Article
Physics, Particles & Fields
Martin Bies, Mirjam Cvetic, Ron Donagi, Ling Lin, Muyang Liu, Fabian Ruehle
Summary: This study combines machine learning and algebraic geometry techniques to analyze line bundle cohomologies on families of holomorphic curves. By generating a large amount of data and training a model to provide intuition for cohomology jumps, the researchers construct additional vector-like Higgs pairs in an F-Theory toy model. Further tools from algebraic geometry, particularly Brill-Noether theory, are needed to quantitatively explain the entire dataset. A diagrammatic approach is introduced to express cohomology jumps across the parameter space of each family of matter curves, reflecting a stratification of the F-theory complex structure moduli space in terms of the vector-like spectrum.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
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Physics, Particles & Fields
Thomas W. Grimm
Summary: We introduce a generalized notion of finiteness and propose a Tameness Conjecture for effective theories coupled to quantum gravity. We provide evidence for this conjecture by studying various effective theories arising from string theory compactifications using recent advances in tame geometry. The finiteness of self-dual flux vacua in F-theory is discussed as the strongest evidence for the Tameness Conjecture.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
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Astronomy & Astrophysics
Jonathan J. Heckman, Andrew P. Turner, Xingyang Yu
Summary: This study presents a detailed realization of the quantum field theory ensembles in D < 4 spacetime dimensions, allowing for a random averaging of coupling constants. The resulting volume, when each member of the ensemble is a conformal field theory with a standard semiclassical holographic dual, can be interpreted as an asymptotically anti-de Sitter space geometry with a distribution of boundary components joined by wormhole configurations. This construction provides a UV completion of the proposal for a high-dimensional Hilbert space for baby universes, while remaining consistent with the proposed swampland constraints.
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Physics, Particles & Fields
Anthony Ashmore, Charles Strickland-Constable, David Tennyson, Daniel Waldram
Summary: This study analyzes the geometry of generic Minkowski N = 1, D = 4 flux compactifications in string theory, using generalized geometry to characterize these compactifications and calculate the massless scalar moduli of GMPT solutions. It also offers a new perspective on the existence of G(2) manifolds.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
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Physics, Particles & Fields
Sergei Gukov, Du Pei, Pavel Putrov, Cumrun Vafa
Summary: By compactifying the topologically twisted 6d (1, 0) theories on 4-manifolds with flavor symmetry backgrounds, a connection between the topology of smooth 4-manifolds and the theory of topological modular forms has been established. The study reveals that the equivariant topological Witten genus of the 2d theory can generate a new invariant, and provides a better understanding of the relationship between 2d (0, 1) theories and TMF spectra.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Min-xin Huang, Sheldon Katz, Albrecht Klemm
Summary: The paper proposes a method for calculating refined Gopakumar-Vafa numbers on elliptically fibered Calabi-Yau 3-folds based on refined holomorphic anomaly equations. It includes a detailed review of existing mathematical methods towards defining and calculating Gopakumar-Vafa invariants and the GVNs on compact Calabi-Yau 3-folds suitable for physicists. The dependence of GVNs on complex structure moduli and orientation choices, as well as comparisons of B-model predictions with geometric calculations, are discussed in the paper.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
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Physics, Particles & Fields
Yotaro Sato, Yuji Tachikawa, Taizan Watari
Summary: This paper argues that an inconsistency arises in a theory with 3+1 and higher dimensions when there is an odd number of Majorana fermion zero modes on a dynamical point-like soliton. This statement is checked in several examples in field theory and in string/M theory.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
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Physics, Particles & Fields
Ross Altman, Jonathan Carifio, Xin Gao, Brent D. Nelson
Summary: We establish an orientifold Calabi-Yau threefold database for h(1,1)(X) <= 6 by considering non-trivial Z(2) divisor exchange involutions, and determine the characteristics and properties of these orientifold Calabi-Yau threefolds.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
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Physics, Particles & Fields
David Tennyson, Daniel Waldram
Summary: The study presents a detailed exploration of a new mathematical object in E-6(6) R+ generalised geometry known as 'exceptional complex structure' (ECS). It discusses the characteristics and classification of ECS as well as its relations to the geometry of generic minimally supersymmetric flux backgrounds of M-theory.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Antonella Grassi, James Halverson, Cody Long, Julius L. Shaneson, Benjamin Sung, Jiahua Tian
Summary: This paper studies the 6D localized charged matter spectrum of F-theory on a singular elliptic Calabi-Yau 3-fold. By utilizing the technology of string junctions, the localized charged matter spectrum at intersections of seven-branes is determined, and the number of massless string junctions is computed. The results are in agreement with the predicted results from 6D anomaly cancellation.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
J. Francois
