Gauge theory for string algebroids

Garcia-Fernandez, Mario; Rubio, Roberto Rodriguez; Tipler, Carl

doi:10.48550/arxiv.2004.11399

Cited by 12 publications

(32 citation statements)

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“…It would be interesting to reconcile these results with the complexified gauge transformations and moment maps in a GIT-type analysis of these solutions studied in [20,21]. There are also examples of mathematical interest, such as that related to the Hopf surface which do not have an obvious valid α -expansion, yet appear to be governed by a (0, 2) superconformal algebra [22].…”

Section: Discussionmentioning

confidence: 94%

“…It would also be interesting to see to what extent the structure discovered in this paper extends to next order in α . We expect the generalised geometry approach of [9,20,21,23,25] to be relevant for these scenarios.…”

Section: Discussionmentioning

confidence: 99%

“…Recently, [21] took (B.7) as the Kähler potential for the moduli space metric to deformations of the first order α Hull-Strominger system assuming the complex structure is fixed. They then related this to the Aeppli and Bott-Chern cohomology.…”

Section: B a Supergravity No-go Theoremmentioning

confidence: 99%

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Heterotic Quantum Cohomology

McOrist¹,

Svanes²

2021

Preprint

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We reexamine the massless spectrum of a heterotic string vacuum at large radius and present two results. The first result is to construct a vector bundle Q and operator D whose kernel amounts to deformations solving 'F-term' type equations. This resolves a dilemma in previous works in which the spin connection is treated as an independent degree of freedom, something that is not the case in string theory. The second result is to utilise the moduli space metric, constructed in previous work, to define an adjoint operator D † . The kernel of D † amounts to deformations solving 'D-term' type equations. Put together, we show there is a vector bundle Q with a metric, a D operator and a gauge fixing (holomorphic gauge) in which the massless spectrum are harmonic representatives of D. This is remarkable as previous work indicated the Hodge decomposition of massless deformations were complicated and in particular not harmonic except at the standard embedding.

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Section: Discussionmentioning

confidence: 94%

Section: Discussionmentioning

confidence: 99%

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Heterotic Quantum Cohomology

McOrist¹,

Svanes²

2021

Preprint

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“…where E fits into the exact sequence 0 → End(T X t )⊕End(E) → E → T X t → 0. In the mathematics literature, there is another approach to the moduli problem via the notion of a string algebroid and symmetries in generalized geometry; see [37,38,39]. Now, using these tools, we are ready to describe the physical interpretation of the special Lagrangians in a topology changing transition to the conformally balanced non-Kahler metric on X t .…”

Section: Relation To Su (3) Structures and Flux Compactificationsmentioning

confidence: 99%

“…The study of non-Kähler Calabi-Yau geometry in theoretical physics was initiated by Strominger [85], and has since grown into an active area of research; see e.g. [3,25,26,29,30,31,34,35,48,71] for examples, see [2,6,5,13,22,40,41,52] for developments in string theory, and see [27,28,36,38,39,58,65,72,73,74,75,84,88,90,91] for research programs in this area.…”

Section: Introductionmentioning

confidence: 99%

Special Lagrangian cycles and Calabi-Yau transitions

Collins¹,

Gukov²,

Picard³

et al. 2021

Preprint

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Heterotic quantum cohomology

McOrist

Svanes

2022

J. High Energ. Phys.

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It is believed, but not demonstrated, that the large radius massless spectrum of a heterotic string theory compactified to four-dimensional Minkowski space should obey equations that split into ‘F-terms’ and ‘D-terms’ in ways analogous to that of four-dimensional supersymmetric field theories. This is not easy to do directly as string theory is first quantised. Nonetheless, in this paper we demonstrate this splitting. We construct an operator $$ \overline{\mathcal{D}} $$ D ¯ whose kernel amounts to deformations solving ‘F-term’ type equations. In many previous works in this field, the spin connection is treated as an independent degree of freedom (and so is spurious or fake); here our results apply on the physical moduli space in which these fake degrees of freedom are eliminated. We utilise the moduli space metric, constructed in previous work, to define an adjoint operator $$ \overline{\mathcal{D}} $$ D ¯ †. The kernel of $$ \overline{\mathcal{D}} $$ D ¯ † amounts to ‘D-term’ type equations. Put together, we show there is a $$ \overline{\mathcal{D}} $$ D ¯ -operator in which the massless spectrum are harmonic representatives of $$ \overline{\mathcal{D}} $$ D ¯ . We conjecture that one could better study the moduli space of heterotic theories by studying the corresponding cohomology, a natural counterpart to studying the $$ \overline{\partial} $$ ∂ ¯ -cohomology groups relevant to moduli of Calabi-Yau manifolds.

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Gauge theory for string algebroids

Cited by 12 publications

References 0 publications

Heterotic Quantum Cohomology

Heterotic Quantum Cohomology

Special Lagrangian cycles and Calabi-Yau transitions

Heterotic quantum cohomology

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