| 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. |
- Braun, Andreas P., et al.
(författare)
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Infinitely many M2-instanton corrections to M-theory on G(2)-manifolds
- 2018
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Ingår i: Journal of High Energy Physics (JHEP). - : SPRINGER. - 1126-6708 .- 1029-8479. ; :9
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Tidskriftsartikel (refereegranskat)abstract
- We consider the non-perturbative superpotential for a class of four-dimensional N = 1 vacua obtained from M-theory on seven-manifolds with holonomy G(2). The class of G(2)-holonomy manifolds we consider are so-called twisted connected sum (TCS) constructions, which have the topology of a K3-fibration over S-3. We show that the non-perturbative superpotential of M-theory on a class of TCS geometries receives infinitely many inequivalent M2-instanton contributions from infinitely many three-spheres, which we conjecture are supersymmetric (and thus associative) cycles. The rationale for our construction is provided by the duality chain of [1], which relates M-theory on TCS G(2) manifolds to E-8 x E-8 heterotic backgrounds on the Schoen Calabi-Yau threefold, as well as to F-theory on a K3-fibered Calabi-Yau fourfold. The latter are known to have an infinite number of instanton corrections to the superpotential and it is these contributions that we trace through the duality chain back to the G(2)-compactification.
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| 4. |
- 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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| 5. |
- 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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| 6. |
- de la Ossa, Xenia, et al.
(författare)
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Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
- 2016
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Ingår i: Journal of High Energy Physics (JHEP). - : SPRINGER. - 1126-6708 .- 1029-8479. ; :11
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Tidskriftsartikel (refereegranskat)abstract
- We describe the infinitesimal moduli space of pairs (Y, V) where Y is a manifold with G(2) holonomy, and V is a vector bundle on Y with an instanton connection. These structures arise in connection to the moduli space of heterotic string compactifications on compact and non-compact seven dimensional spaces, e.g. domain walls. Employing the canonical G(2) cohomology developed by Reyes-Carrion and Fern\'andez and Ugarte, we show that the moduli space decomposes into the sum of the bundle moduli H-d(sic)A(1)(Y, End(V)) plus the moduli of the G(2) structure preserving the instanton condition. The latter piece is contained in H-d(sic)theta(1)(Y, TY), and is given by the kernel of a map F(sic) which generalises the concept of the Atiyah map for holomorphic bundles on complex manifolds to the case at hand. In fact, the map F(sic) is given in terms of the curvature of the bundle and maps H-d(sic)theta(1)(Y, TY) into H-d(sic)A(2) (Y, End(V)), and moreover can be used to define a cohomology on an extension bundle of TY by End(V). We comment further on the resemblance with the holomorphic Atiyah algebroid and connect the story to physics, in particular to heterotic compactifications on (Y,V) when alpha'=0.
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| 7. |
- de la Ossa, Xenia, et al.
(författare)
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Restrictions of Heterotic G2 Structures and Instanton Connections
- 2017
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Ingår i: Proceedings, Nigel Hitchin’s 70th Birthday Conference. - Oxford : Oxford University Press. - 9780198802020
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Konferensbidrag (refereegranskat)abstract
- This note revisits recent results regarding the geometry and moduli of solutions of the heterotic string on manifolds Y with a G2 structure. In particular, such heterotic G2 systems can be rephrased in terms of a differential Dˇ acting on a complex Ωˇ∗(Y,Q), where Q=T∗Y⊕End(TY)⊕End(V), and Dˇ is an appropriate projection of an exterior covariant derivative D which satisfies an instanton condition. The infinitesimal moduli are further parametrized by the first cohomology H1Dˇ(Y,Q). We proceed to restrict this system to manifolds X with an SU(3) structure corresponding to supersymmetric compactifications to four-dimensional Minkowski space, often referred to as Strominger–Hull solutions. In doing so, we derive a new result: the Strominger-Hull system is equivalent to a particular holomorphic Yang–Mills covariant derivative on Q|X=T∗X⊕End(TX)⊕End(V).
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| 8. |
- 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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| 9. |
- de la Ossa, Xenia, et al.
(författare)
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The Infinitesimal Moduli Space of Heterotic G2 Systems
- 2018
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Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 360:2, s. 727-775
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Tidskriftsartikel (refereegranskat)abstract
- Heterotic string compactifications on integrable G(2) structure manifolds Y with instanton bundles (V, A), (TY, (theta) over tilde )yield supersymmetric three-dimensional vacua that are of interest in physics. In this paper, we define a covariant exterior derivative D and show that it is equivalent to a heterotic G(2) system encoding the geometry of the heterotic string compactifications. This operator D acts on a bundle Q = T*Y circle plus End (V) circle plus End (TY) and satisfies a nilpotency condition (sic)(2) = 0, for an appropriate projection of D. Furthermore, we determine the infinitesimal moduli space of these systems and show that it corresponds to the finite-dimensional cohomology group (sic)(1)((sic)) (Q). We comment on the similarities and differences of our result with Atiyah's well-known analysis of deformations of holmorphic vector bundles over complex manifolds. Our analysis leads to results that are of relevance to all orders in the alpha' expansion.
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| 10. |
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