Lectures on Gauged Supergravity and Flux Compactifications

Abstract

The low-energy effective theories describing string compactifications in the presence of fluxes are so-called gauged supergravities: deformations of the standard abelian supergravity theories. The deformation parameters can be identified with the various possible (geometric and non-geometric) flux components. In these lecture notes we review the construction of gauged supergravities in a manifestly duality covariant way and illustrate the construction in several examples.

48 pages, lectures given at the RTN Winter School on Strings, Supergravity and Gauge Theories, CERN, January 2008

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• Axionic symmetry gaugings in N=4 supergravities and their higher-dimensional origin
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• Gauged Double Field Theory
• Duality orbits of non-geometric fluxes
• Duality Invariant M-theory: Gauged supergravities and Scherk-Schwarz reductions
• Double Field Theory Formulation of Heterotic Strings
• Non-geometric backgrounds, doubled geometry and generalised T-duality
• Lectures on Generalized Complex Geometry for Physicists
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Gauged Supergravities
• Universal Kaluza-Klein reductions of type IIB to N=4 supergravity in five dimensions
• Non-Geometric Fluxes in Supergravity and Double Field Theory
• Flux moduli stabilisation, Supergravity algebras and no-go theorems
• Type IIB supergravity on squashed Sasaki-Einstein manifolds
• Wrapped M5-branes, consistent truncations and AdS/CMT
• Generalised geometry for string corrections
• A supersymmetric consistent truncation for conifold solutions
• Exceptional field theory: $SO(5,5)$
• Geometry and fluxes of SL(5) exceptional field theory
• Critical behavior of charged black holes in Gauss-Bonnet gravity`s rainbow
• Non-geometric backgrounds in string theory
• Holographic microstate counting for AdS${}_4$ black holes in massive IIA supergravity
• Dyonic ISO(7) supergravity and the duality hierarchy
• The Odd story of ${\alpha }^{\prime }$-corrections
• Gauge theory of Kaluza-Klein and winding modes
• The exceptional story of massive IIA supergravity
• Gauged supergravities in 5 and 6 dimensions from generalised Scherk-Schwarz reductions
• Double Field Theory on Group Manifolds
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• Type II origin of dyonic gaugings
• Type-IIA flux compactifications and N=4 gauged supergravities
• U-dual fluxes and Generalized Geometry
• Systematics of consistent truncations from generalised geometry
• E7(7) formulation of N=2 backgrounds
• Supersymmetric Consistent Truncations of IIB on T(1,1)
• Tri-Sasakian consistent reduction
• Gauged supergravities and spontaneous SUSY breaking from the double copy
• On Type IIB moduli stabilization and N = 4, 8 supergravities
• Flux Compactifications, Gauge Algebras and De Sitter
• Janus solutions in six-dimensional gauged supergravity
• Generalised Scherk-Schwarz reductions from gauged supergravity
• Spontaneous N=2 to N=1 Supersymmetry Breaking in Supergravity and Type II String Theory
• 3D Supergravity from wrapped D3-branes
• Consistent Compactification of Double Field Theory on Non-geometric Flux Backgrounds
• A Chern-Simons Pandemic
• The Embedding Tensor, Leibniz-Loday Algebras, and Their Higher Gauge Theories
• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Non-geometric flux vacua, S-duality and algebraic geometry
• On new maximal supergravity and its BPS domain-walls
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• Exceptional Flux Compactifications
• Tensor hierarchies and Leibniz algebras
• The Boundaries of KKLT
• Vaidya Spacetime in Massive Gravity's Rainbow
• BPS objects in D=7 supergravity and their M-theory origin
• On the Hidden Maxwell Superalgebra underlying D=4 Supergravity
• A special road to AdS vacua
• Mass deformations of 5d SCFTs via holography
• $\mathcal{N}=2$ supersymmetric S-folds
• Holographic glueballs from the circle reduction of Romans supergravity
• Flux compactifications, twisted tori and doubled geometry
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• Heterotic compactifications on SU(2)-structure backgrounds
• Laplacian spectrum on a nilmanifold, truncations and effective theories
• N=2 Einstein-Yang-Mills' static two-center solutions
• The supersymmetric tensor hierarchy of N=1,d=4 supergravity
• Flux Formulation of DFT on Group Manifolds and Generalized Scherk-Schwarz Compactifications
• $\mathcal{N}=2$ consistent truncations from wrapped M5-branes
• The embedding tensor of Scherk-Schwarz flux compactifications from eleven dimensions
• Exceptional N=6 and N=2 AdS_4 Supergravity, and Zero-Center Modules
• The Euler characteristic correction to the Kaehler potential - revisited
