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

Seung-Joo Lee, Wolfgang Lerche, Timo Weigand

TL;DR

The paper investigates infinite-distance, weak-coupling limits for 2-form gauge fields in gravity and shows that such limits produce tensionless strings whose oscillator and KK towers drive the emergent, dual weakly coupled descriptions. In six-dimensional F-theory and Type IIB on K3, the limits realize dual frames: a tensionless heterotic string in the F-theory frame and a tensionless Type IIB string in the K3 geometry, respectively, with the towers reproducing the low-energy couplings in the emergent theories. A contrast with M-theory on K3 reveals an emergent extra dimension in the weak-coupling limit, via the F-theory/M-theory correspondence, rather than tensionless strings in six dimensions. The results support the Swampland Distance Conjecture and the broader emergence program, and they outline a path to applying these ideas to four-dimensional compactifications.

Abstract

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.

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

TL;DR

The paper investigates infinite-distance, weak-coupling limits for 2-form gauge fields in gravity and shows that such limits produce tensionless strings whose oscillator and KK towers drive the emergent, dual weakly coupled descriptions. In six-dimensional F-theory and Type IIB on K3, the limits realize dual frames: a tensionless heterotic string in the F-theory frame and a tensionless Type IIB string in the K3 geometry, respectively, with the towers reproducing the low-energy couplings in the emergent theories. A contrast with M-theory on K3 reveals an emergent extra dimension in the weak-coupling limit, via the F-theory/M-theory correspondence, rather than tensionless strings in six dimensions. The results support the Swampland Distance Conjecture and the broader emergence program, and they outline a path to applying these ideas to four-dimensional compactifications.

Abstract

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.

Paper Structure

This paper contains 12 sections, 96 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction and Summary
  2. Emergent heterotic string from 6d F-theory
  3. Geometric setup
  4. Weak coupling limit for 2-form potentials
  5. Emergent heterotic string at weak coupling
  6. Emergent fundamental strings from Type IIB strings on K3
  7. Large distance limits in the moduli space ${\cal M}_{(5,21)}$
  8. Geometric weak coupling limits in Kähler moduli space of K3
  9. The solitonic string as a Type IIB fundamental string
  10. Emergent strings and duality in the geometric weak coupling limit
  11. Emergent F-theory from M-theory on K3 in Weak Coupling Limit
  12. Conclusions, and Prospects for Four-dimensional Strings

Figures (1)

  • Figure 1: Dynkin Diagram of the $U$-duality group $SO(5,21)$, which encodes the non-perturbative moduli space ${\cal M}_{(5,21)}$, as per ref. Aspinwall:1995td. The black dots denote five non-compact directions in which one can take large distance limits. The directions $V_1$ and $V_2$ correspond to the standard limits of weak 10d dilaton and large volume, respectively. Note that the basis of the $V_i$ is not the same as the basis of $S_i$ which correspond to the weak coupling limits of 2-forms that we consider.

Theorems & Definitions (2)

  • Claim 1
  • Claim 2