Abstract
We study confinement in 4d $\mathcal{N}=1$ $SU(N)$ Super-Yang Mills (SYM) from a holographic point of view, focusing on the 1-form symmetry and its relation to chiral symmetry breaking. In the 5d supergravity dual, obtained by truncation of the Klebanov-Strassler solution, we identify the topological couplings that determine the 1-form symmetry and its 't Hooft anomalies. One such coupling is a mixed 0-form/1-form symmetry anomaly closely related to chiral symmetry breaking in gapped confining vacua. From the dual gravity description we also identify the infra-red (IR) 4d topological field theory (TQFT), which realises chiral symmetry breaking and matches the mixed anomaly. Finally, complementing this, we derive the chiral and mixed anomalies from the Little String Theory realization of pure SYM.
Highlights
Generalized global symmetries and their ’t Hooft anomalies can highly constrain the dynamics of gauge theories
A prime example is the role of 1-form symmetries in confinement of N 1⁄4 1 SUðNÞ super Yang-Mills (SYM) or adjoint QCD theories
What we show is that the dual supergravity theory captures the background fields for the higher-form symmetries, and their anomalies, and provides a derivation of the 4d TQFT that governs the IR confining phase of the theory
Summary
Generalized global symmetries and their ’t Hooft anomalies can highly constrain the dynamics of gauge theories. A prime example is the role of 1-form symmetries in confinement of N 1⁄4 1 SUðNÞ super Yang-Mills (SYM) or adjoint QCD theories. In this case the 1-form symmetry Γð1Þ 1⁄4 ZN and corresponds to the center of the gauge group, which acts on line operators [1,2] and provides a diagnostic of confinement. What we show is that the dual supergravity theory captures the background fields for the higher-form symmetries, and their anomalies, and provides a derivation of the 4d TQFT that governs the IR confining phase of the theory. Provides an exposition of a more general methodology: utilizing supergravity couplings to determine anomalies and IR sectors of quantum field theories (QFTs). We expect our work to open up the exciting prospect of revisiting these setups and sharpening their predictions and extending the scope of such scenarios
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