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U-duality and M-Theory
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This work is intended as a pedagogical introduction to M-theory and to its maximally supersymmetric toroidal compactifications, in the frameworks of 11D supergravity, type II string theory and M(atrix) theory. U-duality is used as the main tool and guideline in uncovering the spectrum of BPS states. We review the 11D supergravity algebra and elementary 1/2-BPS solutions, discuss T-duality in the perturbative and non-perturbative sectors from an algebraic point of view, and apply the same tools to the analysis of U-duality at the level of the effective action and the BPS spectrum, with a particular emphasis on Weyl and Borel generators. We derive the U-duality multiplets of BPS particles and strings, U-duality invariant mass formulae for 1/2- and 1/4-BPS states for general toroidal compactifications on skew tori with gauge backgrounds, and U-duality multiplets of constraints for states to preserve a given fraction of supersymmetry. A number of mysterious states are encountered in D<=3, whose existence is implied by T-duality and 11D Lorentz invariance. We then move to the M(atrix) theory point of view, give an introduction to Discrete Light Cone Quantization (DLCQ) in general and DLCQ of M-theory in particular. We discuss the realization of U-duality as electric-magnetic dualities of the Matrix gauge theory, display the Matrix gauge theory BPS spectrum in detail, and discuss the conjectured extended U-duality group in this scheme.
Forward citations
Cited by 14 Pith papers
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Taxonomy of branes in infinite distance limits
Under the Emergent String Conjecture and a no-sliding assumption, particle and brane charges must sit on a finite set of lattices, reproducing known string spectra and predicting new branes.
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The Double EFT Expansion in Quantum Gravity
Quantum gravity EFT actions organize higher-curvature corrections into a field-theoretic expansion suppressed by the lightest new mass and a quantum-gravitational expansion suppressed by the species scale.
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Moduli-Space Laplacians, Asymptotic Geometry, and the Emergent String Conjecture
Under the Emergent String Conjecture, the logarithm of any principal tower mass has a moduli-space Laplacian eigenvalue quantized to N/(D-d) for KK towers and N/2 for string oscillators, equal to the instanton-weighte...
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EFTs with Symmetric Moduli Spaces: the Landscape and the Swampland
Using weight polytopes of irreducible representations, a finite list of symmetric moduli spaces satisfies the SDC decay rates; most embed from an E8(8) EFT but three cannot be obtained from string or M-theory compacti...
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Isolated Critical Points for Scherk-Schwarz Compactifications of M-theory
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Bordisms between 9d type IIB supergravities and commutator widths of duality groups
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EFT strings and dualities in 4d $\mathcal{N}=1$
The Integer Scaling relation m^2 ~ T^w with w in {1,2,3} is verified for all convex-hull-generating towers in a wide range of 4d N=1 string compactifications, including subleading towers.
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Super-$\mathrm{Lie}_\infty$ T-Duality and M-Theory
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Worldsheet Formalism for Decoupling Limits in String Theory
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Mock modularity at work, or black holes in a forest
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