Summary: By utilizing principal bundle geometry, this study explores the presymplectic structure of two classes of gauge theories: invariant theories and non-invariant theories that meet two specific assumptions. The research reveals the emergence of twisted geometry in the study of non-invariant gauge theories. The results demonstrate that the association of a symplectic structure to gauge theories over bounded regions is a common feature in both classes.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
James T. Liu, Ruben Minasian, Raffaele Savelli, Andreas Schachner
Summary: We study the non-linear structure of Type IIB couplings involving the metric and the complexified three-form G(3). By analyzing five-point string amplitudes, we find that the kinematics in the maximally R-symmetry-violating sector matches with standard superspace integrals and superparticle amplitudes in M-theory on a two-torus. The effective action in this sector is determined and its invariance under SL(2, Z) duality is verified. We also discuss the general structure of higher-point kinematics and provide tests and applications through compactifications to lower dimensions.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Thomas W. Grimm, Stefano Lanza, Chongchuo Li
Summary: The article discusses the combination of the Distance Conjecture and the Tameness Conjecture, proposing a method to divide the region near the infinite distance point into finite sectors to establish path-independent statements for the associated towers of states. Additionally, a more constrained class of tame functions is introduced to describe known string theory effective actions. It is found that the multi-field dependence of these functions can be reconstructed by one-dimensional linear test paths in each sector.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Pramod Shukla
Summary: In this article, a pheno-inspired classification for the divisor topologies of Calabi Yau threefolds is presented. The study provides empirical observations and conjectures about the classification of coordinate divisors into two categories. The Hodge numbers of a large number of coordinate divisors are also presented, which can be useful for studying the divisor topologies of Calabi Yau threefolds with higher h(1,1).
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Manki Kim
Summary: In this note, we prove combinatorial formulas for the Hodge number h(2,1) of prime toric divisors in an arbitrary toric hypersurface Calabi-Yau fourfold Y-4. We show that it is possible to find a toric hypersurface Calabi-Yau in which there are more than h(1,1)(Y-4) non-perturbative superpotential terms with trivial intermediate Jacobian.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Martin Bies, Christoph Mayrhofer, Timo Weigand
JOURNAL OF HIGH ENERGY PHYSICS
(2017)
Article
Mathematics, Applied
Martin Bies, Sebastian Posur
Summary: This paper provides explicit constructions for right exact monoidal structures on the category of finitely presented functors, and verifies the correctness of the constructions through the proof of the universal property of Freyd categories. In addition, the construction is compared with the Day convolution, and a criterion for closure is provided.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
(2022)
Article
Physics, Particles & Fields
Martin Bies, Mirjam Cvetic, Ron Donagi, Muyang Liu, Marielle Ong
Summary: This study examines the structure and origin of root bundles and spin bundles in relation to F-theory gauge potentials, particularly in the context of constructing the F-theory Standard Model without vector-like exotics. By analyzing the constraints on matter curves, a lower bound for combinations of root bundles and spin bundles satisfying the absence of vector-like pairs is determined. The results of this systematic study provide valuable insights into the vector-like spectra in F-theory geometry.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Martin Bies, Mirjam Cvetic, Ron Donagi, Marielle Ong
Summary: This study focuses on root bundles in 4d F-theory compactifications and their relevance to phenomenology. The analysis suggests that a large majority of root bundles in a certain geometry have no vector-like exotics. Furthermore, by studying a few nodal curves, it is possible to understand the vector-like spectra of the entire family of geometries. The study introduces a computer algorithm to compute the cohomologies of the root bundles.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Astronomy & Astrophysics
Martin Bies, Mirjam Cvetic, Muyang Liu
Summary: This study focuses on analyzing F-theory Standard Models with gauge coupling unification and no chiral exotics using root bundles, and identifies promising toric base threefolds for establishing models with exactly three quark doublets and no vectorlike exotics. By studying triangulations of 708 polytopes, the research derives lower bounds on the number of root bundles with three sections on specific curves. The findings suggest that induced root bundles on certain threefolds have three global sections and no exotic vectorlike quark-doublet modes.
Article
Physics, Particles & Fields
Martin Bies, Mirjam Cvetic, Ron Donagi, Ling Lin, Muyang Liu, Fabian Ruehle
Summary: This study combines machine learning and algebraic geometry techniques to analyze line bundle cohomologies on families of holomorphic curves. By generating a large amount of data and training a model to provide intuition for cohomology jumps, the researchers construct additional vector-like Higgs pairs in an F-Theory toy model. Further tools from algebraic geometry, particularly Brill-Noether theory, are needed to quantitatively explain the entire dataset. A diagrammatic approach is introduced to express cohomology jumps across the parameter space of each family of matter curves, reflecting a stratification of the F-theory complex structure moduli space in terms of the vector-like spectrum.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)