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<p>In this note we consider examples of decomposition (in which a local QFT is equivalent to a disjoint union of multiple independent theories, known as universes) where there is a continuous family of universes, rather than a finite or countably infinite collection. In particular, this allows us to consistently eliminate all instantons in a local QFT via a suitable topological gauging of the (<i>−</i>1)-form symmetry. In two dimensional U(1) gauge theories, this is equivalent to changing the gauge group to <i>ℝ</i>. This makes both locality as well as the instanton restriction explicit. We apply this to clarify the Gross-Taylor string interpretation of the decomposition of two-dimensional pure Yang-Mills. We also apply decomposition to study two-dimensional <i>ℝ</i> gauge theories, such as the pure <i>ℝ</i> Maxwell theory, and two-dimensional supersymmetric gauged linear sigma models whose gauge groups have factors of <i>ℝ</i>. In that context, we find that analogues of the Witten effect for dyons, here rotating between universes, play a role in relating anomalies of the individual universes to (different) anomalies in the disjoint union. Finally, we discuss limits of the Tanizaki-Ünsal construction, which accomplish instanton restriction by topologically gauging a <i>ℚ</i>/<i>ℤ</i> (<i>−</i>1)-form symmetry, and speculate in two-dimensional theories on possible interpretations of those limits in terms of the adelic solenoid.</p>

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Total instanton restriction via multiverse interference: Noncompact gauge theories and (−1)-form symmetries

  • 期刊论文

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  • 发表日期：

    2026年5月19日

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  • Alonso Perez-Lona,
  • Eric Sharpe,
  • Xingyang Yu,
  • Hao Zhang

摘要

In this note we consider examples of decomposition (in which a local QFT is equivalent to a disjoint union of multiple independent theories, known as universes) where there is a continuous family of universes, rather than a finite or countably infinite collection. In particular, this allows us to consistently eliminate all instantons in a local QFT via a suitable topological gauging of the (−1)-form symmetry. In two dimensional U(1) gauge theories, this is equivalent to changing the gauge group to ℝ. This makes both locality as well as the instanton restriction explicit. We apply this to clarify the Gross-Taylor string interpretation of the decomposition of two-dimensional pure Yang-Mills. We also apply decomposition to study two-dimensional ℝ gauge theories, such as the pure ℝ Maxwell theory, and two-dimensional supersymmetric gauged linear sigma models whose gauge groups have factors of ℝ. In that context, we find that analogues of the Witten effect for dyons, here rotating between universes, play a role in relating anomalies of the individual universes to (different) anomalies in the disjoint union. Finally, we discuss limits of the Tanizaki-Ünsal construction, which accomplish instanton restriction by topologically gauging a ℚ/ℤ (−1)-form symmetry, and speculate in two-dimensional theories on possible interpretations of those limits in terms of the adelic solenoid.