| 1. |
- Anderson, Lara B., et al.
(författare)
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Generalized vanishing theorems for Yukawa couplings in heterotic compactifications
- 2021
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :5
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Tidskriftsartikel (refereegranskat)abstract
- Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be topological in nature. Recent results used differential geometric methods to explain the origin of some of this structure [1, 2]. A vanishing theorem was given which showed that the effect could be attributed, in part, to the embedding of the Calabi-Yau manifolds of interest inside higher dimensional ambient spaces, if the gauge bundles involved descended from vector bundles on those larger manifolds. In this paper, we utilize an algebro-geometric approach to provide an alternative derivation of some of these results, and are thus able to generalize them to a much wider arena than has been considered before. For example, we consider cases where the vector bundles of interest do not descend from bundles on the ambient space. In such a manner we are able to highlight the ubiquity with which textures of vanishing Yukawa couplings can be expected to arise in heterotic compactifications, with multiple different constraints arising from a plethora of different geometric features associated to the gauge bundle.
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| 2. |
- Braun, Andreas P., et al.
(författare)
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Gauged 2-form symmetries in 6D SCFTs coupled to gravity
- 2021
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :12
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Tidskriftsartikel (refereegranskat)abstract
- We study six dimensional supergravity theories with superconformal sectors (SCFTs). Instances of such theories can be engineered using type IIB strings, or more generally F-Theory, which translates field theoretic constraints to geometry. Specifically, we study the fate of the discrete 2-form global symmetries of the SCFT sectors. For both (2, 0) and (1, 0) theories we show that whenever the charge lattice of the SCFT sectors is non-primitively embedded into the charge lattice of the supergravity theory, there is a subgroup of these 2-form symmetries that remains unbroken by BPS strings. By the absence of global symmetries in quantum gravity, this subgroup much be gauged. Using the embedding of the charge lattices also allows us to determine how the gauged 2-form symmetry embeds into the 2-form global symmetries of the SCFT sectors, and we present several concrete examples, as well as some general observations. As an alternative derivation, we recover our results for a large class of models from a dual perspective upon reduction to five dimensions.
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| 3. |
- de la Ossa, Xenia, et al.
(författare)
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Almost contact structures on manifolds with a G(2) structure
- 2022
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Ingår i: Advances in Theoretical and Mathematical Physics. - : INT PRESS BOSTON, INC. - 1095-0761 .- 1095-0753. ; 26:1, s. 143-216
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Tidskriftsartikel (refereegranskat)abstract
- We review the construction of almost contact metric (three-) struc-tures, abbreviated ACM(3)S, on manifolds with a G2 structure. These are of interest for certain supersymmetric configurations in string and M-theory. We compute the torsion of the SU(3) struc-ture associated to an ACMS and apply these computations to het -erotic G2 systems and supersymmetry enhancement. We initiate the study of the space of ACM3Ss, which is an infinite dimensional space with a local product structure and interesting topological features. Tantalising links between ACM3Ss and associative and coassociative submanifolds are observed.
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| 4. |
- de la Ossa, Xenia, et al.
(författare)
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Almost contact structures on manifolds with a G2 structure
- 2021
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We review the construction of almost contact metric (three-) structures, abbreviated ACM(3)S, on manifolds with a G2 structure. These are of interest for certain supersymmetric configurations in string and M-theory. We compute the torsion of the SU(3) structure associated to an ACMS and apply these computations to heterotic G2 systems and supersymmetry enhancement. We initiate the study of the space of ACM3Ss, which is an infinite dimensional space with a local product structure and interesting topological features. Tantalising links between ACM3Ss and associative and coassociative submanifolds are observed.
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| 5. |
- de la Ossa, Xenia, et al.
