The General Warped Solution with Conical Branes in Six-dimensional Supergravity

We present the general regular warped solution with 4D Minkowski spacetime in six-dimensional gauged supergravity. In this framework, we can easily embed multiple conical branes into the warped geometry by choosing an undetermined holomorphic function. As an example, for the holomorphic function with many zeroes, we find warped solutions with multi-branes and discuss the generalized flux quantization in this case.Comment: 1+19 pages, no figure, JHEP style, version to appear in JHE

Local SU(5) Unification from the Heterotic String

We construct a 6D supergravity theory which emerges as intermediate step in the compactification of the heterotic string to the supersymmetric standard model in four dimensions. The theory has N=2 supersymmetry and a gravitational sector with one tensor and two hypermultiplets in addition to the supergravity multiplet. Compactification to four dimensions occurs on a T^2/Z_2 orbifold which has two inequivalent pairs of fixed points with unbroken SU(5) and SU(2)xSU(4) symmetry, respectively. All gauge, gravitational and mixed anomalies are cancelled by the Green-Schwarz mechanism. The model has partial 6D gauge-Higgs unification. Two quark-lepton generations are localized at the SU(5) branes, the third family is composed of split bulk hypermultiplets. The top Yukawa coupling is given by the 6D gauge coupling, all other Yukawa couplings are generated by higher-dimensional operators at the SU(5) branes. The presence of the SU(2)xSU(4) brane breaks SU(5) and generates split gauge and Higgs multiplets with N=1 supersymmetry in four dimensions. The third generation is obtained from two split \bar{5}-plets and two split 10-plets, which together have the quantum numbers of one \bar{5}-plet and one 10-plet. This avoids unsuccessful SU(5) predictions for Yukawa couplings of ordinary 4D SU(5) grand unified theories.Comment: 38 pages. v2: Typos correcte

F-theory duals of singular heterotic K3 mode

We study F-theory duals of singular heterotic K3 models that correspond to Abelian toroidal orbifolds ${T}^{4}/{\mathbb{Z}}_{N}$. While our focus is on the standard embedding, we also comment on models with Wilson lines and more general gauge embeddings. In the process of constructing the duals, we work out a Weierstrass description of the heterotic toroidal orbifold models, which exhibit singularities of Kodaira type ${I}_{0}^{*}$, ${IV}^{*}$, ${III}^{*}$, and ${II}^{*}$. This construction unveils properties like the instanton number per fixed point and a correlation between the orbifold order and the multiplicities in the Dynkin diagram. The results from the Weierstrass description are then used to restrict the complex structure of the F-theory Calabi–Yau threefold such that the gauge group and the matter spectrum of the heterotic theories are reproduced. We also comment on previous approaches that have been employed to construct the duality and point out the differences and limitations in our case. Our results show explicitly how the various orbifold models are connected and described in F-theory

F-Theory Duals of Singular Heterotic K3 Models

We study F-theory duals of singular heterotic K3 models that correspond to abelian toroidal orbifolds T4/ZN. While our focus is on the standard embedding, we also comment on models with Wilson lines and more general gauge embeddings. In the process of constructing the duals, we work out a Weierstrass description of the heterotic toroidal orbifold models, which exhibit singularities of Kodaira type I∗0,IV∗,III∗, and II∗. This construction unveils properties like the instanton number per fixed point and a correlation between the orbifold order and the multiplicities in the Dynkin diagram. The results from the Weierstrass description are then used to restrict the complex structure of the F-theory Calabi-Yau threefold such that the gauge group and the matter spectrum of the heterotic theories are reproduced. We also comment on previous approaches that have been employed to construct the duality and point out the differences to our case. Our results show explicitly how the various orbifold models are connected and described in F-theory