Aditi Chandra, Andrei Constantin, Cristofero S. Fraser-Taliente, Thomas R. Harvey, Andre Lukas
{"title":"Enumerating Calabi-Yau Manifolds: Placing Bounds on the Number of Diffeomorphism Classes in the Kreuzer-Skarke List","authors":"Aditi Chandra, Andrei Constantin, Cristofero S. Fraser-Taliente, Thomas R. Harvey, Andre Lukas","doi":"10.1002/prop.202300264","DOIUrl":"10.1002/prop.202300264","url":null,"abstract":"<p>The diffeomorphism class of simply connected smooth Calabi-Yau threefolds with torsion-free cohomology is determined via certain basic topological invariants: the Hodge numbers, the triple intersection form, and the second Chern class. In the present paper, we shed some light on this classification by placing bounds on the number of diffeomorphism classes present in the set of smooth Calabi-Yau threefolds constructed from the Kreuzer-Skarke (KS) list of reflexive polytopes up to Picard number six. The main difficulty arises from the comparison of triple intersection numbers and divisor integrals of the second Chern class up to basis transformations. By using certain basis-independent invariants, some of which appear here for the first time, we are able to place lower bounds on the number of classes. Upper bounds are obtained by explicitly identifying basis transformations, using constraints related to the index of line bundles. Extrapolating our results, we conjecture that the favorable entries of the KS list of reflexive polytopes lead to some <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mn>10</mn>\u0000 <mn>400</mn>\u0000 </msup>\u0000 <annotation>$10^{400}$</annotation>\u0000 </semantics></math> diffeomorphically distinct Calabi-Yau threefolds.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"72 5","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/prop.202300264","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140564273","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}
{"title":"Extending Anisotropic Interiors admitting Vanishing Complexity in Charged f (R, T) Theory","authors":"Tayyab Naseer, M. Sharif","doi":"10.1002/prop.202300254","DOIUrl":"10.1002/prop.202300254","url":null,"abstract":"<p>This paper extends the definition of the complexity factor for a charged self-gravitating structure in the background of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <mi>R</mi>\u0000 <mo>,</mo>\u0000 <mi>T</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$f(mathbf {R},mathbf {T})$</annotation>\u0000 </semantics></math> gravity. For this purpose, the modified Einstein-Maxwell field equations and the mass function in terms of interior charge are calculated corresponding to a static sphere. The Reissner-Nordström exterior spacetime and match it with the spherical interior at the hypersurface to determine the junction conditions are adopted then. The curvature tensor is also decomposed orthogonally, resulting in several scalar functions. Only <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>Y</mi>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mi>F</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$mathbf {Y}_{TF}$</annotation>\u0000 </semantics></math> encompasses all the required parameters and fulfills the proposed criteria to be the complexity factor for the considered setup is noticed. Moreover, some constraints to minimize the degrees of freedom in the field equations are chosen. To achieve this, complexity-free constraint with four additional conditions depending on the matter sector that lead to different models is employed. The stability of the developed models is also analyzed in the presence and absence of charge through the standard model <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 <mo>+</mo>\u0000 <mn>2</mn>\u0000 <msub>\u0000 <mi>ξ</mi>\u0000 <mn>3</mn>\u0000 </msub>\u0000 <mi>T</mi>\u0000 </mrow>\u0000 <annotation>$mathbf {R}+2xi _3mathbf {T}$</annotation>\u0000 </semantics></math> by varying the values of the model parameter <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ξ</mi>\u0000 <mn>3</mn>\u0000 </msub>\u0000 <annotation>$xi _3$</annotation>\u0000 </semantics></math>. The presence of charge in compact models corresponding to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>P</mi>\u0000 <mi>r</mi>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$mathrm{P}_r=0$</annotation>\u0000 </semantics></math>, a polytropic and a linear equation of state make them stable for specific values of <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 ","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"72 5","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140298608","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}
{"title":"Exploring T-Duality for Self-Dual Fields","authors":"Subhroneel Chakrabarti, Madhusudhan Raman","doi":"10.1002/prop.202400023","DOIUrl":"10.1002/prop.202400023","url":null,"abstract":"<p>Avatars of T-duality within Sen's formalism for self-dual field strengths in various dimensions are studied. This formalism is shown to naturally accommodate the T-duality relation between Type IIA/IIB theories when compactified on a circle without the need for imposing the self-duality constraint by hand, as is usually done. The study of this formalism is continued on two-dimensional target spacetimes and its study as a worldsheet theory is initiated. In particular, it is shown that Sen's action provides a natural worldsheet-based understanding of twisted and asymmetrically twisted strings. Finally, it is shown that the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mover>\u0000 <mi>T</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 </mrow>\u0000 <annotation>$mathrm{T}bar{mathrm{T}}$</annotation>\u0000 </semantics></math>-deformed theory of left- and right-chiral bosons described in Sen's formalism possesses a scaling limit that is related via field-theoretic T-duality to a recently studied integrable deformation of quantum mechanics.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"72 5","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/prop.202400023","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140200446","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}
{"title":"On the Relations between Fermion Masses and Isospin Couplings in the Microscopic Model","authors":"Bodo Lampe","doi":"10.1002/prop.202300258","DOIUrl":"10.1002/prop.202300258","url":null,"abstract":"<p>Quark and lepton masses and mixings are considered in the framework of the microscopic model. The most general ansatz for the interactions among tetrons leads to a Hamiltonian <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>H</mi>\u0000 <mi>T</mi>\u0000 </msub>\u0000 <annotation>$H_T$</annotation>\u0000 </semantics></math> involving Dzyaloshinskii-Moriya (DM), Heisenberg and torsional isospin forces. Diagonalization of the Hamiltonian provides for 24 eigenvalues which are identified as the quark and lepton masses. While the masses of the third and second family arise from DM and Heisenberg type of isospin interactions, light family masses are related to torsional interactions among tetrons. Neutrino masses turn out to be special in that they are given in terms of tiny isospin non-conserving DM, Heisenberg and torsional couplings. The approach not only leads to masses, but also allows to calculate the quark and lepton eigenstates, an issue, which is important for the determination of the CKM and PMNS mixing matrices. Compact expressions for the eigenfunctions of <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>H</mi>\u0000 <mi>T</mi>\u0000 </msub>\u0000 <annotation>$H_T$</annotation>\u0000 </semantics></math> are given. The almost exact isospin conservation of the system dictates the form of the lepton states and makes them independent of all the couplings in <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>H</mi>\u0000 <mi>T</mi>\u0000 </msub>\u0000 <annotation>$H_T$</annotation>\u0000 </semantics></math>. As a consequence, a parameter-free analytic expression for the PMNS matrix is derived which fits numerically all the measured matrix components. The formula includes a prediction of the leptonic Jarlskog invariant <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>J</mi>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 <mi>M</mi>\u0000 <mi>N</mi>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <mo>−</mo>\u0000 <mn>0.0106</mn>\u0000 </mrow>\u0000 <annotation>$J_{PMNS}=-0.0106$</annotation>\u0000 </semantics></math>. An outlook is given on the treatment of the CKM matrix.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"72 5","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152984","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}