Kähler cone substructure

Sharpe, Eric

doi:10.4310/atmp.1998.v2.n6.a7

Cited by 46 publications

(90 citation statements)

References 36 publications

(82 reference statements)

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“…For example, it would be interesting to understand how these correlation functions change when the Kähler class passes through a stability subcone wall [25], which would be the heterotic analogue of a flop.…”

Section: Discussionmentioning

confidence: 99%

“…Let us now explicitly compute the classical correlation functions listed in equation (20) and the four-point functions listed in equations (30), (28), (26), (22), and (25). The classical contributions to these four-point functions all vanish, and the only worldsheet instanton contributions can come from the (1, 0) and (0, 1) sectors.…”

Section: Computation Of the Correlation Functionsmentioning

confidence: 99%

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Notes on Certain (0,2) Correlation Functions

Katz

Sharpe

2005

Commun. Math. Phys.

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249

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In this paper we shall describe some correlation function computations in perturbative heterotic strings that, for example, in certain circumstances can lend themselves to a heterotic generalization of quantum cohomology calculations. Ordinary quantum chiral rings reflect worldsheet instanton corrections to correlation functions involving products of elements of Dolbeault cohomology groups on the target space. The heterotic generalization described here involves computing worldsheet instanton corrections to correlation functions defined by products of elements of sheaf cohomology groups. One must not only compactify moduli spaces of rational curves, but also extend a sheaf (determined by the gauge bundle) over the compactification, and linear sigma models provide natural mechanisms for doing both. Euler classes of obstruction bundles generalize to this language in an interesting way.

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Section: Discussionmentioning

confidence: 99%

Section: Computation Of the Correlation Functionsmentioning

confidence: 99%

Notes on Certain (0,2) Correlation Functions

Katz

Sharpe

2005

Commun. Math. Phys.

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249

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“…Naively, therefore, one might expect this Abelian group to be unbroken. However, as is well documented in this context [47][48][49][50][51][52], this U(1) gains a mass through the Green-Schwarz mechanism. In this process the U(1) gauge boson is made massive and one entire hypermultiplet from the K3 metric moduli is removed from the low energy spectrum.…”

Section: Su(7)mentioning

confidence: 99%

“…Splitting one of these two bundles in this fashion would induce an extra U(1) factor in the commutant of the bundle structure group inside E 8 . This additional abelian factor will be Green-Schwarz anomalous however [47][48][49][50][51][52].…”

Section: Jhep04(2016)080mentioning

confidence: 99%

“…That is, at the level of group theory, any SU(7) symmetry arising in a heterotic theory must be accompanied by an additional abelian gauge symmetry. Generically, by the Green-Schwarz mechanism, this enhanced U(1) couples to the Kähler axions of the base CY geometry (which transforms via shift symmetries) and becomes massive (see [47][48][49][50]52]). Since the presence of Green-Schwarz massive U(1)s in F-theory has been the topic of much recent interest (see for example [71][72][73][74][75][76][77][78]), we turn now to the appearance of this enhanced U(1) in heterotic/F-theory pair described above.…”

Section: Jhep04(2016)080mentioning

confidence: 99%

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Matter in transition

Anderson

Gray

Raghuram

et al. 2016

J. High Energ. Phys.

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We explore a novel type of transition in certain 6D and 4D quantum field theories, in which the matter content of the theory changes while the gauge group and other parts of the spectrum remain invariant. Such transitions can occur, for example, for SU(6) and SU(7) gauge groups, where matter fields in a three-index antisymmetric representation and the fundamental representation are exchanged in the transition for matter in the two-index antisymmetric representation. These matter transitions are realized by passing through superconformal theories at the transition point. We explore these transitions in dual F-theory and heterotic descriptions, where a number of novel features arise. For example, in the heterotic description the relevant 6D SU(7) theories are described by bundles on K3 surfaces where the geometry of the K3 is constrained in addition to the bundle structure. On the F-theory side, non-standard representations such as the threeindex antisymmetric representation of SU(N ) require Weierstrass models that cannot be realized from the standard SU(N ) Tate form. We also briefly describe some other situations, with groups such as Sp (3), SO(12), and SU(3), where analogous matter transitions can occur between different representations. For SU(3), in particular, we find a matter transition between adjoint matter and matter in the symmetric representation, giving an explicit Weierstrass model for the F-theory description of the symmetric representation that complements another recent analogous construction.

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Transitions in the web of heterotic vacua

Anderson

Gray

Ovrut

2011

Fortschritte der Physik

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We analyze transitions between heterotic vacua with distinct gauge bundles using two complementary methods -the effective four-dimensional field theory and the corresponding geometry. From the viewpoint of effective field theory, such transitions occur between flat directions of the potential energy associated with heterotic stability walls. Geometrically, this branch structure corresponds to smooth deformations of the gauge bundle coupled to the chamber structure of Kähler moduli space. We demonstrate how such transitions can change important properties of the effective theory, including the gauge symmetry and the massless spectrum. Geometrically, this study is divided into deformations of the vector bundle which preserve the rank of the gauge bundle and those which change the rank. In the latter case, our results provide explicit solutions to a class of Li-Yau type deformation problems. Finally, we use the framework of stability walls and their effective theory to study Donaldson-Thomas invariants on Calabi-Yau threefolds.

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Kähler cone substructure

Cited by 46 publications

References 36 publications

Notes on Certain (0,2) Correlation Functions

Notes on Certain (0,2) Correlation Functions

Matter in transition

Transitions in the web of heterotic vacua

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