(författare)
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Superpotential of three dimensional N=1 heterotic supergravity
- 2020
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Ingår i: Journal of High Energy Physics (JHEP). - : SPRINGER. - 1126-6708 .- 1029-8479. ; :1
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Tidskriftsartikel (refereegranskat)abstract
- We dimensionally reduce the ten dimensional heterotic supergravity action on spacetimes of the form M-(1,M- 2) x Y, where M-(1,M- 2) is three dimensional maximally symmetric Anti de Sitter or Minkowski space, and Y is a compact seven dimensional manifold with G(2) structure. In doing so, we derive the real superpotential functional of the corresponding three dimensional N = 1 theory. We confirm that extrema of this functional correspond to supersymmetric heterotic compacti:fications on manifolds of G(2) structure in the large volume, weak coupling limit to first order in a'. We make some comments on the role of the superpotential functional with respect to the coupled moduli problem of instanton bundles over G(2) manifolds.
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| 6. |
- Kohl, Finn Bjarne, et al.
(författare)
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F-theory on 6D symmetric toroidal orbifolds
- 2022
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479.
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Tidskriftsartikel (refereegranskat)abstract
- In this work we study F-theory on symmetric toroidal orbifolds that exhibit roto-translations, which are point group rotations accompanied by fractional lattice shifts. These geometries admit a rich class of effects, such as twisted affine folded fibers, multiple fibers, and up to three distinct torus-fibrations that yield different M/F-theory lifts. We discuss the six-dimensional physics of the F-theory lifts, which generically host superconformal subsectors and a IIB axio-dilaton fixed to strong coupling. In addition we find that these theories exhibit a rich set of p = 0,1, 2 discrete p-form gauge symmetries. We discuss six-dimensional gauge and supergravity anomalies and match the rank and tensor branch dimension to the Hodge numbers that were computed using heterotic world sheet techniques.
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| 7. |
- Larfors, Magdalena, 1978-, et al.
(författare)
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Explore and Exploit with Heterotic Line Bundle Models
- 2020
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Ingår i: Fortschritte der Physik. - : Wiley. - 0015-8208 .- 1521-3978. ; 68:5
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Tidskriftsartikel (refereegranskat)abstract
- We use deep reinforcement learning to explore a class of heterotic SU(5) GUT models constructed from line bundle sums over Complete Intersection Calabi Yau (CICY) manifolds. We perform several experiments where A3C agents are trained to search for such models. These agents significantly outperform random exploration, in the most favourable settings by a factor of 1700 when it comes to finding unique models. Furthermore, we find evidence that the trained agents also outperform random walkers on new manifolds. We conclude that the agents detect hidden structures in the compactification data, which is partly of general nature. The experiments scale well with h((1, 1)), and may thus provide the key to model building on CICYs with large h((1, 1)).
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| 8. |
- Larfors, Magdalena, 1978-, et al.
(författare)
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Heterotic line bundle models on generalized complete intersection Calabi Yau manifolds
- 2021
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; :5
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Tidskriftsartikel (refereegranskat)abstract
- The systematic program of heterotic line bundle model building has resulted in a wealth of standard-like models (SLM) for particle physics. In this paper, we continue this work in the setting of generalised Complete Intersection Calabi Yau (gCICY) manifolds. Using the gCICYs constructed in ref. [1], we identify two geometries that, when combined with line bundle sums, are directly suitable for heterotic GUT models. We then show that these gCICYs admit freely acting Z(2) symmetry groups, and are thus amenable to Wilson line breaking of the GUT gauge group to that of the standard model. We proceed to a systematic scan over line bundle sums over these geometries, that result in 99 and 33 SLMs, respectively. For the first class of models, our results may be compared to line bundle models on homotopically equivalent Complete Intersection Calabi Yau manifolds. This shows that the number of realistic configurations is of the same order of magnitude.
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| 9. |
- Larfors, Magdalena, 1978-, et al.
(författare)
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Learning Size and Shape of Calabi-Yau Spaces
- 2021
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Ingår i: Machine Learning and the Physical Sciences Workshop at the 35th Conference on Neural Information Processing Systems (NeurIPS) December 13, 2021.
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Konferensbidrag (refereegranskat)abstract
- We present a new machine learning library for computing metrics of string compact-ification spaces. We benchmark the performance on Monte-Carlo sampled integralsagainst previous numerical approximations and find that our neural networks aremore sample- and computation-efficient. We are the first to provide the possibilityto compute these metrics for arbitrary, user-specified shape and size parameters ofthe compact space and observe a linear relation between optimization of the partialdifferential equation we are training against and vanishing Ricci curvature
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| 10. |
- Larfors, Magdalena, 1978-, et al.
