D5D_5D5​ elliptic fibrations: non-Kodaira fibers and new orientifold limits of F-theory (original) (raw)

On the duality between the heterotic string and F-theory in 8 dimensions

Physics Letters B, 1996

In this note we compare the moduli spaces of the heterotic string compactified on a two-torus and F-Theory compactified on an elliptic K3 surface for the case of an unbroken E 8 ×E 8 gauge group. The explicit map relating the deformation parameters α and β of the F-Theory K3 surface to the moduli T and U of the heterotic torus is found using the close relationship between the K3 discriminant and the discriminant of the Calabi-Yau-threefold X 1,1,2,8,12 (24) in the limit of a large base P 1 .

Topological strings on genus one fibered Calabi-Yau 3-folds and string dualities

Journal of High Energy Physics, 2019

We calculate the generating functions of BPS indices using their modular properties in Type II and M-theory compactifications on compact genus one fibered CY 3-folds with singular fibers and additional rational sections or just N -sections, in order to study string dualities in four and five dimensions as well as rigid limits in which gravity decouples. The generating functions are Jacobi-forms of Γ1(N) with the complexified fiber volume as modular parameter. The string coupling λ, or the ϵ± parameters in the rigid limit, as well as the masses of charged hypermultiplets and non-Abelian gauge bosons are elliptic parameters. To understand this structure, we show that specific auto-equivalences act on the category of topological B-branes on these geometries and generate an action of Γ1(N) on the stringy Kähler moduli space. We argue that these actions can always be expressed in terms of the generic Seidel-Thomas twist with respect to the 6-brane together with shifts of the B-field and ...

New branches of string compactifications and their F-theory duals

Nuclear Physics B, 1997

We study heterotic E 8 × E 8 models that are dual to compactifications of Ftheory and type IIA string on certain classes of elliptically fibered Calabi-Yau manifolds. Different choices for the specific torus in the fibration have heterotic duals that are most easily understood in terms of E 8 × E 8 models with gauge backgrounds of type H × U(1) 8−d , where H is a non-Abelian factor. The case with d = 8 corresponds to the well known E 8 × E 8 compactifications with non-Abelian instanton backgrounds (k 1 , k 2 ) whose F-theory duals are built through compactifications on fibrations of the torus IP (1,2,3) 2

NS5-brane, D5-brane, D3-brane) bound state, open D3-brane, open D5-brane limits, and SL(2,Z) duality

Physical Review D, 2002

We generalize the non-threshold bound state in type IIB supergravity of the form (NS5, D5, D3) constructed by the present authors (in hep-th/0011236) to non-zero asymptotic value of the axion (χ 0 ). We identify the decoupling limits corresponding to both the open D3-brane theory and open D5-brane theory for this supergravity solution as expected. However, we do not find any non-commutative Yang-Mills theory (NCYM) limit for this solution in the presence of NS5 branes. We then study the SL(2, Z) duality symmetry of type IIB theory for both OD3-limit and OD5-limit. We find that for OD3 theory, a generic SL(2, Z) duality always gives another OD3-theory irrespective of the value of χ 0 being rational or not. This indicates that OD3-theory is selfdual. But, under a special set of SL(2, Z) transformations for which χ 0 is rational OD3-theory goes over to a 5+1 dimensional NCYM theory and these two theories in this case are related to each other by strong-weak duality symmetry. On the other hand, for OD5-theory, a generic SL(2, Z) duality gives another OD5-theory if χ 0 is irrational, but when χ 0 is rational it gives the little string theory limit indicating that OD5-theory is S-dual to the type IIB little string theory. *

Strong coupling singularities and non-abelian gauge symmetries in N=2 string theory

Nuclear Physics B, 1996

We study a class of extremal transitions between topological distinct Calabi-Yau manifolds which have an interpretation in terms of the special massless states of a type II string compactification. In those cases where a dual heterotic description exists the exceptional massless states are due to genuine strong (string-) coupling effects. A new feature is the appearance of enhanced non-abelian gauge symmetries in the exact nonperturbative theory.

