Quantum field theory creates fermions via abstract operators exciting abstract fields, with a specific field for each type of specific particle. This operator algebra lends itself well to quantum statistics, neverthel...Quantum field theory creates fermions via abstract operators exciting abstract fields, with a specific field for each type of specific particle. This operator algebra lends itself well to quantum statistics, nevertheless, our physical understanding of this process is nonintuitive at best. In this paper we analyze the creation of fermions from primordial gauge field quantum gravity loops in the context of Calabi-Yau manifold theory. I extend a prior mass-gap treatment based on Yang-Mills gauge theory of higher order self-interaction to include the half-integral spin of fermions.展开更多
This is a survey of using NMSP method to study higher genus Gromov-Witten invariants of Calabi-Yau quintics.It emphasizes on how and why the various methods are introduced to solve several important conjectures for hi...This is a survey of using NMSP method to study higher genus Gromov-Witten invariants of Calabi-Yau quintics.It emphasizes on how and why the various methods are introduced to solve several important conjectures for higher genus Gromov-Witten invariants of Calabi-Yau quintics.展开更多
We construct an N = 2 superconformal vertex algebra（SCVA） from a generalized Calabi-Yau manifold and compute the BRST cohomology of its associated topological vertex algebras. We show that the BRST cohomology coinci...We construct an N = 2 superconformal vertex algebra（SCVA） from a generalized Calabi-Yau manifold and compute the BRST cohomology of its associated topological vertex algebras. We show that the BRST cohomology coincides with the generalized Dobeault cohomology. We show that the two topological vertex algebras constructed from the N = 2 SCVA by A and B twist respectively are mirror pairs.展开更多
The authors give a discription of the finite representation type over an algebraically stable categories of selfinjective algebras of closed field, which admits indecomposable Calabi-Yau obdjects. For selfinjective al...The authors give a discription of the finite representation type over an algebraically stable categories of selfinjective algebras of closed field, which admits indecomposable Calabi-Yau obdjects. For selfinjective algebras with such properties, the ones whose stable categories are not Calabi-Yau are determined. For the remaining ones, i.e., those selfinjective algebras whose stable categories are actually Calabi-Yau, the difference between the Calabi-Yau dimensions of the indecomposable Calabi-Yau objects and the Calabi-Yau dimensions of the stable categories is described.展开更多
Math and physics proceed from assumptions to conclusions via a logical path. Artificial intelligence possesses the ability to follow logic, herein specifically applied to the problem of defining ontologically real 2D ...Math and physics proceed from assumptions to conclusions via a logical path. Artificial intelligence possesses the ability to follow logic, herein specifically applied to the problem of defining ontologically real 2D manifolds in a 3D continuum. Vortices and tori in fluids exhibit effective 2D surfaces, which, treated as manifolds, allow application of calculus on the boundaries of the structures. Recent papers in primordial field theory (PFT) have employed Calabi-Yau geometry and topology to develop a fermion structure. We desire a logical justification of this application and herein explore the use of artificial intelligence to assist in logic verification. A proof is outlined by the author and formalized by the AI.展开更多
A theory of quantum gravity has recently been developed by the author based on the concept that all forces converge to one at the moment of Creation. This primordial field can only interact with itself, as no other fi...A theory of quantum gravity has recently been developed by the author based on the concept that all forces converge to one at the moment of Creation. This primordial field can only interact with itself, as no other field exists, contrasting with the Standard Model of Particle Physics in which each elementary particle is an excitation in its own quantum field. The primordial field theory of quantum gravity has produced a model of a fermion with a mass gap, ½-integral spin, discrete charge, and magnetic moment. The mass gap is based on an existence theorem that is anchored in Yang-Mills, while Calabi-Yau anchors ½-integral spin, with charge and magnetic moment based on duality. Based on N-windings, this work is here extended to encompass fractional charge, with the result applied to quarks, yielding fermion mass and charge in agreement with experiment and novel size correlations and a unique quantum gravity-based ontological understanding of quarks.展开更多
