Conformal invariance of (0, 2) sigma models on Calabi-Yau manifolds

Jardine, Ian T.; Quigley, Callum

doi:10.1007/jhep03(2018)090

Cited by 5 publications

(5 citation statements)

References 35 publications

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“…As a guide, one might start by comparing the heterotic moduli space with the spectrum of holomorphic βγ systems and the chiral de Rham complex [65][66][67][68][69][70]. Several other approaches to the (0, 2) world-sheet have appeared over the years (see [47,[70][71][72][73][74][75][76][77] and references therein). It would be interesting to investigate how these methods connect with the approach outlined in the present paper.…”

Section: Discussionmentioning

confidence: 99%

“…If the solution to the Hull-Strominger system admits an α ′ → 0 limit, the α ′ = 0 solution is simply Calabi-Yau. In this case it is known that the superpotential receives no α ′ corrections (to finite order) and so, although the α ′ -corrected geometry is not longer Calabi-Yau, the tree-level superpotential is exact [22,47]. This means equations (4.31)-(4.33) will be correct even after α ′ corrections.…”

Section: Vanishing Of the Superpotentialmentioning

confidence: 98%

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Finite deformations from a heterotic superpotential: holomorphic Chern-Simons and an L∞ algebra

Ashmore

Ossa

Minasian

et al. 2018

J. High Energ. Phys.

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We consider finite deformations of the Hull-Strominger system. Starting from the heterotic superpotential, we identify complex coordinates on the off-shell parameter space. Expanding the superpotential around a supersymmetric vacuum leads to a third-order Maurer-Cartan equation that controls the moduli. The resulting complex effective action generalises that of both Kodaira-Spencer and holomorphic Chern-Simons theory. The supersymmetric locus of this action is described by an L 3 algebra. C The off-shell N = 1 parameter space and holomorphicity of Ω 41 C.1 SU(3) × SO(6) structures in the NS-NS sector 41 C.2 SU(3) × SO(6 + n) structures in heterotic supergravity 44 C.3 The off-shell hermitian structure on V 45 D Comments on D-terms 48 D.1 Massless deformations 48 D.2 Including bundle moduli 52 D.3 Polystable bundles 54 D.4 Full Maurer-Cartan equations 56 E Massless moduli 571 More precisely, it is the complex vector bundle V C (defined in appendix C.3) that is a holomorphic bundle. 2 The curvature R in the Bianchi identity is the curvature of a connection on T X, satisfying its own hermitian Yang-Mills conditions in order for the equations of motion to be fulfilled [33]. To O(α ′ ), this connection is ∇ − , given by taking the connection in (A.7) with the opposite sign for H.

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Section: Discussionmentioning

confidence: 99%

Section: Vanishing Of the Superpotentialmentioning

confidence: 98%

Finite deformations from a heterotic superpotential: holomorphic Chern-Simons and an L∞ algebra

Ashmore

Ossa

Minasian

et al. 2018

J. High Energ. Phys.

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“…In any case, whenever they are preserved, these symmetries put strong constraints on the dynamics of the σ-model and should guide the study of string vacua in the α ′ expansion from a world-sheet point of view [88][89][90]. They might find applications for instance to generalise the results of [91] to target spaces other than Calabi-Yau manifolds [92,93].…”

Section: Resultsmentioning

confidence: 99%

$$ \mathcal{G} $$-structure symmetries and anomalies in (1, 0) non-linear σ-models

Ossa

Fiset

2019

J. High Energ. Phys.

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A new symmetry of (1, 0) supersymmetric non-linear σ-models in two dimensions with Fermi and mass sectors is introduced. It is a generalisation of the so-called special holonomy W-symmetry of Howe and Papadopoulos associated with structure group reductions of the target space M. Our symmetry allows in particular non-trivial flux and instanton-like connections on vector bundles over M. We also investigate potential anomalies and show that cohomologically non-trivial terms in the quantum effective action are invariant under a corrected version of our symmetry. Consistency with heterotic supergravity at first order in α ′ is manifest and discussed.

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“…In any case, whenever they are preserved, these symmetries put strong constraints on the dynamics of the σ-model and should guide the study of string vacua in the α ′ expansion from a world-sheet point of view [GW86, GvdVZ86, CFP + 86]. They might find applications for instance to generalise the results of [NS86] to target spaces other than Calabi-Yau manifolds [JQ18,BRW14].…”

Section: Discussionmentioning

confidence: 99%

$\mathcal{G}$-structure symmetries and anomalies in $(1,0)$ non-linear $σ$-models

de la Ossa,

Fiset

2018

Preprint

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A new symmetry of (1, 0) supersymmetric non-linear σ-models in two dimensions with Fermi and mass sectors is introduced. It is a generalisation of the so-called special holonomy W -symmetry of Howe and Papadopoulos associated with structure group reductions of the target space M. Our symmetry allows in particular non-trivial flux and instanton-like connections on vector bundles over M. We also investigate potential anomalies and show that cohomologically non-trivial terms in the quantum effective action are invariant under a corrected version of our symmetry. Consistency with heterotic supergravity at first order in α ′ is manifest and discussed.

show abstract

Conformal invariance of (0, 2) sigma models on Calabi-Yau manifolds

Cited by 5 publications

References 35 publications

Finite deformations from a heterotic superpotential: holomorphic Chern-Simons and an L∞ algebra

Finite deformations from a heterotic superpotential: holomorphic Chern-Simons and an L∞ algebra

$$ \mathcal{G} $$-structure symmetries and anomalies in (1, 0) non-linear σ-models

$\mathcal{G}$-structure symmetries and anomalies in $(1,0)$ non-linear $σ$-models

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