将非线性σ模型扩展到强耦合区域的模糊球模型推广到3D N味SU(2)量子色动力学
Generalizing Deconfined Criticality to 3D $N$-Flavor $\mathrm{SU}(2)$ Quantum Chromodynamics on the Fuzzy Sphere
AI总结：
研究通过量子蒙特卡洛方法探讨了3D N味SU(2)量子色动力学在模糊球模型中的临界行为，发现N≥4时存在新的临界相，并验证了共形对称性的涌现。
摘要：
规范理论与物质耦合的红外行为仍然是量子场论中的开放问题。对于给定的规范群，此类理论预计会在费米子或标量味数的范围内流到一个相互作用的共形固定点，称为“共形窗口”。其性质对于理解超越Landau范式之外的临界相和相变，如非约束量子临界点（DQCP）至关重要，但仍然对传统非微扰方法具有挑战性。在本工作中，我们研究了一类模糊球模型，对应于具有Sp(N)全局对称性的非线性σ模型，并扩展到强耦合区域。这些理论预计具有由3维时空中的SU(2)量子色动力学（QCD）描述的红外固定点，具有N种费米子味。它们可以视为SO(5) DQCP的推广，对应于N=2。我们使用量子蒙特卡洛方法研究N至16的情况。我们发现，对于N≥4，相图中包含一个临界相，这在N=2时似乎不存在。在该相中，我们测量了两点相关函数和激发谱，这些表现出涌现的共形对称性。我们还提取了主导算符的标度维度Δ_ϕ，并发现与大N期望一致。
英文摘要：
The infra-red behaviour of gauge theories coupled to matter remains an open problem in quantum field theory. For a given gauge group, such theories are expected to flow to an interacting conformal fixed point over a range of fermion or scalar flavours, known as the `conformal window.' Their nature is important for understanding critical phases and phase transitions beyond the Landau paradigm like the deconfined quantum critical point (DQCP), yet remains challenging for conventional non-perturbative approaches. In this work, we study a family of fuzzy-sphere models corresponding to non-linear sigma models with $\mathrm{Sp}(N)$ global symmetry extended to the strongly-coupled region. These theories are expected have an infra-red fixed point described by $\mathrm{SU}(2)$ quantum chromodynamics (QCD) in three space-time dimensions with $N$ flavours of fermions. They can be viewed as a generalisation of the $\mathrm{SO}(5)$ DQCP, corresponding to $N=2$. We investigate them using quantum Monte Carlo for $N$ up to $16$. We find evidence that for $N\geq4$ the phase diagram contains a critical phase that appears to be absent for $N=2$. Within this phase, we measure the two-point correlation function and the excitation spectrum, which exhibit emergent conformal symmetry. We also extract the scaling dimension $Δ_ϕ$ of a leading operator and find consistency with large-$N$ expectations.
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