U-manifolds

Kumar, Alok; Vafa, Cumrun

doi:10.1016/s0370-2693(97)00108-1

Cited by 86 publications

(148 citation statements)

References 14 publications

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“…In this section, we present the details of this split and give the precise relationships between the fields of the exceptional field theory and those of supergravity. 6 …”

Section: Relationship To Supergravitymentioning

confidence: 99%

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An action for F-theory: $\mathrm{SL}(2){{\mathbb{R}}}^{+}$ exceptional field theory

Berman¹,

Blair²,

Malek³

et al. 2016

Class. Quantum Grav.

112

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We construct the 12-dimensional exceptional field theory associated to the group SL(2)× R + . Demanding the closure of the algebra of local symmetries leads to a constraint, known as the section condition, that must be imposed on all fields. This constraint has two inequivalent solutions, one giving rise to 11-dimensional supergravity and the other leading to F-theory. Thus SL(2) × R + exceptional field theory contains both F-theory and M-theory in a single 12-dimensional formalism.

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“…In this section, we present the details of this split and give the precise relationships between the fields of the exceptional field theory and those of supergravity. 6 …”

Section: Relationship To Supergravitymentioning

confidence: 99%

“…F-theory provides a geometric interpretation of this duality. An idea which was raised swiftly after the introduction of F-theory was whether there exist similar geometrisations of the U-duality symmetries which one finds after descending in dimension [6].…”

Section: Introductionmentioning

confidence: 99%

An action for F-theory: $\mathrm{SL}(2){{\mathbb{R}}}^{+}$ exceptional field theory

Berman¹,

Blair²,

Malek³

et al. 2016

Class. Quantum Grav.

112

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“…The K3 fibered case in particular could be very interesting, and could be compared to the work of [4]. Finally, one can expand the analysis to include U-duality groups, such as that of M-theory on a torus (see [54,5,55,39,40,56,57,2]). It would be very interesting to understand how far one could push such a program, and whether one could find interesting solutions with a controlled low energy theory.…”

Section: Advantages and Puzzlesmentioning

confidence: 99%

Toroidal orientifolds in IIA with general NS-NS fluxes

Ihl

Robbins

Wrase

2007

J. High Energy Phys.

184

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Type IIA toroidal orientifolds offer a promising toolkit for model builders, especially when one includes not only the usual fluxes from NS-NS and R-R field strengths, but also fluxes that are T-dual to the NS-NS three-form flux. These new ingredients are known as metric fluxes and non-geometric fluxes, and can help stabilize moduli or can lead to other new features. In this paper we study two approaches to these constructions, by effective field theory or by toroidal fibers twisted over a toroidal base. Each approach leads us to important observations, in particular the presence of D-terms in the four-dimensional effective potential in some cases, and a more subtle treatment of the quantization of the general NS-NS fluxes. Though our methods are general, we illustrate each approach on the example of an orientifold of T 6 /Z 4 .

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“…[7], [8]. The emphasis in that work was on finding a higher-dimensional geometric description of the construction which we do not require.…”

Section: Stringy Cosmic Fivebranesmentioning

confidence: 99%

“…Table 4: Massless bosonic spectrum in the asymmetric orbifold limit 8 To fix the normalization C, consider the example dual to K3 × K3, where the map (6.5)…”

Section: )mentioning

confidence: 99%

Geometric Constructions of Nongeometric String Theories

Hellerman¹

2002

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We advocate a framework for constructing perturbative closed string compactifications which do not have large-radius limits. The idea is to augment the class of vacua which can be described as fibrations by enlarging the monodromy group around the singular fibers to include perturbative stringy duality symmetries. As a controlled laboratory for testing this program, we study in detail six-dimensional (1,0) supersymmetric vacua arising from two-torus fibrations over a two-dimensional base. We also construct some examples of two-torus fibrations over four-dimensional bases, and comment on the extension to other fibrations.August, 2002 Weakly coupled supersymmetric string vacua without geometryIn this paper we will examine a new method for constructing supersymmetric, nongeometric string theories. The examples on which we focus most closely make up a class of solutions to supergravity in 7 + 1 dimensions with 32 supercharges. These solutions will involve nontrivial behavior of the metric and Neveu-Schwarz (NS) B-field, but not of any of the Ramond-Ramond fields, nor of the eight dimensional dilaton. (The ten-dimensional dilaton will vary, but only in such a way that the eight dimensional effective coupling is held fixed.) We will argue that these backgrounds are likely to represent sensible backgrounds for string propagation on which the dynamics of string worldsheets are determined by a two-dimensional conformal field theory of critical central charge, with a controlled genus expansion whose expansion parameter can be made arbitrarily small.Almost all known examples of perturbative string backgrounds are descibed by nonlinear sigma models, that is, by field theories containing scalar fields X µ parametrizing a topologically and geometrically nontrivial target space. The lagrangian for these theories, for weak curvatures R αβγδ R αβγδ << 1 in string units. Therefore the condition for conformal invariance is approximately the same as the Einstein equation for the target space metric. So a nonlinear sigma model whose target space is a smooth Ricci-flat manifold at large volume will always be approximately conformal, an approximation which improves if one scales up the manifold G µν → ΛG µν .The existence of a large-volume limit of a family of solutions or approximate solutions gives rise to the moduli problem: there are usually several massless scalars in the lowerdimensional effective field theory corresponding to Ricci-flat deformations of the target space. There is always at least one light scalar, or approximate modulus -namely, the overall size of the compact space -if flat ten-dimensional space is an exact solution to the string equations of motion at the quantum level. In critical superstring theory, to which we will restrict our attention exclusively in this paper, flat ten dimensional space is a solution to the equations of motion at the quantum level.1 So the overall volume modulus is an intrinsic difficulty for geometric compactifications of superstring theory. Even if potentials are generated for the volu...

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U-manifolds

Cited by 86 publications

References 14 publications

An action for F-theory: $\mathrm{SL}(2){{\mathbb{R}}}^{+}$ exceptional field theory

An action for F-theory: $\mathrm{SL}(2){{\mathbb{R}}}^{+}$ exceptional field theory

Toroidal orientifolds in IIA with general NS-NS fluxes

Geometric Constructions of Nongeometric String Theories

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