On emergent directions in weakly coupled, large N c N $$ \mathcal{N} $$ = 1 SYM

Abstract The SU(N) Yang-Mills theory compactified on ℝ3 × S L 1 $$ {S}_L^1 $$ with small L has many merits, for example the long range effective theory is weakly coupled and adopts rich topological structures, making it semi-classically solvable. Due to the SU(N) → U(1) N−1 symmetry breaking by gaug...

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Main Authors: Baiyang Zhang, Aditya Dhumuntarao
Format: Article
Language:English
Published: SpringerOpen 2025-05-01
Series:Journal of High Energy Physics
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Online Access:https://doi.org/10.1007/JHEP05(2025)012
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author Baiyang Zhang
Aditya Dhumuntarao
author_facet Baiyang Zhang
Aditya Dhumuntarao
author_sort Baiyang Zhang
collection DOAJ
description Abstract The SU(N) Yang-Mills theory compactified on ℝ3 × S L 1 $$ {S}_L^1 $$ with small L has many merits, for example the long range effective theory is weakly coupled and adopts rich topological structures, making it semi-classically solvable. Due to the SU(N) → U(1) N−1 symmetry breaking by gauge holonomy, the low-energy effective theory can be described in terms of unbroken U(1) photons and gauge holonomy. With the addition of N f adjoint light fermions, the center symmetry breaking phase transition can be studied using the twisted partition function, i.e., fermions with periodic boundary conditions, which preserve the supersymmetry in the massless case. In this paper, we show that in the large-N abelian limit with N f = 1 and an N-independent W-boson mass, the long-range 3d effective theory can be regarded as a bosonic field theory in 4d with an emergent spatial dimension. The emergent dimension is flat in the confining phase, but conformally flat in the center-symmetry broken phase with a ℤ2 reflection symmetry. The center symmetry breaking phase transition itself is due to the competition between instanton-monopoles, magnetic and neutral bions controlled by the fermion mass, whose critical value at the transition point is given analytically in the large N limit.
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spelling doaj-art-79dfe40a6b5f4f8084ab7d34f664ec902025-08-20T03:10:28ZengSpringerOpenJournal of High Energy Physics1029-84792025-05-012025512310.1007/JHEP05(2025)012On emergent directions in weakly coupled, large N c N $$ \mathcal{N} $$ = 1 SYMBaiyang Zhang0Aditya Dhumuntarao1Institute of Contemporary Mathematics, School of Mathematics and Statistics, Henan UniversityQuantum Information Science, Sandia National LaboratoriesAbstract The SU(N) Yang-Mills theory compactified on ℝ3 × S L 1 $$ {S}_L^1 $$ with small L has many merits, for example the long range effective theory is weakly coupled and adopts rich topological structures, making it semi-classically solvable. Due to the SU(N) → U(1) N−1 symmetry breaking by gauge holonomy, the low-energy effective theory can be described in terms of unbroken U(1) photons and gauge holonomy. With the addition of N f adjoint light fermions, the center symmetry breaking phase transition can be studied using the twisted partition function, i.e., fermions with periodic boundary conditions, which preserve the supersymmetry in the massless case. In this paper, we show that in the large-N abelian limit with N f = 1 and an N-independent W-boson mass, the long-range 3d effective theory can be regarded as a bosonic field theory in 4d with an emergent spatial dimension. The emergent dimension is flat in the confining phase, but conformally flat in the center-symmetry broken phase with a ℤ2 reflection symmetry. The center symmetry breaking phase transition itself is due to the competition between instanton-monopoles, magnetic and neutral bions controlled by the fermion mass, whose critical value at the transition point is given analytically in the large N limit.https://doi.org/10.1007/JHEP05(2025)012Effective Field TheoriesNonperturbative EffectsSolitons Monopoles and InstantonsConfinement
spellingShingle Baiyang Zhang
Aditya Dhumuntarao
On emergent directions in weakly coupled, large N c N $$ \mathcal{N} $$ = 1 SYM
Journal of High Energy Physics
Effective Field Theories
Nonperturbative Effects
Solitons Monopoles and Instantons
Confinement
title On emergent directions in weakly coupled, large N c N $$ \mathcal{N} $$ = 1 SYM
title_full On emergent directions in weakly coupled, large N c N $$ \mathcal{N} $$ = 1 SYM
title_fullStr On emergent directions in weakly coupled, large N c N $$ \mathcal{N} $$ = 1 SYM
title_full_unstemmed On emergent directions in weakly coupled, large N c N $$ \mathcal{N} $$ = 1 SYM
title_short On emergent directions in weakly coupled, large N c N $$ \mathcal{N} $$ = 1 SYM
title_sort on emergent directions in weakly coupled large n c n mathcal n 1 sym
topic Effective Field Theories
Nonperturbative Effects
Solitons Monopoles and Instantons
Confinement
url https://doi.org/10.1007/JHEP05(2025)012
work_keys_str_mv AT baiyangzhang onemergentdirectionsinweaklycoupledlargencnmathcaln1sym
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