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McKay quivers and decomposition
Shani Meynet1, Robert Moscrop1
1Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden.
Letters in Mathematical Physics
|June 7, 2023
Summary
Quantum field theories with global symmetries decompose into simpler theories. This study demonstrates the equivalence between this decomposition in orbifold sigma-models and disconnected McKay quivers, providing geometric meaning to quiver components.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
- Algebraic Geometry
Background:
- Quantum field theories (QFTs) in d-spacetime dimensions can exhibit global (d-1)-form symmetries.
- Such symmetries allow for the decomposition of a theory into disjoint unions of other theories.
- This decomposition has implications for understanding the physical quantities and constituent theories.
Purpose of the Study:
- To establish the equivalence between the decomposition of orbifold sigma-models and disconnected McKay quivers.
- To provide a geometric interpretation for each component of a McKay quiver using decomposition formulas.
- To offer a group and representation theoretic derivation for McKay quivers under specific conditions.
Main Methods:
- Analysis of global (d-1)-form symmetries in quantum field theories.
- Decomposition of orbifold sigma-models.
- Investigation of disconnected McKay quivers.
- Application of decomposition formulas to assign geometric meaning to quiver components.
- Group and representation theoretic derivations for McKay quiver construction.
Main Results:
- Demonstrated equivalence between orbifold sigma-model decomposition and disconnected McKay quivers.
- Provided definitive geometric meaning for each component of McKay quivers through decomposition formulae.
- Derived McKay quivers using group and representation theory for cases with a central trivially acting orbifold group part.
- Confirmed compatibility of derived quivers with sigma-models on 'banded' gerbes.
Conclusions:
- The decomposition of quantum field theories with global symmetries is intrinsically linked to McKay quivers.
- Orbifold sigma-models and McKay quivers offer complementary perspectives on theoretical physics structures.
- The geometric interpretation of McKay quiver components deepens the understanding of QFT decomposition.
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