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Communications in Number Theory and Physics最新文献

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On $E_1$-degeneration for the special fiber of a semistable family 关于一个半稳定族的特殊纤维的$E_1$-退化
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2019-03-24 DOI: 10.4310/cntp.2020.v14.n3.a4
Mao Sheng, Junchao Shentu
{"title":"On $E_1$-degeneration for the special fiber of a semistable family","authors":"Mao Sheng, Junchao Shentu","doi":"10.4310/cntp.2020.v14.n3.a4","DOIUrl":"https://doi.org/10.4310/cntp.2020.v14.n3.a4","url":null,"abstract":"We study the $E_1$-degeneration of the logarithmic Hodge to de Rham spectral sequence of the special fiber of a semistable family over a discrete valuation ring. On the one hand, we prove that the $E_1$-degeneration property is invariant under admissible blow-ups. Assuming functorial resolution of singularities over $mathbb{Z}$, this implies that the $E_1$-degeneration property depends only on the generic fiber. On the other hand, we show by explicit examples that the decomposability of the logarithmic de Rham complex is not invariant under admissible blow-ups, which answer negatively an open problem of L. Illusie (Problem 7.14 cite{Illusie2002}). We also give an algebraic proof of an $E_1$-degeneration result in characteristic zero due to Steenbrink and Kawamata-Namikawa.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2019-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43070263","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: 0
Modular graph functions and asymptotic expansions of Poincaré series 模图函数与Poincaré级数的渐近展开
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2019-03-21 DOI: 10.4310/cntp.2019.v13.n3.a3
Daniele Dorigoni, A. Kleinschmidt
{"title":"Modular graph functions and asymptotic expansions of Poincaré series","authors":"Daniele Dorigoni, A. Kleinschmidt","doi":"10.4310/cntp.2019.v13.n3.a3","DOIUrl":"https://doi.org/10.4310/cntp.2019.v13.n3.a3","url":null,"abstract":"In this note we study $SL(2,mathbb{Z})$-invariant functions such as modular graph functions or coefficient functions of higher derivative corrections in type IIB string theory. The functions solve inhomogeneous Laplace equations and we choose to represent them as Poincare series. In this way we can combine different methods for asymptotic expansions and obtain the perturbative and non-perturbative contributions to their zero Fourier modes. In the case of the higher derivative corrections, these terms have an interpretation in terms of perturbative string loop effects and pairs of instantons/anti-instantons.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42571051","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
On the arithmetic of Landau–Ginzburg model of a certain class of threefolds 一类三叠体的Landau-Ginzburg模型的算法
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2019-01-01 DOI: 10.4310/cntp.2019.v13.n1.a5
Genival da Silva
{"title":"On the arithmetic of Landau–Ginzburg model of a certain class of threefolds","authors":"Genival da Silva","doi":"10.4310/cntp.2019.v13.n1.a5","DOIUrl":"https://doi.org/10.4310/cntp.2019.v13.n1.a5","url":null,"abstract":"","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":"1 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70422884","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: 0
A note on BPS structures and Gopakumar–Vafa invariants 关于BPS结构和Gopakumar-Vafa不变量的注解
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-12-18 DOI: 10.4310/cntp.2019.v13.n3.a5
J. Stoppa
{"title":"A note on BPS structures and Gopakumar–Vafa invariants","authors":"J. Stoppa","doi":"10.4310/cntp.2019.v13.n3.a5","DOIUrl":"https://doi.org/10.4310/cntp.2019.v13.n3.a5","url":null,"abstract":"We regard the work of Maulik and Toda, proposing a sheaf-theoretic approach to Gopakumar-Vafa invariants, as defining a BPS structure, that is, a collection of BPS invariants together with a central charge. Assuming their conjectures, we show that a canonical flat section of the flat connection corresponding to this BPS structure, at the level of formal power series, reproduces the Gromov-Witten partition function for all genera, up to some error terms in genus 0 and 1. This generalises a result of Bridgeland and Iwaki for the contribution from genus 0 Gopakumar-Vafa invariants.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47879366","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
