Calabi-Yau Fourfold Compactifications in String Theory

Haack, Michael

doi:10.1002/1521-3978(200201)50:1<3::aid-prop3>3.0.co;2-5

Cited by 7 publications

(8 citation statements)

References 152 publications

(452 reference statements)

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“…While most of this work has concentrated on Calabi-Yau three-folds, primarily in order to connect string theory to four-dimensional physics, Calabi-Yau four-folds have been used, for example in F-theory compactifications [2], and compactification on K3 has played an important rôle in uncovering elementary duality relations [3,4]. Calabi-Yau four-folds have also appeared in string-/M-theory compactifications to two and three dimensions [5,6]. To the best of our knowledge, the first time Calabi-Yau five-folds have appeared in the physics literature was in Ref.…”

Section: Introductionmentioning

confidence: 99%

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M-theory on Calabi-Yau Five-Folds

Haupt

Lukas

Stelle

2009

J. High Energy Phys.

131

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We study the compactification of M-theory on Calabi-Yau five-folds and the resulting N = 2 super-mechanics theories. By explicit reduction from 11 dimensions, including both bosonic and fermionic terms, we calculate the one-dimensional effective action and show that it can be derived from an N = 2 super-space action. We find that the Kähler and complex structure moduli of the five-fold reside in 2a and 2b supermultiplets, respectively. Constrained 2a super-multiplets arise from zero-modes of the M-theory three-form and lead to cross-couplings between 2a and 2b multiplets. Fermionic zero modes which arise from the (1, 3) sector of the 11-dimensional gravitino do not have bosonic super-partners and have to be described by purely fermionic super-multiplets in one dimension. We also study the inclusion of flux and discuss the consistency of the scalar potential with one-dimensional N = 2 supersymmetry and how it can be described in terms of a superpotential. This superpotential can also be obtained from a Gukovtype formula which we present. Supersymmetric vacua, obtained by solving the F-term equations, always have vanishing vacuum energy due to the form of this scalar potential. We show that such supersymmetric solutions exist for particular examples. Two substantial appendices develop the topology and geometry of Calabi-Yau five-folds and the structure of one-dimensional N = 2 supersymmetry and supergravity to the level of generality required for our purposes.Keywords: M-Theory, Flux compactifications, Field Theories in Lower Dimensions, Superspaces. 65 C.2 Local N = 2 supersymmetry 69 -1 -will demonstrate that this can indeed frequently be achieved. In particular, we show that the consistency condition can be satisfied for the Calabi-Yau five-fold defined by the zero locus of a septic polynomial in P 6 . The "septic" is arguably the simplest five-fold and the analogue of the quintic three-fold in P 4 . The one-dimensional effective action will be calculated as an expansion in powers of β. As a first step we consider the situation at zeroth order in β. Effects from flux or membranes only come in at order β and are, therefore, not relevant at this stage. In particular, we clarify the relation between Calabi-Yau topology/geometry and the structure of the onedimensional supermechanics induced by M-theory at this lowest order in β. Many aspects of this relation are analogous to what happens for compactifications on lower-dimensional Calabi-Yau manifolds, others, as we will see, are perhaps less expected. The topology of a Calabi-Yau five-fold X is characterised by six a priori independent Hodge numbers, namely h 1,1 (X), h 1,2 (X), h 1,3 (X), h 2,2 (X), h 1,4 (X) and h 2,3 (X). In analogy with the four-fold case [15], an index theorem calculation together with the Calabi-Yau condition c 1 (X) = 0, leads to one relation between those six numbers. The moduli space of a Calabi-Yau manifold consists (locally) of a direct product of a Kähler and a complex structure moduli space [16]. For Calabi-Yau five-folds, these two par...

