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String Universality in Six Dimensions

Vijay Kumar, Washington Taylor

TL;DR

In six dimensions, anomaly cancellation for ${\mathcal N}= (1,0)$ theories tightly constrains possible gauge/matter content and, for several model classes, coincides with tadpole/matter constraints from string compactifications on K3. The authors demonstrate a close match between consistent 6D supergravity theories and string realizations in the ${SU(N)\times SO(M)}$ class, identify infinite anomaly-factorizing families that are pathological, and propose a concrete conjecture of string universality: ${\mathcal G}= {\mathcal L}$ for a controlled 6D sector. They formalize a framework distinguishing gravity theories from their string completions and discuss extensions beyond the minimal tensor multiplet, as well as implications for predictivity. The work provides a roadmap for proving that all consistent 6D supergravity theories with a Lagrangian description have string UV completions, refining our understanding of the 6D landscape and swampland.

Abstract

In six dimensions, cancellation of gauge, gravitational, and mixed anomalies strongly constrains the set of quantum field theories which can be coupled consistently to gravity. We show that for some classes of six-dimensional supersymmetric gauge theories coupled to gravity, the anomaly cancellation conditions are equivalent to tadpole cancellation and other constraints on the matter content of heterotic/type I compactifications on K3. In these cases, all consistent 6D supergravity theories have a realization in string theory. We find one example which may arise from a novel string compactification, and we identify a new infinite family of models satisfying anomaly factorization. We find, however, that this infinite family of models, as well as other infinite families of models previously identified by Schwarz are pathological. We suggest that it may be feasible to demonstrate that there is a string theoretic realization of all consistent six-dimensional supergravity theories which have Lagrangian descriptions with arbitrary gauge and matter content. We attempt to frame this hypothesis of string universality as a concrete conjecture.

String Universality in Six Dimensions

TL;DR

In six dimensions, anomaly cancellation for theories tightly constrains possible gauge/matter content and, for several model classes, coincides with tadpole/matter constraints from string compactifications on K3. The authors demonstrate a close match between consistent 6D supergravity theories and string realizations in the class, identify infinite anomaly-factorizing families that are pathological, and propose a concrete conjecture of string universality: for a controlled 6D sector. They formalize a framework distinguishing gravity theories from their string completions and discuss extensions beyond the minimal tensor multiplet, as well as implications for predictivity. The work provides a roadmap for proving that all consistent 6D supergravity theories with a Lagrangian description have string UV completions, refining our understanding of the 6D landscape and swampland.

Abstract

In six dimensions, cancellation of gauge, gravitational, and mixed anomalies strongly constrains the set of quantum field theories which can be coupled consistently to gravity. We show that for some classes of six-dimensional supersymmetric gauge theories coupled to gravity, the anomaly cancellation conditions are equivalent to tadpole cancellation and other constraints on the matter content of heterotic/type I compactifications on K3. In these cases, all consistent 6D supergravity theories have a realization in string theory. We find one example which may arise from a novel string compactification, and we identify a new infinite family of models satisfying anomaly factorization. We find, however, that this infinite family of models, as well as other infinite families of models previously identified by Schwarz are pathological. We suggest that it may be feasible to demonstrate that there is a string theoretic realization of all consistent six-dimensional supergravity theories which have Lagrangian descriptions with arbitrary gauge and matter content. We attempt to frame this hypothesis of string universality as a concrete conjecture.

Paper Structure

This paper contains 12 sections, 26 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Examples of 6D models
  3. Gauge group $SU(N) \times SO(M)$
  4. Infinite families with factorized anomalies
  5. On the existence of infinite families
  6. String Universality
  7. ${\mathcal{G}}$: Supersymmetric field theories with gravity in six dimensions
  8. ${\mathcal{L}}$: The six-dimensional SUSY string landscape
  9. Statement of conjecture
  10. Extending the conjecture
  11. Predictivity
  12. Conclusions

Figures (1)

  • Figure 1: The set of consistent six-dimensional gravity theories ${\mathcal{G}}$ contains the set of models realized through compactification of string theory to six dimensions ${\mathcal{L}}$. The conjecture of string universality states that ${\mathcal{G}} ={\mathcal{L}}$. If all models in ${\mathcal{G}}$ can be identified by features of the low-energy Lagrangian, then the swampland can be identified as ${\mathcal{S}}={\mathcal{G}} \setminus{\mathcal{L}}$, and in this situation string universality would imply that the 6D SUSY swampland is empty (${\mathcal{S}} =\{ \}$).