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具有两种味道的SU(2)伴随QCD$_4$的候选相：来自$\mathcal{N}=2$超对称杨-米尔斯理论

Candidate Phases for SU(2) Adjoint QCD$_4$ with Two Flavors from $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory

Clay Cordova, Thomas T. Dumitrescu

备注：
94 pages, 1 figure
发表信息：
SciPost Phys. 16, 139 (2024)
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AI总结：

该研究通过将SU(2)伴随QCD嵌入$\mathcal{N}=2$超对称杨-米尔斯理论并施加超对称破缺质量形变，探索其候选红外相，发现奇异Coulomb相与磁单极子诱导的禁闭相，并预言$\mathbb{CP}^1$相在大质量极限下占主导。

摘要：

我们研究具有规范群SU(2)和两种Weyl费米子味道的四维伴随QCD，该理论具有$SU(2)_R$手征对称性。该理论的红外行为尚未被确定。我们通过将伴随QCD嵌入到被一个保持所有全局对称性和't Hooft反常的超对称破缺标量质量M形变的$\mathcal{N}=2$超对称杨-米尔斯理论中来探索候选红外相。这包括仅在理论被置于不允许自旋结构的流形上时才可见的't Hooft反常。该过程的一致性由涉及$SU(2)_R$对称性的非阿贝尔自旋-电荷关系保证，该关系在拓扑扭曲的$\mathcal{N}=2$理论中是常见的。由于$\mathcal{N}=2$理论Coulomb支上的每个真空必然匹配所有't Hooft反常，我们可以通过在这些真空中的理论进行形变同时保持所有对称性和't Hooft反常来生成伴随QCD的候选相。一种这样的形变是超对称破缺标量质量M本身，当M较小时可以可靠地分析。在该区域，它产生一个没有手征对称性破缺的奇异Coulomb相。相比之下，靠近磁单极子和双荷子点的理论可以被形变以实现一个具有磁单极子诱导的禁闭和手征对称性破缺的候选相。低能理论由两个$\mathbb{CP}^1$西格玛模型副本组成，我们对其进行了详细分析。该$\mathbb{CP}^1$模型中可能存在的某些拓扑耦合将该模型的禁闭孤子弦转变为拓扑绝缘体。我们还研究了各种候选相在费米子质量形变下的行为。我们推测形变的$\mathcal{N}=2$理论可能的大的M行为，并猜想$\mathbb{CP}^1$相最终变得主导。

英文摘要：

We study four-dimensional adjoint QCD with gauge group SU(2) and two Weyl fermion flavors, which has an $SU(2)_R$ chiral symmetry. The infrared behavior of this theory is not firmly established. We explore candidate infrared phases by embedding adjoint QCD into $\mathcal{N}=2$ supersymmetric Yang-Mills theory deformed by a supersymmetry-breaking scalar mass M that preserves all global symmetries and 't Hooft anomalies. This includes 't Hooft anomalies that are only visible when the theory is placed on manifolds that do not admit a spin structure. The consistency of this procedure is guaranteed by a nonabelian spin-charge relation involving the $SU(2)_R$ symmetry that is familiar from topologically twisted $\mathcal{N}=2$ theories. Since every vacuum on the Coulomb branch of the $\mathcal{N}=2$ theory necessarily matches all 't Hooft anomalies, we can generate candidate phases for adjoint QCD by deforming the theories in these vacua while preserving all symmetries and 't Hooft anomalies. One such deformation is the supersymmetry-breaking scalar mass M itself, which can be reliably analyzed when M is small. In this regime it gives rise to an exotic Coulomb phase without chiral symmetry breaking. By contrast, the theory near the monopole and dyon points can be deformed to realize a candidate phase with monopole-induced confinement and chiral symmetry breaking. The low-energy theory consists of two copies of a $\mathbb{CP}^1$ sigma model, which we analyze in detail. Certain topological couplings that are likely to be present in this $\mathbb{CP}^1$ model turn the confining solitonic string of the model into a topological insulator. We also examine the behavior of various candidate phases under fermion mass deformations. We speculate on the possible large-M behavior of the deformed $\mathcal{N}=2$ theory and conjecture that the $\mathbb{CP}^1$ phase eventually becomes dominant.

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