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

Spacetime Reduction of Large N Flavor Models: A Fundamental Theory of Emergent Local Geometry?

We introduce a novel spacetime reduction procedure for the fields of a supergravity-Yang-Mills theory in generic curved spacetime background, and with large N flavor group, to linearized forms on an infinitesimal patch of local tangent space at a point in the spacetime manifold. Our new prescription for spacetime reduction preserves all of the local symmetries of the continuum field theory Lagrangian in the resulting zero-dimensional matrix Lagrangian, thereby obviating difficulties encountered in previous matrix proposals for emergent spacetime in recovering the full nonlinear symmetries of Einstein gravity. We conjecture that the zero-dimensional matrix model obtained by this prescription for spacetime reduction of the circle-compactified type I-I'-mIIA-IIB-heterotic supergravity-Yang-Mills theory with sixteen supercharges and large N flavor group, and inclusive of the full spectrum of Dpbrane charges, offers a potentially complete framework for nonperturbative string/M theory. We explain the relationship of our conjecture for a fundamental theory of emergent local spacetime geometry to recent investigations of the hidden symmetry algebra of M theory, stressing insights that are to be gained from the algebraic perspective. We conclude with a list of open questions and directions for future work.Comment: 30pgs. v6: Ref [4] added, some terminology corrected in Intro, sections 5,6. Footnote 2 clarifies the relation to hep-th/0201129v1. Acknowledgments adde

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

Condensing Nielsen-Olesen strings and the vortex-boson duality in 3+1 and higher dimensions

The vortex-boson (or Abelian-Higgs, XY) duality in 2+1 dimensions demonstrates that the quantum disordered superfluid is equivalent to an ordered superconductor and the other way around. Such a duality structure should be ubiquitous but in 3+1 (and higher) dimensions a precise formulation of the duality is lacking. The problem is that the topological defects become extended objects, strings in 3+1D. We argue how the condensate of such vortex strings must behave from the known physics of the disordered superfluid, namely the Bose-Mott insulator. A flaw in earlier proposals is repaired, and a more direct viewpoint, avoiding gauge fields, in terms of the physical supercurrent is laid out, that also easily generalizes to higher-dimensional and more complicated systems. Furthermore topological defects are readily identified; we demonstrate that the Bose-Mott insulator supports line defects, which may be seen in cold atom experiments.Comment: LaTeX, 25 pages, 5 figures; several revisions and addition