Monopole-vortex continuity of ${\mathcal N}=1$ super Yang-Mills theory on $\mathbb{R}^2 \times S^1 \times S^1$ with 't Hooft twist

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Main Authors: Hayashi, Yui, Misumi, Tatsuhiro, Tanizaki, Yuya
Format: Preprint
Published: 2024
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author Hayashi, Yui
Misumi, Tatsuhiro
Tanizaki, Yuya
author_facet Hayashi, Yui
Misumi, Tatsuhiro
Tanizaki, Yuya
contents We study ${\mathcal N} = 1$ $SU(N)$ super Yang-Mills (SYM) theory on $\mathbb{R}^2\times (S^1)_3\times (S^1)_4$ with the 't Hooft twist. The theory becomes weakly coupled if the length $L_4$ of $(S^1)_4$ is sufficiently small, $NL_4Λ\ll 1$. We explore the nonperturbative dynamics at the weak-coupling regime by changing the size of $L_3$ and uncover how $3$d monopole/bion-based effective theory for $L_3\gg L_4$ is related to the $2$d vortex-based theory for $L_3\approx L_4$. The highlights of our results are (1) the smooth "weak-weak" continuity of the vacuum structure and gluino condensate during the $3$d-$2$d dimensional reduction, (2) the switching of Wilson loop behavior from the area law in $3$d to the perimeter law in $2$d via a "double-string" picture, (3) the role of mass deformation in breaking discrete chiral symmetry and restoring the area law in $2$d, and (4) the microscopic investigation of bions during the reduction from $3$d to $2$d and the cancellation of the vacuum energy due to the hidden topological angle. We also discuss the generalization of our results for (1)--(3) from $\mathcal{N}=1$ SYM to QCD with adjoint quarks.
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id arxiv_https___arxiv_org_abs_2410_21392
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Monopole-vortex continuity of ${\mathcal N}=1$ super Yang-Mills theory on $\mathbb{R}^2 \times S^1 \times S^1$ with 't Hooft twist
Hayashi, Yui
Misumi, Tatsuhiro
Tanizaki, Yuya
High Energy Physics - Theory
We study ${\mathcal N} = 1$ $SU(N)$ super Yang-Mills (SYM) theory on $\mathbb{R}^2\times (S^1)_3\times (S^1)_4$ with the 't Hooft twist. The theory becomes weakly coupled if the length $L_4$ of $(S^1)_4$ is sufficiently small, $NL_4Λ\ll 1$. We explore the nonperturbative dynamics at the weak-coupling regime by changing the size of $L_3$ and uncover how $3$d monopole/bion-based effective theory for $L_3\gg L_4$ is related to the $2$d vortex-based theory for $L_3\approx L_4$. The highlights of our results are (1) the smooth "weak-weak" continuity of the vacuum structure and gluino condensate during the $3$d-$2$d dimensional reduction, (2) the switching of Wilson loop behavior from the area law in $3$d to the perimeter law in $2$d via a "double-string" picture, (3) the role of mass deformation in breaking discrete chiral symmetry and restoring the area law in $2$d, and (4) the microscopic investigation of bions during the reduction from $3$d to $2$d and the cancellation of the vacuum energy due to the hidden topological angle. We also discuss the generalization of our results for (1)--(3) from $\mathcal{N}=1$ SYM to QCD with adjoint quarks.
title Monopole-vortex continuity of ${\mathcal N}=1$ super Yang-Mills theory on $\mathbb{R}^2 \times S^1 \times S^1$ with 't Hooft twist
topic High Energy Physics - Theory
url https://arxiv.org/abs/2410.21392