Recently,a novel bootstrap method for numerical calculations in matrix models and quantum mechanical systems was proposed.We apply the method to certain quantum mechanical systems derived from some well-known local to...Recently,a novel bootstrap method for numerical calculations in matrix models and quantum mechanical systems was proposed.We apply the method to certain quantum mechanical systems derived from some well-known local toric Calabi-Yau geometries,where the exact quantization conditions have been conjecturally related to topological string theory.We find that the bootstrap method provides a promising alternative for the precision numerical calculations of the energy eigenvalues.An improvement in our approach is to use a larger set of two-dimensional operators instead of one-dimensional ones.We also apply our improved bootstrap methods to some non-relativistic models in the recent literature and demonstrate better numerical accuracies.展开更多
For a one parameter family of Calabi-Yau threefolds, Green et al.(2009) expressed the total singularities in terms of the degrees of Hodge bundles and Euler number of the general fiber. In this paper,we show that the ...For a one parameter family of Calabi-Yau threefolds, Green et al.(2009) expressed the total singularities in terms of the degrees of Hodge bundles and Euler number of the general fiber. In this paper,we show that the total singularities can be expressed by the sum of asymptotic values of BCOV(BershadskyCecotti-Ooguri-Vafa) invariants, studied by Fang et al.(2008). On the other hand, by using Yau's Schwarz lemma, we prove Arakelov type inequalities and Euler number bound for Calabi-Yau family over a compact Riemann surface.展开更多
We study the modularity problem of Calabi-Yau varieties from the conformal field theo- retic point of view.We express the modular forms associated to all 1-dimensional Calabi-Yau orbifolds in terms of products of Dede...We study the modularity problem of Calabi-Yau varieties from the conformal field theo- retic point of view.We express the modular forms associated to all 1-dimensional Calabi-Yau orbifolds in terms of products of Dedekind eta functions,which is hoped to shed light on the modularity questions for higher dimensional Calabi-Yau varieties.展开更多
We give a differential-geometric construction of Calabi-Yau fourfolds by the‘doubling’method,which was introduced in Doi and Yotsutani(N Y J Math 20:1203-1235,2014)to construct Calabi-Yau threefolds.We also give exa...We give a differential-geometric construction of Calabi-Yau fourfolds by the‘doubling’method,which was introduced in Doi and Yotsutani(N Y J Math 20:1203-1235,2014)to construct Calabi-Yau threefolds.We also give examples of Calabi-Yau fourfolds from toric Fano fourfolds.Ingredients in our construction are admissible pairs,which were first dealt with by Kovalev(J Reine Angew Math 565:125-160,2003).Here in this paper an admissible pair(X,D)consists of a compact Kähler manifold X and a smooth anticanonical divisor D on X.If two admissible pairs(X_(1),D_(1))and(X_(2),D_(2))with dimC X_(i)=4 satisfy the gluing condition,we can glue X_(1)\D_(1)and X_(2)\D_(2)together to obtain a compact Riemannian 8-manifold(M,g)whose holonomy group Hol(g)is contained in Spin(7).Furthermore,if theA-genus of M equals 2,then M is a Calabi-Yau fourfold,i.e.,a compact Ricci-flat Kähler fourfold with holonomy SU(4).In particular,if(X_(1),D_(1))and(X_(2),D_(2))are identical to an admissible pair(X,D),then the gluing condition holds automatically,so that we obtain a compact Riemannian 8-manifold M with holonomy contained in Spin(7).Moreover,we show that if the admissible pair is obtained from any of the toric Fano fourfolds,then the resulting manifold M is a Calabi-Yau fourfold by computing^A(M)=2.展开更多