Brezin–Gross–Witten tau function and isomonodromic deformations Brezin–Gross–Witten-tau函数与等单调变形
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-12-05 DOI: 10.4310/cntp.2019.v13.n4.a4
M. Bertola, Giulio Ruzza
{"title":"Brezin–Gross–Witten tau function and isomonodromic deformations","authors":"M. Bertola, Giulio Ruzza","doi":"10.4310/cntp.2019.v13.n4.a4","DOIUrl":"https://doi.org/10.4310/cntp.2019.v13.n4.a4","url":null,"abstract":"The Brezin-Gross-Witten tau function is a tau function of the KdV hierarchy which arises in the weak coupling phase of the Brezin-Gross-Witten model. It falls within the family of generalized Kontsevich matrix integrals, and its algebro--geometric interpretation has been unveiled in recent works of Norbury. We prove that a suitably generalized Brezin-Gross-Witten tau function is the isomonodromic tau function of a $2times 2$ isomonodromic system and consequently present a study of this tau function purely by means of this isomonodromic interpretation. Within this approach we derive effective formulae for the generating functions of the correlators in terms of simple generating series, the Virasoro constraints, and discuss the relation with the Painlev'{e} XXXIV hierarchy.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46530836","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: 13
CHL Calabi–Yau threefolds: curve counting, Mathieu moonshine and Siegel modular forms CHL Calabi–Yau三重：曲线计数、Mathieu moonshine和Siegel模块形式
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-11-14 DOI: 10.4310/cntp.2020.v14.n4.a3
J. Bryan, G. Oberdieck
{"title":"CHL Calabi–Yau threefolds: curve counting, Mathieu moonshine and Siegel modular forms","authors":"J. Bryan, G. Oberdieck","doi":"10.4310/cntp.2020.v14.n4.a3","DOIUrl":"https://doi.org/10.4310/cntp.2020.v14.n4.a3","url":null,"abstract":"A CHL model is the quotient of $mathrm{K3} times E$ by an order $N$ automorphism which acts symplectically on the K3 surface and acts by shifting by an $N$-torsion point on the elliptic curve $E$. We conjecture that the primitive Donaldson-Thomas partition function of elliptic CHL models is a Siegel modular form, namely the Borcherds lift of the corresponding twisted-twined elliptic genera which appear in Mathieu moonshine. The conjecture matches predictions of string theory by David, Jatkar and Sen. We use the topological vertex to prove several base cases of the conjecture. Via a degeneration to $mathrm{K3} times mathbb{P}^1$ we also express the DT partition functions as a twisted trace of an operator on Fock space. This yields further computational evidence. An extension of the conjecture to non-geometric CHL models is discussed. \u0000We consider CHL models of order $N=2$ in detail. We conjecture a formula for the Donaldson-Thomas invariants of all order two CHL models in all curve classes. The conjecture is formulated in terms of two Siegel modular forms. One of them, a Siegel form for the Iwahori subgroup, has to our knowledge not yet appeared in physics. This discrepancy is discussed in an appendix with Sheldon Katz.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49510302","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: 11
Stringy Hirzebruch classes of Weierstrass fibrations weerstrass纤维的弦状Hirzebruch类
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-10-24 DOI: 10.4310/cntp.2020.v14.n3.a1
J. Fullwood, M. V. Hoeij
{"title":"Stringy Hirzebruch classes of Weierstrass fibrations","authors":"J. Fullwood, M. V. Hoeij","doi":"10.4310/cntp.2020.v14.n3.a1","DOIUrl":"https://doi.org/10.4310/cntp.2020.v14.n3.a1","url":null,"abstract":"A Weierstrass fibration is an elliptic fibration $Yto B$ whose total space $Y$ may be given by a global Weierstrass equation in a $mathbb{P}^2$-bundle over $B$. In this note, we compute stringy Hirzebruch classes of singular Weierstrass fibrations associated with constructing non-Abelian gauge theories in $F$-theory. For each Weierstrass fibration $Yto B$ we then derive a generating function $chi^{text{str}}_y(Y;t)$, whose degree-$d$ coefficient encodes the stringy $chi_y$-genus of $Yto B$ over an unspecified base of dimension $d$, solely in terms of invariants of the base. To facilitate our computations, we prove a formula for general characteristic classes of blowups along (possibly singular) complete intersections.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47521181","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
