105 research outputs found

### Special Geometry and Mirror Symmetry for Open String Backgrounds with N=1 Supersymmetry

We review an approach for computing non-perturbative, exact superpotentials
for Type II strings compactified on Calabi-Yau manifolds, with extra fluxes and
D-branes on top. The method is based on an open string generalization of mirror
symmetry, and takes care of the relevant sphere and disk instanton
contributions. We formulate a framework based on relative (co)homology that
uniformly treats the flux and brane sectors on a similar footing. However, one
important difference is that the brane induced potentials are of much larger
functional diversity than the flux induced ones, which have a hidden N=2
structure and depend only on the bulk geometry. This introductory lecture is
meant for an audience unfamiliar with mirror symmetry.Comment: latex, 35p, 2 figs, refs added; brief comments about duality to
fourfolds added in the concluding sectio

### Instanton Geometry and Quantum A-infinity structure on the Elliptic Curve

We first determine and then study the complete set of non-vanishing A-model
correlation functions associated with the ``long-diagonal branes'' on the
elliptic curve. We verify that they satisfy the relevant A-infinity consistency
relations at both classical and quantum levels. In particular we find that the
A-infinity relation for the annulus provides a reconstruction of annulus
instantons out of disk instantons. We note in passing that the naive
application of the Cardy-constraint does not hold for our correlators,
confirming expectations. Moreover, we analyze various analytical properties of
the correlators, including instanton flops and the mixing of correlators with
different numbers of legs under monodromy. The classical and quantum A-infinity
relations turn out to be compatible with such homotopy transformations. They
lead to a non-invariance of the effective action under modular transformations,
unless compensated by suitable contact terms which amount to redefinitions of
the tachyon fields.Comment: 24 pages, 6 figures, LaTeX2

### On a Boundary CFT Description of Nonperturbative N=2 Yang-Mills Theory

We describe a simple method for determining the strong-coupling BPS spectrum of four dimensional N=2 supersymmetric Yang-Mills theory. The idea is to represent the magnetic monopoles and dyons in terms of D-brane boundary states of a non-compact d=2 N=2 Landau-Ginzburg model. In this way the quantum truncated BPS spectrum at the origin of the moduli space can be directly mapped to the finite number of primary fields of the superconformal minimal models

### Emergent Strings, Duality and Weak Coupling Limits for Two-Form Fields

We systematically analyse weak coupling limits for 2-form tensor fields in
the presence of gravity. Such limits are significant for testing various
versions of the Weak Gravity and Swampland Distance Conjectures, and more
broadly, the phenomenon of emergence. The weak coupling limits for 2-forms
correspond to certain infinite-distance limits in the moduli space of string
compactifications, where asymptotically tensionless, solitonic strings arise.
These strings are identified as weakly coupled fundamental strings in a dual
frame, which makes the idea of emergence manifest. Concretely we first consider
weakly coupled tensor fields in six-dimensional compactifications of F-theory,
where the arising tensionless strings play the role of dual weakly coupled
heterotic strings. As the main part of this work, we consider certain infinite
distance limits of Type IIB strings on K3 surfaces, for which we show that the
asymptotically tensionless strings describe dual fundamental Type IIB strings,
again on K3 surfaces. By contrast the analogous weak coupling limits of
M-theory compactifications are found to correspond to an F-theory limit where
an extra dimension emerges rather than tensionless strings. We comment on
extensions of our findings to four-dimensional compactifications.Comment: 30 pages, 1 figure; v2: cosmetic changes and minor comments adde