• Abelian Hypermultiplet Gaugings and BPS Vacua in N = 2 Supergravity
• Tensor Hierarchies of 5- and 6-Dimensional Field Theories
• Introductory Lectures on Extended Supergravities and Gaugings
• SL(2,Z) symmetries, Supermembranes and Symplectic Torus Bundles
• The controlling $L_{\infty }$-algebra, cohomology and homotopy of embedding tensors and Lie-Leibniz triples
• Type II compactifications on manifolds with SU(2) x SU(2) structure
• Implementing odd-axions in dimensional oxidation of non-geometric type IIB action
• Generalized Parallelizable Spaces from Exceptional Field Theory
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• BPS domain walls in N=4 supergravity and dual flows
• Towards top-down holographic composite Higgs: minimal coset from maximal supergravity
• Non-Abelian discrete gauge symmetries in F-theory
• Locally non-geometric fluxes and missing momenta in M-theory
• Maximally Supersymmetric AdS Solutions and their Moduli Spaces
• 6D (1,1) Gauged Supergravities from Orientifold Compactifications
• Deformations of vector-scalar models
• Heterotic Supergravity with Internal Almost-Kähler Spaces, Instantons for $SO(32)$, or $E_8\times E_8$, Gauge Groups, and Deformed Black Holes with Soliton, Quasiperiodic and/or Pattern-forming Structures
• Dilatonic states near holographic phase transitions
• The N=4 effective action of type IIA supergravity compactified on SU(2)-structure manifolds
• Supermembrane origin of type II gauged supergravities in 9D
• Consistent Truncations and Dualities
• Critical points of maximal D=8 gauged supergravities
• Off-Diagonal Deformations of Kerr Metrics and Black Ellipsoids in Heterotic Supergravity
• Consistent Kaluza-Klein truncations and two-dimensional gauged supergravity
• Order ${\alpha }^{\prime }$ heterotic domain walls with warped nearly Kähler geometry
• Type IIA orientifold compactification on SU(2)-structure manifolds
• Exceptional algebroids and type IIB superstrings
• All maximal gauged supergravities with uplift
• The higher-dimensional origin of five-dimensional $\mathcal{N}=2$ gauged supergravities
• Gauged supergravities and their symmetry-breaking vacua in F-theory
• On the off-shell formulation of N=2 supergravity with tensor multiplets
• Symplectically invariant flow equations for N=2, D=4 gauged supergravity with hypermultiplets
• Exact holographic RG flows in extended SUGRA
• Gauge symmetry enhancing-breaking from a Double Field Theory perspective
• Classification of M2-brane 2-torus bundles, U-duality invariance and type II gauged supergravities
• Heating up branes in gauged supergravity
• Vacua of $\omega$-deformed SO(8) supergravity
• Higher Gauge Theory
• Non-supersymmetric Extremal RN-AdS Black Holes in N=2 Gauged Supergravity
• Interpolation of partial and full supersymmetry breakings in $\mathcal{N}=2$ supergravity
• Left-invariant Einstein metrics on $S^3\times S^3$
• Double Field Theory description of Heterotic gauge symmetry enhancing-breaking
• Vacua of N=10 three dimensional gauged supergravity
• Uplifts of maximal supergravities and transitions to non-geometric vacua
• Maximal Nine Dimensional Supergravity, General gaugings and the Embedding Tensor
• T-duality Invariance of the Supermembrane
• A note on "gaugings" in four spacetime dimensions and electric-magnetic duality
• Integrability structures in string theory
• 3D N=6 Gauged Supergravity: Admissible Gauge Groups, Vacua and RG Flows
• Classification of maximally supersymmetric backgrounds in supergravity theories
• Geometry of ${\mathbb{R}}^{+}\times E_{3(3)}$ Exceptional Field Theory and F-theory
• Exotic potentials and Bianchi identities in SL(5) exceptional field theory
• Smarr's Formula in Eleven-Dimensional Supergravity
• Self-Dual Tensors and Partial Supersymmetry Breaking in Five Dimensions
• Gauged $\mathcal{N}=3,D=4$ Supergravity: a new web of marginally connected vacua
• Extended Doubled Structures of Algebroids for Gauged Double Field Theory
• On the role of torsion and higher forms in off-shell supergravity
• On gauged maximal d=8 supergravities
• Partial Breaking in Rigid Limit of $\mathcal{N}=2$ Gauged Supergravity
• Spherically symmetric solution in a space-time with torsion
• Behaviors of two supersymmetry breaking scales in $\mathcal{N}=2$ supergravity
• New N=5,6, 3D gauged supergravities and holography
• Generalized Geometry and Partial Supersymmetry Breaking
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• Adjusting Higher Chern-Simons Theory
• The canonical formulation of E${}_{6(6)}$ exceptional field theory
• Consistent truncations with massive modes and holography
• ALP Constraints in Gauged $\mathcal{N}=2$ Supergravity
• On global aspects of duality invariant theories: M2-brane vs DFT
• A Massive S-duality in 4 dimensions