In this paper, we consider two kinds of 2-Calabi-Yau triangulated categories with finitely many indecomposable objects up to isomorphisms, called An,t =D^b（KA（2t＋1）（n＋1）-3）/τ^t（n＋1）-1[1], where n,t ≥ 1, a...In this paper, we consider two kinds of 2-Calabi-Yau triangulated categories with finitely many indecomposable objects up to isomorphisms, called An,t =D^b（KA（2t＋1）（n＋1）-3）/τ^t（n＋1）-1[1], where n,t ≥ 1, and Dn,t = Db（KD2t（n＋1））/τ^（n＋1）φ^n, where n,t ≥ 1, and φ is induced by an automorphism of D2t（n＋1） of order 2. Except the categories An,1, they all contain non-zero maximal rigid objects which are not cluster tilting. An,1 contain cluster tilting objects. We define the cluster complex of An,t （resp. Dn,t） by using the geometric description of cluster categories of type A （resp. type D）. We show that there is an isomorphism from the cluster complex of An,t （resp. Dn,t） to the cluster complex of root system of type Bn. In particular, the maximal rigid objects are isomorphic to clusters. This yields a result proved recently by Buan-Palu-Reiten： Let RAn,t, resp. RDn,t, be the full subcategory of An,t, resp. Dn,t, generated by the rigid objects. Then RAn,t≈RAn,1 and TDn,t≈TAn,1 as additive categories, for all t 〉 1.展开更多
文摘Quantum field theory creates fermions via abstract operators exciting abstract fields, with a specific field for each type of specific particle. This operator algebra lends itself well to quantum statistics, nevertheless, our physical understanding of this process is nonintuitive at best. In this paper we analyze the creation of fermions from primordial gauge field quantum gravity loops in the context of Calabi-Yau manifold theory. I extend a prior mass-gap treatment based on Yang-Mills gauge theory of higher order self-interaction to include the half-integral spin of fermions.
基金Supported by Hong Kong GRF16301515,GRF16301717,GRF16304119 and GRF16306222。
文摘This is a survey of using NMSP method to study higher genus Gromov-Witten invariants of Calabi-Yau quintics.It emphasizes on how and why the various methods are introduced to solve several important conjectures for higher genus Gromov-Witten invariants of Calabi-Yau quintics.
文摘We construct an N = 2 superconformal vertex algebra（SCVA） from a generalized Calabi-Yau manifold and compute the BRST cohomology of its associated topological vertex algebras. We show that the BRST cohomology coincides with the generalized Dobeault cohomology. We show that the two topological vertex algebras constructed from the N = 2 SCVA by A and B twist respectively are mirror pairs.
基金supported by the National Natural Science Foundation of China (No. 10801099)the Zhejiang Provincial Natural Science Foundation of China (No. J20080154)the grant from Science Technology Department of Zhejiang Province (No. 2011R10051)
文摘The authors give a discription of the finite representation type over an algebraically stable categories of selfinjective algebras of closed field, which admits indecomposable Calabi-Yau obdjects. For selfinjective algebras with such properties, the ones whose stable categories are not Calabi-Yau are determined. For the remaining ones, i.e., those selfinjective algebras whose stable categories are actually Calabi-Yau, the difference between the Calabi-Yau dimensions of the indecomposable Calabi-Yau objects and the Calabi-Yau dimensions of the stable categories is described.
文摘Math and physics proceed from assumptions to conclusions via a logical path. Artificial intelligence possesses the ability to follow logic, herein specifically applied to the problem of defining ontologically real 2D manifolds in a 3D continuum. Vortices and tori in fluids exhibit effective 2D surfaces, which, treated as manifolds, allow application of calculus on the boundaries of the structures. Recent papers in primordial field theory (PFT) have employed Calabi-Yau geometry and topology to develop a fermion structure. We desire a logical justification of this application and herein explore the use of artificial intelligence to assist in logic verification. A proof is outlined by the author and formalized by the AI.
文摘A theory of quantum gravity has recently been developed by the author based on the concept that all forces converge to one at the moment of Creation. This primordial field can only interact with itself, as no other field exists, contrasting with the Standard Model of Particle Physics in which each elementary particle is an excitation in its own quantum field. The primordial field theory of quantum gravity has produced a model of a fermion with a mass gap, ½-integral spin, discrete charge, and magnetic moment. The mass gap is based on an existence theorem that is anchored in Yang-Mills, while Calabi-Yau anchors ½-integral spin, with charge and magnetic moment based on duality. Based on N-windings, this work is here extended to encompass fractional charge, with the result applied to quarks, yielding fermion mass and charge in agreement with experiment and novel size correlations and a unique quantum gravity-based ontological understanding of quarks.
