Superstring theoryをめぐって(放談室)

Despite much recent progress in model building with $D$-branes, it has been problematic to find a completely convincing explanation of gauge coupling unification. We extend the class of models by considering $F$-theory compactifications, which may incorporate unification more naturally. We explain how to derive the charged chiral spectrum and Yukawa couplings in $N = 1$ compactifications of $F$-theory with $G$-flux. In a class of models which admit perturbative heterotic duals, we show that the $F$-theory and heterotic computations match.

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Model building with $F$-theory

We review some theoretical and phenomenological aspects of massive gravities in 4 dimensions. We start from the Fierz–Pauli theory with Lorentz-invariant mass terms and then proceed to Lorentz-violating masses. Unlike the former theory, some models with Lorentz violation have no pathologies in the spectrum in flat and nearly flat backgrounds and lead to an interesting phenomenology.

https://iopscience.iop.org/article/10.1070/PU2008v051n08ABEH006600/pdf

Infrared-modified gravities and massive gravitons

Author(s): Heckman, JJ; Morrison, DR; Rudelius, T; Vafa, C | Abstract: We use F-theory to classify possibly all six-dimensional superconformal field theories (SCFTs). This involves a two step process: We first classify all possible tensor branches allowed in F-theory (which correspond to allowed collections of contractible spheres) and then classify all possible configurations of seven-branes wrapped over them. We describe the first step in terms of "atoms" joined into "radicals" and "molecules," using an analogy from chemistry. The second step has an interpretation via quiver-type gauge theories constrained by anomaly cancellation. A very surprising outcome of our analysis is that all of these tensor branches have the structure of a linear chain of intersecting spheres with a small amount of possible decoration at the two ends. The resulting structure of these SCFTs takes the form of a generalized quiver consisting of ADE-type nodes joined by conformal matter. A collection of highly non-trivial examples involving E8 small instantons probing an ADE singularity is shown to have an F-theory realization. This yields a classification of homomorphisms from ADE subgroups of SU(2) into E8 in purely geometric terms, matching results obtained in the mathematics literature from an intricate group theory analysis.

/pdf/atomic-classification-of-6d-scfts-232fm3kbg4.pdf

Atomic classification of 6D SCFTs

https://pure.mpg.de/pubman/item/item_2533988_4/component/file_2533987/1712.03107.pdf

Dynamical systems applied to cosmology: dark energy and modified gravity

With model building applications in mind, we collect and develop basic techniques to analyze the landscape of D7-branes in type IIB compact Calabi-Yau orientifolds, in three different pictures: F-theory, the D7 worldvolume theory and D9-anti-D9 tachyon condensation. A significant complication is that consistent D7-branes in the presence of O7− planes are generically singular, with singularities locally modeled by the Whitney Umbrella. This invalidates the standard formulae for charges, moduli space and flux lattice dimensions. We infer the correct formulae by comparison to F-theory and derive them independently and more generally from the tachyon picture, and relate these numbers to the closed string massless spectrum of the orientifold compactification in an interesting way. We furthermore give concrete recipes to explicitly and systematically construct nontrivial D-brane worldvolume flux vacua in arbitrary Calabi-Yau orientifolds, illustrate how to read off D-brane flux content, enhanced gauge groups and charged matter spectra from tachyon matrices, and demonstrate how brane recombination in general leads to flux creation, as required by charge conservation and by equivalence of geometric and gauge theory moduli spaces.

/pdf/d-brane-deconstructions-in-iib-orientifolds-2l9zss0a94.pdf

D-brane deconstructions in IIB orientifolds

G-flux in F-theory and algebraic cycles

With model building applications in mind, we collect and develop basic techniques to analyze the landscape of D7-branes in type IIB compact Calabi-Yau orientifolds, in three different pictures: F-theory, the D7 worldvolume theory and D9-anti-D9 tachyon condensation. A significant complication is that consistent D7-branes in the presence of O7^- planes are generically singular, with singularities locally modeled by the Whitney Umbrella. This invalidates the standard formulae for charges, moduli space and flux lattice dimensions. We infer the correct formulae by comparison to F-theory and derive them independently and more generally from the tachyon picture, and relate these numbers to the closed string massless spectrum of the orientifold compactification in an interesting way. We furthermore give concrete recipes to explicitly and systematically construct nontrivial D-brane worldvolume flux vacua in arbitrary Calabi-Yau orientifolds, illustrate how to read off D-brane flux content, enhanced gauge groups and charged matter spectra from tachyon matrices, and demonstrate how brane recombination in general leads to flux creation, as required by charge conservation and by equivalence of geometric and gauge theory moduli spaces.

D-brane Deconstructions in IIB Orientifolds

We discuss E3-brane instantons in N = 1 F-theory compactifications to four dimensions and clarify the structure of E3-E3 zero modes for general world-volume fluxes. We consistently incorporate SL(2, ℤ monodromies and highlight the relation between F- theory and perturbative IIB results. We explicitly show that world-volume fluxes can lift certain fermionic zero-modes, whose presence would prevent the generation of non- perturbative superpotential terms, and we discuss in detail the geometric interpretation of the zero-mode lifting mechanism. We provide a IIB derivation of the index for generation of superpotential terms and of its modification to include world-volume fluxes, which re-produces and generalizes available results. We apply our general analysis to the explicit, though very simple, example of compactification on ℙ3 and its orientifold weak-coupling limit. In particular, we provide an example in which a non-rigid divisor with fluxes contributes to the superpotential.

Magnetized E3-brane instantons in F-theory.

In this paper, a procedure is developed to construct compact F-theory fourfolds corresponding to perturbative IIB O7/O3 models on CICY threefolds with permutation involutions. The method is explained in generality, and then applied to specific examples where the involution permutes two Del Pezzo surfaces. The fourfold construction is successfully tested by comparing the D3 charges predicted by F-theory and IIB string theory.

Andrés Collinucci

Papers

D-brane deconstructions in IIB orientifolds

G-flux in F-theory and algebraic cycles

D-brane Deconstructions in IIB Orientifolds

Magnetized E3-brane instantons in F-theory.

New F-theory lifts II: permutation orientifolds and enhanced singularities