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Section: Introductionmentioning

confidence: 99%

“…vertical part, denoted H (2,2) V , of H (2,2) (see, for example, Ref. [6]). The total space H (2,2) is given by…”

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confidence: 99%

M-theory on Calabi-Yau Five-Folds

Haupt

Lukas

Stelle

2009

J. High Energy Phys.

131

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“…Moreover complex structure and Kähler deformations are independent of each other, which implies that at least locally the moduli space M of Ricci flat metrics has a direct-product structure, M = M c × M k , where M c and M k are the complex structure and Kähler moduli spaces repsectively, see e.g. [33] and references therein. A choice of Ω, J thus specifies a point in M c , M k respectively, and hence a point M. As we move in M c the holomorphic top form Ω varies holomorphically with Z α .…”

Section: Jhep09(2015)107mentioning

confidence: 99%

3d N = 1 $$ \mathcal{N}=1 $$ effective supergravity and F-theory from M-theory on fourfolds

Prins

Tsimpis

2015

J. High Energ. Phys.

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Abstract:We consider 3d N = 1 M-theory compactifications on Calabi-Yau fourfolds, and the effective 3d theory of light modes obtained by reduction from eleven dimensions. We study in detail the mass spectrum at the vacuum and, by decoupling the massive multiplets, we derive the effective 3d N = 1 theory in the large-volume limit up to quartic fermion terms. We show that in general it is an ungauged N = 1 supergravity of the form expected from 3d supersymmetry. In particular the massless bosonic fields consist of the volume modulus and the axions originating from the eleven-dimensional three-form, while the moduli-space metric is locally isometric to hyperbolic space. We consider the F-theory interpretation of the 3d N = 1 M-theory vacua in the light of the F-theory effective action approach. We show that these vacua generally have F-theory duals with circle fluxes, thus breaking 4d Poincaré invariance.

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“…The independence of right and left moving sector is valid also for the choice of boundary conditions. Therefore, we have four possibilities for {ψ μ + , ψ μ − } that we will denote with NS-NS, R-R, NS-R and R-NS sectors 7 . Remember that in the R sector there are fermionic states while in the NS sector there are bosonic states.…”

Section: Superstring Theory In a Nutshellmentioning

confidence: 99%

“…The M-theory cartoon: the 5 known superstring theories and d = 11, N = 1 sugra are conjectured to be different limits of the same unique theory. Figure taken from[7].…”

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confidence: 99%

Phenomenological aspects of type IIB flux compactifications

Pajer

2009

Fortschritte der Physik

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The purpose of this work is to investigate how phenomenologically successful constructions in the field of high energy physics can be embedded into a fundamental theory, and what we can learn from this procedure. In fact, the synergy of an effective and a fundamental approach might be very fruitful. On the one hand, it poses several theoretical challenges to potential candidates for a fundamental theory, which might be ruled out or restricted in their generality. On the other hand, this mutual interplay can inspire new experiments and observations or suggest correlations which are invisible from an effective point of view. Our starting point is that string theory is entitled to be a valid candidate for a fundamental theory by a series of properties such as the fact that it is a consistent, UV‐finite, anomaly‐free quantum theory and it describes, in appropriate limits, quantum field theory and general relativity, hence providing a unified description of the four known forces. Within string theory, we choose to work in the framework of type IIB flux compactifications where the issue of moduli stabilization can be successfully addressed. On the phenomenological side, we focus on particle physics and cosmology, and in particular on the MSSM and the mechanism of inflation, respectively. We construct and study two different models of inflation in string theory. These are models of brane inflation, i.e. models where the primordial exponential expansion of the universe is driven by a scalar field representing the position of a D3‐brane (a 3+1‐dimensional dynamical object) in a compact space. We show explicitly that, allowing for fine tuning, a prolonged stage of slow‐roll inflation can be achieved during which perturbations are generated in good agreement with the CMB data. In addition, we give an example of the fruitful synergy we mentioned above. One of our two models, namely inflation at the tip, might induce also DBI inflation which produces peculiar features in the spectrum of density perturbations that might be looked for using CMB data. On the particle physics side, we consider a model, the large volume scenario (LVS), which, among other things, provides a rationale for a low scale susy‐breaking. We perform some checks on the consistency of LVS as a string theory model. To this end, we formulate an educated guess for the form of string loop corrections. We then show that physical predictions such as the soft susy‐breaking terms are actually surprisingly robust against the inclusion of these corrections.

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Calabi-Yau Fourfold Compactifications in String Theory

Cited by 7 publications

References 152 publications

M-theory on Calabi-Yau Five-Folds

M-theory on Calabi-Yau Five-Folds

3d N = 1 $$ \mathcal{N}=1 $$ effective supergravity and F-theory from M-theory on fourfolds

Phenomenological aspects of type IIB flux compactifications

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