基金supported in parts by the National Natural Science Foundation of China(Grants No.11947301 and No.12047502)
文摘Recently,a novel bootstrap method for numerical calculations in matrix models and quantum mechanical systems was proposed.We apply the method to certain quantum mechanical systems derived from some well-known local toric Calabi-Yau geometries,where the exact quantization conditions have been conjecturally related to topological string theory.We find that the bootstrap method provides a promising alternative for the precision numerical calculations of the energy eigenvalues.An improvement in our approach is to use a larger set of two-dimensional operators instead of one-dimensional ones.We also apply our improved bootstrap methods to some non-relativistic models in the recent literature and demonstrate better numerical accuracies.
基金supported by National Natural Science Foundation of China (Grant No. 11531012)
文摘For a one parameter family of Calabi-Yau threefolds, Green et al.(2009) expressed the total singularities in terms of the degrees of Hodge bundles and Euler number of the general fiber. In this paper,we show that the total singularities can be expressed by the sum of asymptotic values of BCOV(BershadskyCecotti-Ooguri-Vafa) invariants, studied by Fang et al.(2008). On the other hand, by using Yau's Schwarz lemma, we prove Arakelov type inequalities and Euler number bound for Calabi-Yau family over a compact Riemann surface.
文摘We study the modularity problem of Calabi-Yau varieties from the conformal field theo- retic point of view.We express the modular forms associated to all 1-dimensional Calabi-Yau orbifolds in terms of products of Dedekind eta functions,which is hoped to shed light on the modularity questions for higher dimensional Calabi-Yau varieties.
文摘We give a differential-geometric construction of Calabi-Yau fourfolds by the‘doubling’method,which was introduced in Doi and Yotsutani(N Y J Math 20:1203-1235,2014)to construct Calabi-Yau threefolds.We also give examples of Calabi-Yau fourfolds from toric Fano fourfolds.Ingredients in our construction are admissible pairs,which were first dealt with by Kovalev(J Reine Angew Math 565:125-160,2003).Here in this paper an admissible pair(X,D)consists of a compact Kähler manifold X and a smooth anticanonical divisor D on X.If two admissible pairs(X_(1),D_(1))and(X_(2),D_(2))with dimC X_(i)=4 satisfy the gluing condition,we can glue X_(1)\D_(1)and X_(2)\D_(2)together to obtain a compact Riemannian 8-manifold(M,g)whose holonomy group Hol(g)is contained in Spin(7).Furthermore,if theA-genus of M equals 2,then M is a Calabi-Yau fourfold,i.e.,a compact Ricci-flat Kähler fourfold with holonomy SU(4).In particular,if(X_(1),D_(1))and(X_(2),D_(2))are identical to an admissible pair(X,D),then the gluing condition holds automatically,so that we obtain a compact Riemannian 8-manifold M with holonomy contained in Spin(7).Moreover,we show that if the admissible pair is obtained from any of the toric Fano fourfolds,then the resulting manifold M is a Calabi-Yau fourfold by computing^A(M)=2.
基金Supported by the NSF of China(Grant No.11671221)
文摘In this paper, we consider two kinds of 2-Calabi-Yau triangulated categories with finitely many indecomposable objects up to isomorphisms, called An,t =D^b（KA（2t＋1）（n＋1）-3）/τ^t（n＋1）-1[1], where n,t ≥ 1, and Dn,t = Db（KD2t（n＋1））/τ^（n＋1）φ^n, where n,t ≥ 1, and φ is induced by an automorphism of D2t（n＋1） of order 2. Except the categories An,1, they all contain non-zero maximal rigid objects which are not cluster tilting. An,1 contain cluster tilting objects. We define the cluster complex of An,t （resp. Dn,t） by using the geometric description of cluster categories of type A （resp. type D）. We show that there is an isomorphism from the cluster complex of An,t （resp. Dn,t） to the cluster complex of root system of type Bn. In particular, the maximal rigid objects are isomorphic to clusters. This yields a result proved recently by Buan-Palu-Reiten： Let RAn,t, resp. RDn,t, be the full subcategory of An,t, resp. Dn,t, generated by the rigid objects. Then RAn,t≈RAn,1 and TDn,t≈TAn,1 as additive categories, for all t 〉 1.