### A Stringy Test of the Scalar Weak Gravity Conjecture

We prove a version of the Weak Gravity Conjecture for 6d F-theory or
heterotic string compactifications with 8 supercharges. This sharpens our
previous analysis by including massless scalar fields. The latter are known to
modify the Weak Gravity Conjecture bound in two a priori independent ways:
First, the extremality condition of a charged black hole is modified, and
second, the test particles required to satisfy the Weak Gravity Conjecture are
subject to additional Yukawa type interactions. We argue on general grounds
that at weak coupling, the two types of effects are equivalent for a tower of
asymptotically massless charged test particles predicted by the Swampland
Distance Conjecture. We then specialise to F-theory compactified on elliptic
Calabi-Yau three-folds and prove that the precise numerical bound on the
charge-to-mass ratio is satisfied at weak coupling. This amounts to an
intriguing coincidence of two a priori different notions of extremality, namely
one based on the balance of gauge, gravitational and scalar forces for extremal
(non-BPS) black holes, and the other encoded in the modular properties of
certain Jacobi forms. In the presence of multiple abelian gauge group factors,
the elliptic genus counting these states is a lattice quasi-Jacobi form of
higher rank, and we exemplify this in a model with two abelian gauge group
factors.Comment: 31 pages, 2 figure

### Modular Fluxes, Elliptic Genera, and Weak Gravity Conjectures in Four Dimensions

We analyse the Weak Gravity Conjecture for chiral four-dimensional F-theory
compactifications with N=1 supersymmetry. Extending our previous work on nearly
tensionless heterotic strings in six dimensions, we show that under certain
assumptions a tower of asymptotically massless states arises in the limit of
vanishing coupling of a U(1) gauge symmetry coupled to gravity. This tower
contains super-extremal states whose charge-to-mass ratios are larger than
those of certain extremal dilatonic Reissner-Nordstrom black holes, precisely
as required by the Weak Gravity Conjecture. Unlike in six dimensions, the tower
of super-extremal states does not always populate a charge sub-lattice. The
main tool for our analysis is the elliptic genus of the emergent heterotic
string in the chiral N=1 supersymmetric effective theories. This also governs
situations where the heterotic string is non-perturbative. We show how it can
be computed in terms of BPS invariants on elliptic four-folds, by making use of
various dualities and mirror symmetry. Compared to six dimensions, the geometry
of the relevant elliptically fibered four-folds is substantially richer than
that of the three-folds, and we classify the possibilities for obtaining
critical, nearly tensionless heterotic strings. We find that the
(quasi-)modular properties of the elliptic genus crucially depend on the choice
of flux background. Our general results are illustrated in a detailed example.Comment: 72 pages, 2 figure

### D-brane effective action and tachyon condensation in topological minimal models

We study D-brane moduli spaces and tachyon condensation in B-type topological
minimal models and their massive deformations. We show that any B-type brane is
isomorphic with a direct sum of `minimal' branes, and that its moduli space is
stratified according to the type of such decompositions. Using the
Landau-Ginzburg formulation, we propose a closed formula for the effective
deformation potential, defined as the generating function of tree-level open
string amplitudes in the presence of D-branes. This provides a direct link to
the categorical description, and can be formulated in terms of holomorphic
matrix models. We also check that the critical locus of this potential
reproduces the D-branes' moduli space as expected from general considerations.
Using these tools, we perform a detailed analysis of a few examples, for which
we obtain a complete algebro-geometric description of moduli spaces and strata.Comment: 36 page

Recommended from our members

### Matrixfaktorisierungen

Im Folgenden soll ein kurzer Abriss des Themas Matrixfaktorisierungen gegeben werden. Wir werden darlegen, warum dieses recht simple Konzept zu erstaunlich tiefen mathematischen GedankengĂ¤ngen fĂĽhrt und auch in der modernen theoretischen Physik wichtige Anwendungen hat

### Superpotentials, A-infinity Relations and WDVV Equations for Open Topological Strings

We give a systematic derivation of the consistency conditions which constrain
open-closed disk amplitudes of topological strings. They include the A-infinity
relations (which generalize associativity of the boundary product of
topological field theory), as well as certain homotopy versions of
bulk-boundary crossing symmetry and Cardy constraint. We discuss integrability
of amplitudes with respect to bulk and boundary deformations, and write down
the analogs of WDVV equations for the space-time superpotential. We also study
the structure of these equations from a string field theory point of view. As
an application, we determine the effective superpotential for certain families
of D-branes in B-twisted topological minimal models, as a function of both
closed and open string moduli. This provides an exact description of tachyon
condensation in such models, which allows one to determine the truncation of
the open string spectrum in a simple manner.Comment: 53 page

- â€¦