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Counting Nambu-Goldstone Modes of Higher-Form Global Symmetries
Yoshimasa Hidaka1,2,3, Yuji Hirono4,5, Ryo Yokokura1,6
1KEK Theory Center, Tsukuba 305-0801, Japan.
Physical Review Letters
|March 5, 2021
Summary
We developed a method to count Nambu-Goldstone (NG) modes from spontaneous breaking of higher-form global symmetries. This formula uses commutators of conserved charges, providing insights into gapless modes in effective field theories.
Area of Science:
- Theoretical Physics
- High Energy Physics
- Condensed Matter Physics
Background:
- Spontaneous symmetry breaking is a key concept in particle physics and condensed matter.
- Higher-form global symmetries present unique theoretical challenges compared to traditional symmetries.
- Understanding Nambu-Goldstone modes is crucial for constructing effective field theories.
Purpose of the Study:
- To develop a systematic method for counting Nambu-Goldstone (NG) modes in systems with spontaneously broken higher-form global symmetries.
- To establish a general formula for the number of gapless NG modes.
- To provide a framework for constructing effective field theories of NG modes based on symmetry-breaking patterns.
Main Methods:
- Development of effective field theories for NG modes.
- Application of a generalized coset construction tailored for higher-form symmetries.
- Derivation of a formula for counting NG modes involving commutators of conserved charges.
Main Results:
- A formula for the number of gapless NG modes has been derived.
- The formula accounts for conserved charges of potentially different degrees.
- The method provides a way to count NG modes based on symmetry-breaking patterns.
Conclusions:
- The derived formula offers a precise way to determine the number of gapless NG modes.
- The generalized coset construction is effective for higher-form symmetries.
- This work advances the understanding of spontaneous symmetry breaking in higher-form gauge theories.
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