Dodgson polynomial identities Dodgson多项式恒等式
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-10-15 DOI: 10.4310/cntp.2019.v13.n4.a1
Marcel Golz
{"title":"Dodgson polynomial identities","authors":"Marcel Golz","doi":"10.4310/cntp.2019.v13.n4.a1","DOIUrl":"https://doi.org/10.4310/cntp.2019.v13.n4.a1","url":null,"abstract":"Dodgson polynomials appear in Schwinger parametric Feynman integrals and are closely related to the well known Kirchhoff (or first Symanzik) polynomial. In this article a new combinatorial interpretation and a generalisation of Dodgson polynomials are provided. This leads to two new identities that relate large sums of products of Dodgson polynomials to a much simpler expression involving powers of the Kirchhoff polynomial. These identities can be applied to the parametric integrand for quantum electrodynamics, simplifying it significantly. This is worked out here in detail on the example of superficially renormalised photon propagator Feynman graphs, but works much more generally.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46298197","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: 6
K3 surfaces from configurations of six lines in $mathbb{P}^2$ and mirror symmetry I 来自$mathbb｛P｝^2｝中六条线的配置和镜像对称I的K3曲面
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-10-01 DOI: 10.4310/cntp.2020.v14.n4.a2
S. Hosono, B. Lian, Hiromichi Takagi, S. Yau
{"title":"K3 surfaces from configurations of six lines in $mathbb{P}^2$ and mirror symmetry I","authors":"S. Hosono, B. Lian, Hiromichi Takagi, S. Yau","doi":"10.4310/cntp.2020.v14.n4.a2","DOIUrl":"https://doi.org/10.4310/cntp.2020.v14.n4.a2","url":null,"abstract":"From the viewpoint of mirror symmetry, we revisit the hypergeometric system $E(3,6)$ for a family of K3 surfaces. We construct a good resolution of the Baily-Borel-Satake compactification of its parameter space, which admits special boundary points (LCSLs) given by normal crossing divisors. We find local isomorphisms between the $E(3,6)$ systems and the associated GKZ systems defined locally on the parameter space and cover the entire parameter space. Parallel structures are conjectured in general for hypergeometric system $E(n,m)$ on Grassmannians. Local solutions and mirror symmetry will be described in a companion paper cite{HLTYpartII}, where we introduce a K3 analogue of the elliptic lambda function in terms of genus two theta functions.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47270622","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: 2
Rationalizing roots: an algorithmic approach 根的合理化:一种算法方法
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2018-09-28 DOI: 10.4310/CNTP.2019.V13.N2.A1
M. Besier, D. Straten, S. Weinzierl
{"title":"Rationalizing roots: an algorithmic approach","authors":"M. Besier, D. Straten, S. Weinzierl","doi":"10.4310/CNTP.2019.V13.N2.A1","DOIUrl":"https://doi.org/10.4310/CNTP.2019.V13.N2.A1","url":null,"abstract":"In the computation of Feynman integrals which evaluate to multiple polylogarithms one encounters quite often square roots. To express the Feynman integral in terms of multiple polylogarithms, one seeks a transformation of variables, which rationalizes the square roots. In this paper, we give an algorithm for rationalizing roots. The algorithm is applicable whenever the algebraic hypersurface associated with the root has a point of multiplicity $(d-1)$, where $d$ is the degree of the algebraic hypersurface. We show that one can use the algorithm iteratively to rationalize multiple roots simultaneously. Several examples from high energy physics are discussed.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2018-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45215194","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: 54
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