kock
{"title":"From Möbius inversion to renormalisation","authors":"Joachim Kock","doi":"10.4310/CNTP.2020.v14.n1.a3","DOIUrl":"https://doi.org/10.4310/CNTP.2020.v14.n1.a3","url":null,"abstract":"This paper traces a straight line from classical Mobius inversion to Hopf-algebraic perturbative renormalisation. This line, which is logical but not entirely historical, consists of just a few main abstraction steps, and some intermediate steps dwelled upon for mathematical pleasure. The paper is largely expository, but contains many new perspectives on well-known results. For example, the equivalence between the Bogoliubov recursion and the Atkinson formula is exhibited as a direct generalisation of the equivalence between the Weisner--Rota recursion and the Hall--Leroux formula for Mobius inversion.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":"14 1","pages":"171-198"},"PeriodicalIF":1.9,"publicationDate":"2018-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45280566","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: 5
Harer–Zagier formula via Fock space 通过Fock空间的Harer–Zagier公式
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-07-30 DOI: 10.4310/cntp.2019.v13.n3.a4
D. Lewanski
{"title":"Harer–Zagier formula via Fock space","authors":"D. Lewanski","doi":"10.4310/cntp.2019.v13.n3.a4","DOIUrl":"https://doi.org/10.4310/cntp.2019.v13.n3.a4","url":null,"abstract":"The goal of this note is to provide a very short proof of Harer-Zagier formula for the number of ways of obtaining a genus g Riemann surface by identifying in pairs the sides of a (2d)-gon, using semi-infinite wedge formalism operators.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48610733","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: 3
Approximating tau-functions by theta-functions 用θ函数逼近tau函数
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-07-09 DOI: 10.4310/CNTP.2019.V13.N1.A7
B. Dubrovin
{"title":"Approximating tau-functions by theta-functions","authors":"B. Dubrovin","doi":"10.4310/CNTP.2019.V13.N1.A7","DOIUrl":"https://doi.org/10.4310/CNTP.2019.V13.N1.A7","url":null,"abstract":"We prove that the logarithm of an arbitrary tau-function of the KdV hierarchy can be approximated, in the topology of graded formal series by the logarithmic expansions of hyperelliptic theta-functions of finite genus, up to at most quadratic terms. As an example we consider theta-functional approximations of the Witten--Kontsevich tau-function.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48375550","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: 1
Asymptotics of the $D^8 mathcal{R}^4$ genus-two string invariant $D^8mathcal｛R｝^4$亏格两字符串不变量的渐近性
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-06-07 DOI: 10.4310/CNTP.2019.V13.N2.A3
E. D'hoker, M. Green, B. Pioline
{"title":"Asymptotics of the $D^8 mathcal{R}^4$ genus-two string invariant","authors":"E. D'hoker, M. Green, B. Pioline","doi":"10.4310/CNTP.2019.V13.N2.A3","DOIUrl":"https://doi.org/10.4310/CNTP.2019.V13.N2.A3","url":null,"abstract":"We continue our investigation of the modular graph functions and string invariants that arise at genus-two as coefficients of low energy effective interactions in Type II superstring theory. In previous work, the non-separating degeneration of a genus-two modular graph function of weight $w$ was shown to be given by a Laurent polynomial in the degeneration parameter $t$ of degree $(w,w)$. The coefficients of this polynomial generalize genus-one modular graph functions, up to terms which are exponentially suppressed in $t$ as $t to infty$. In this paper, we evaluate this expansion explicitly for the modular graph functions associated with the $D^8 {cal R}^4$ effective interaction for which the Laurent polynomial has degree $(2,2)$. We also prove that the separating degeneration is given by a polynomial in the degeneration parameter $ln (|v|)$ up to contributions which are power-behaved in $v$ as $v to 0$. We further extract the complete, or tropical, degeneration and compare it with the independent calculation of the integrand of the sum of Feynman diagrams that contributes to two-loop type II supergravity expanded to the same order in the low energy expansion. We find that the tropical limit of the string theory integrand reproduces the supergravity integrand as its leading term, but also includes sub-leading terms proportional to odd zeta values that are absent in supergravity and can be ascribed to higher-derivative stringy interactions.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43155499","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: 25
Fermions on replica geometries and the $Theta$ - $theta$ relation 复制几何上的费米子与$Theta$-$Theta$关系
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-05-28 DOI: 10.4310/CNTP.2019.V13.N1.A8
S. Mukhi, S. Murthy
{"title":"Fermions on replica geometries and the $Theta$ - $theta$ relation","authors":"S. Mukhi, S. Murthy","doi":"10.4310/CNTP.2019.V13.N1.A8","DOIUrl":"https://doi.org/10.4310/CNTP.2019.V13.N1.A8","url":null,"abstract":"In arXiv:1706:09426 we conjectured and provided evidence for an identity between Siegel $Theta$-constants for special Riemann surfaces of genus $n$ and products of Jacobi $theta$-functions. This arises by comparing two different ways of computing the nth Renyi entropy of free fermions at finite temperature. Here we show that for $n=2$ the identity is a consequence of an old result due to Fay for doubly branched Riemann surfaces. For $n>2$ we provide a detailed matching of certain zeros on both sides of the identity. This amounts to an elementary proof of the identity for $n=2$, while for $nge 3$ it gives new evidence for it. We explain why the existence of additional zeros renders the general proof difficult.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49283108","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: 1
