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<p>We study the fractionalization of 0-form global symmetries on line operators in theories without 1-form global symmetries. The projective transformation properties of line operators are renormalization group invariant, and we derive constraints which are similar to the consequences of exact 1-form symmetries. For instance, symmetry fractionalization can lead to exact selection rules for line operators in twisted sectors, and in theories with ’t Hooft anomalies involving the fractionalization class, these selection rules can further imply that certain twisted sectors have exact finite-volume vacuum degeneracies. Along the way, we define topological operators on open codimension-1 manifolds, which we call ‘disk operators’, that provide a convenient way of encoding the projective action of 0-form symmetries on lines. In addition, we discuss the possible ways symmetry fractionalization can be matched along renormalization group flows.</p>

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Consequences of symmetry fractionalization without 1-form global symmetries

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月24日

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  • T. Daniel Brennan,
  • Theodore Jacobson,
  • Konstantinos Roumpedakis

摘要

We study the fractionalization of 0-form global symmetries on line operators in theories without 1-form global symmetries. The projective transformation properties of line operators are renormalization group invariant, and we derive constraints which are similar to the consequences of exact 1-form symmetries. For instance, symmetry fractionalization can lead to exact selection rules for line operators in twisted sectors, and in theories with ’t Hooft anomalies involving the fractionalization class, these selection rules can further imply that certain twisted sectors have exact finite-volume vacuum degeneracies. Along the way, we define topological operators on open codimension-1 manifolds, which we call ‘disk operators’, that provide a convenient way of encoding the projective action of 0-form symmetries on lines. In addition, we discuss the possible ways symmetry fractionalization can be matched along renormalization group flows.