3,322 research outputs found

### Combinatorics in N = 1 Heterotic Vacua

We briefly review an algorithmic strategy to explore the landscape of
heterotic E8 \times E8 vacua, in the context of compactifying smooth Calabi-Yau
three-folds with vector bundles. The Calabi-Yau three-folds are algebraically
realised as hypersurfaces in toric varieties and a large class of vector
bundles are constructed thereon as monads. In the spirit of searching for
Standard-like heterotic vacua, emphasis is placed on the integer combinatorics
of the model-building programme.Comment: 14 pages. An introductory review prepared for the special issue
"Computational Algebraic Geometry in String and Gauge Theory" of Advances in
High Energy Physic

### Swampland Bounds on the Abelian Gauge Sector

We derive bounds on the number of abelian gauge group factors in
six-dimensional gravitational theories with minimal supersymmetry and in their
F-theoretic realisations. These bounds follow by requiring consistency of
certain BPS strings in the spectrum of the theory, as recently proposed in the
literature. Under certain assumptions this approach constrains the number of
abelian gauge group factors in six-dimensional supergravity theories with at
least one tensor multiplet to be $N \leq 20$ (or $N \leq 22$ in absence of
charged matter). For any geometric F-theory realisation with at least one
tensor multiplet we establish the bound $N \leq 16$ by demanding unitarity of a
heterotic solitonic string which exists even in absence of a perturbative
heterotic dual. This result extends to four-dimensional F-theory vacua on any
blowup of a rational fibration. Our findings lead to universal bounds on the
rank of the Mordell-Weil group of elliptically fibered Calabi-Yau threefolds.Comment: 10 pages, 2-column forma

### 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

### Abelianization of BPS Quivers and the Refined Higgs Index

We count Higgs "phase" BPS states of general non-Abelian quiver, possibly
with loops, by mapping the problem to its Abelian, or toric, counterpart and
imposing Weyl invariance later. Precise Higgs index computation is particularly
important for quivers with superpotentials; the Coulomb "phase" index is
recently shown to miss important BPS states, dubbed intrinsic Higgs states or
quiver invariants. We demonstrate how the refined Higgs index is naturally
decomposed to a sum over partitions of the charge. We conjecture, and show in
simple cases, that this decomposition expresses the Higgs index as a sum over a
set of partition-induced Abelian quivers of the same total charge but
generically of smaller rank. Unlike the previous approach inspired by a similar
decomposition of the Coulomb index, our formulae compute the quiver invariants
directly, and thus offer a self-complete routine for counting BPS states.Comment: 38 pages, 13 figure

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