(författare)
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Numerical metrics for complete intersection and Kreuzer-Skarke Calabi-Yau manifolds
- 2022
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Ingår i: Machine Learning. - : Institute of Physics (IOP). - 2632-2153. ; 3:3
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Tidskriftsartikel (refereegranskat)abstract
- We introduce neural networks (NNs) to compute numerical Ricci-flat Calabi-Yau (CY) metrics for complete intersection and Kreuzer-Skarke (KS) CY manifolds at any point in Kahler and complex structure moduli space, and introduce the package cymetric which provides computation realizations of these techniques. In particular, we develop and computationally realize methods for point-sampling on these manifolds. The training for the NNs is carried out subject to a custom loss function. The Kahler class is fixed by adding to the loss a component which enforces the slopes of certain line bundles to match with topological computations. Our methods are applied to various manifolds, including the quintic manifold, the bi-cubic manifold and a KS manifold with Picard number two. We show that volumes and line bundle slopes can be reliably computed from the resulting Ricci-flat metrics. We also apply our results to compute an approximate Hermitian-Yang-Mills connection on a specific line bundle on the bi-cubic.
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| 11. |
- Magill, Matthew
(författare)
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Aspects of vacuum moduli in string theory
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we explore geometric aspects of the space of vacua in supersymmetric string compactifications. More specifically, we will look at heterotic strings compactified on Calabi-Yau manifolds and, separately, G2 structure manifolds. After reviewing the basic concepts underlying the thesis, specifically dimensional reduction of supergravity theories and G structures on manifolds, we begin looking at the vacua leading to supersymmetric three dimensional theories. The underlying compact manifold has a G2 structure. We investigate some structures that further refine the G2 structure: almost contact metric three-structures. We report on a relation between these structures and (co)associative cycles in the G2 structure manifold, and initiate an exploration of the topological properties of the moduli space of such structures. Next, we identify a superpotential whose critical locus is precisely the moduli space of supersymmetry preserving backgrounds, including both gauge and geometric fields. Finally, we study the Yukawa couplings of heterotic string compactifications on Calabi-Yau manifolds. Using sheaf cohomological tools, we find widely applicable vanishing theorems, which can constrain the Yukawa couplings of the effective four dimensional theory.
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| 12. |
- Schneider, Robin
(författare)
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Heterotic Compactifications in the Era of Data Science
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The goal of this thesis is to review and investigate recent applications of machine learning to problems in string theory. String theory, the leading candidate for a unification of gravity and the standard model of particle physics, requires the introduction of additional space-time dimensions. To match experimental observations of our universe, these additional dimensions need to be curled up on a compact space. The most common choice to describe this compact space are manifolds of Calabi-Yau type. These manifolds come with favourable mathematical and phenomenological properties.In the first half of this thesis Calabi-Yau manifolds, which are complex Kähler manifolds admitting a Ricci-flat metric, are introduced. The popular construction as complete intersections in products of complex projective space is explained and the necessary mathematical machinery to compute their topological quantities presented. This part is followed by a review of machine learning applications to study their Hodge numbers and the cohomologies of line bundles. In a next step the new Python library cymetric is presented for modeling numerical approximations of the unknown Ricci-flat metric. The metric tensor is a required component in the calculation of Yukawa couplings. It is learned by a neural network trained against a custom loss function, that encodes all the necessary mathematical properties.In the second half Calabi-Yau manifolds are used to compactify the heterotic string and con-struct standard model like vacua. Those are vacua which match the particle content and gaugegroup of a supersymmetric extension of the standard model. First, the popular compactificationprocedure utilising line bundle sums is reviewed and applied to the newly discovered construc-tions of generalized complete intersection Calabi-Yau manifolds. Second, an exploration ofsuch models is initiated in so far uncharted territories. This includes two Calabi-Yau manifoldswith more than 7 Kähler moduli, which are beyond systematic computational reach. In total19538 new models are found by using Actor-Critic agents from deep reinforcement learning.
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