S-duality and tensionless 5-branes in compactified heterotic string theory,” JHEP 9912

Journal of High Energy Physics, 1999

We give a simple proof of the known S-duality of Heterotic String theory compactified on a T 6. Using this S-duality we calculate the tensions for a class of BPS 5-branes in Heterotic String theory on a S 1. One of these, the Kaluza-Klein monopole, becomes tensionless when the radius of the S 1 is equal to the string length. We study the question of stability of the Heterotic NS5-brane with a transverse circle. For large radii the NS5-brane is absolutely stable. However for small radii it is only marginally stable. We also study the moduli space of 2 Kaluza-Klein monopoles and show that it is equal to the moduli space of a Heterotic A 1 singularity.

On Local F-Theory Geometries and Intersecting D7-BRANES

International Journal of Geometric Methods in Modern Physics, 2009

We discuss local F-theory geometries and theirs gauge theory dualities in terms of intersecting D7-branes wrapped four-cycles in Type IIB superstring. The manifolds are built as elliptic K3 surface fibrations over intersecting F 0 = CP 1 × CP 1 base geometry according to ADE Dynkin Diagrams. The base is obtained by blowing up the extended ADE hyper-Kähler singularities of eight dimensional manifolds considered as sigma model target spaces with eight supercharges. The resulting gauge theory of such local F-theory models are given in terms of Type IIB D7-branes wrapped intersecting F 0 . The four dimensional N = 1 anomaly cancelation requirement translates into a condition on the associated affine Lie algebras.

S-duality and tensionless 5-branes in compactified heterotic string theory

Journal of High Energy Physics, 1999

We give a simple proof of the known S-duality of Heterotic String theory compactified on a T 6. Using this S-duality we calculate the tensions for a class of BPS 5-branes in Heterotic String theory on a S 1. One of these, the Kaluza-Klein monopole, becomes tensionless when the radius of the S 1 is equal to the string length. We study the question of stability of the Heterotic NS5-brane with a transverse circle. For large radii the NS5-brane is absolutely stable. However for small radii it is only marginally stable. We also study the moduli space of 2 Kaluza-Klein monopoles and show that it is equal to the moduli space of a Heterotic A 1 singularity.

$\mathbb{P}^1$-fibrations in F-theory and String Dualities

2021

In this work we study F-theory compactifications on elliptically fibered Calabi-Yau n-folds which have P-fibered base manifolds. Such geometries, which we study in both 4and 6-dimensions, are both ubiquitous within the set of Calabi-Yau manifolds and play a crucial role in heterotic/Ftheory duality. We discuss the most general formulation of P-bundles of this type, as well as fibrations which degenerate at higher codimension loci. In the course of this study, we find a number of new phenomena. For example, in both 4and 6-dimensions we find transitions whereby the base of a P-bundle can change nature, or “jump”, at certain loci in complex structure moduli space. We discuss the implications of this jumping for the associated heterotic duals. We argue that P-bundles with only rational sections lead to heterotic duals where the Calabi-Yau manifold is elliptically fibered over the section of the P bundle, and not its base. As expected, we see that degenerations of the P fibration of the ...

String-string dualities in D=6,4 dimensions

Nuclear Physics B - Proceedings Supplements, 1997

We study heterotic Es x Es models that are dual to compactifications of F-theory and type IIA string on certain classes of elliptically fibered Calabi-Yau manifolds. Different choices for the specific torus in the fibration have heterotic duals that are most easily understood in terms of Es x Es models with gauge backgrounds of type H x U(1) s-d, where H is a non-Abelian factor. The case with d = 8 corresponds to the well known Es x Es compactifications with non-Abelian instanton backgrounds (kl, ks) whose F-theory duals are built through compactifications on fibrations of the torus p~l,2,s)[6] over IF,,. The new cases with d < 8 correspond to other choices for the elliptic fiber over the same base and yield unbroken U(1)'s, some of which are anomalous and acquire a mass by swallowing zero modes of the antisymmetric BMN field. We also study transitions to models with no tensor multiplets in D = 6 and find evidence of Ed instanton dynamics.