Quantum Langlands dualities of boundary conditions, $D$-modules, and conformal blocks 边界条件的量子Langlands对偶、$D$-模和共形块
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-05-01 DOI: 10.4310/cntp.2020.v14.n2.a1
E. Frenkel, D. Gaiotto
{"title":"Quantum Langlands dualities of boundary conditions, $D$-modules, and conformal blocks","authors":"E. Frenkel, D. Gaiotto","doi":"10.4310/cntp.2020.v14.n2.a1","DOIUrl":"https://doi.org/10.4310/cntp.2020.v14.n2.a1","url":null,"abstract":"We review and extend the vertex algebra framework linking gauge theory constructions and a quantum deformation of the Geometric Langlands Program. The relevant vertex algebras are associated to junctions of two boundary conditions in a 4d gauge theory and can be constructed from the basic ones by following certain standard procedures. Conformal blocks of modules over these vertex algebras give rise to twisted D-modules on the moduli stacks of G-bundles on Riemann surfaces which have applications to the Langlands Program. In particular, we construct a series of vertex algebras for every simple Lie group G which we expect to yield D-module kernels of various quantum Geometric Langlands dualities. We pay particular attention to the full duality group of gauge theory, which enables us to extend the standard qGL duality to a larger duality groupoid. We also discuss various subtleties related to the spin and gerbe structures and present a detailed analysis for the U(1) and SU(2) gauge theories.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49391479","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: 43
Local energy optimality of periodic sets 周期集的局部能量最优性
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-02-06 DOI: 10.4310/CNTP.2021.v15.n3.a2
R. Coulangeon, Achill Schurmann
{"title":"Local energy optimality of periodic sets","authors":"R. Coulangeon, Achill Schurmann","doi":"10.4310/CNTP.2021.v15.n3.a2","DOIUrl":"https://doi.org/10.4310/CNTP.2021.v15.n3.a2","url":null,"abstract":"We study the local optimality of periodic point sets in $mathbb{R}^n$ for energy minimization in the Gaussian core model, that is, for radial pair potential functions $f_c(r)=e^{-c r}$ with $c>0$. By considering suitable parameter spaces for $m$-periodic sets, we can locally rigorously analyze the energy of point sets, within the family of periodic sets having the same point density. We derive a characterization of periodic point sets being $f_c$-critical for all $c$ in terms of weighted spherical $2$-designs contained in the set. Especially for $2$-periodic sets like the family $mathsf{D}^+_n$ we obtain expressions for the hessian of the energy function, allowing to certify $f_c$-optimality in certain cases. For odd integers $ngeq 9$ we can hereby in particular show that $mathsf{D}^+_n$ is locally $f_c$-optimal among periodic sets for all sufficiently large~$c$.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47674843","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
Weyl invariant $E_8$ Jacobi forms Weyl不变$E_8$ Jacobi形式
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-01-25 DOI: 10.4310/cntp.2021.v15.n3.a3
Haowu Wang
{"title":"Weyl invariant $E_8$ Jacobi forms","authors":"Haowu Wang","doi":"10.4310/cntp.2021.v15.n3.a3","DOIUrl":"https://doi.org/10.4310/cntp.2021.v15.n3.a3","url":null,"abstract":"We investigate $W(E_8)$-invariant Jacobi forms which are the Jacobi forms invariant under the action of the Weyl group of the root system $E_8$. This type of Jacobi forms has applications in mathematics and physics, but very little has been known about its structure. In this paper we show that the bigraded ring of weak $W(E_8)$-invariant Jacobi forms is not a polynomial algebra over $C$ and prove that every $W(E_8)$-invariant Jacobi form can be expressed uniquely as a polynomial in nine algebraically independent holomorphic Jacobi forms introduced by Sakai with coefficients which are meromorphic $SL_2(Z)$ modular forms. The latter result implies that the graded ring of weak $W(E_8)$-invariant Jacobi forms of fixed index is a free module over the ring of $SL_2(Z)$ modular forms and the number of generators can be calculated by a generating series. We also determine and construct all generators of small index. These results extend Wirthm\"{u}ller's theorem proved in 1992 to the last open case.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43760275","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
Aspects of $(2,2)$ and $(0,2)$ hybrid models $(2,2)$和$(0,2)$混合模型的方面
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-01-12 DOI: 10.4310/cntp.2020.v14.n2.a3
Marco Bertolini, Mauricio Romo
{"title":"Aspects of $(2,2)$ and $(0,2)$ hybrid models","authors":"Marco Bertolini, Mauricio Romo","doi":"10.4310/cntp.2020.v14.n2.a3","DOIUrl":"https://doi.org/10.4310/cntp.2020.v14.n2.a3","url":null,"abstract":"In this work we study the topological rings of two dimensional (2,2) and (0,2) hybrid models. In particular, we use localization to derive a formula for the correlators in both cases, focusing on the B- and B/2-twists. Although our methods apply to a vast range of hybrid CFTs, we focus on hybrid models suitable for compactifications of the heterotic string. In this case, our formula provides unnormalized Yukawa couplings of the spacetime superpotential. We apply our techniques to hybrid phases of linear models, and we find complete agreement with known results in other phases. We also obtain a prediction for a certain class of correlators involving twisted operators in (2,2) Landau-Ginzburg orbifolds. For (0,2) theories, our argument does not rely on the existence of a (2,2) locus. Finally, we derive vanishing conditions concerning worldsheet instanton corrections in (0,2) B/2-twisted hybrid models.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45633174","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: 15
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信
小红书