$2$的质谱--格点上的$\mathcal{N}=(2,2)$维超Yang-Mills理论
Mass spectrum of $2$-dimensional $\mathcal{N}=(2,2)$ super Yang-Mills theory on the lattice
摘要：
在本工作中，我们分析了$\mathcal{N}=(2,2)$超对称杨米尔斯（SYM）理论在二维的晶格模拟。该理论是作为$\mathcal{N}=1$ SYM理论的四维降维而产生的。与其他具有扩展超对称性的规范理论一样，经典标量势具有平坦的方向，这可能会使数值模拟不稳定。此外，费米子行列式不一定是正的，这个符号问题可能会在随机处理中引起进一步的问题。我们证明了$\mathcal{N}=(2,2)$超杨-米尔斯理论实际上没有符号问题，并且平坦方向被提升，从而通过量子修正而稳定。在这个有限理论中，只有标量的裸质量经历有限的加性重整化。在具有不同晶格常数的各种晶格上，我们确定了超对称破坏项最小的标量质量和跳跃参数。通过研究四个沃德恒等式和监测的$π$质量，我们表明，超对称性确实恢复在连续极限。在第二部分中，我们计算了低束缚态的质量。我们发现在无限体积和超对称连续极限下，Veneziano-Yankielowicz超多重态变为无质量，Farrar-Gabadadze-Schwetz超多重态从理论上消失.此外，我们估计了Veneziano-Yankielowicz多重态中激发态介子的质量。我们观察到胶子球的质量与激发态介子的质量相当。
英文摘要：
In the present work we analyse $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills (SYM) theory in two dimensions by means of lattice simulations. The theory arises as dimensional reduction of $\mathcal{N}=1$ SYM theory in four dimensions. As in other gauge theories with extended supersymmetry, the classical scalar potential has flat directions which may destabilize numerical simulations. In addition, the fermion determinant need not be positive and this sign-problem may cause further problems in a stochastic treatment. We demonstrate that $\mathcal{N}=(2,2)$ super Yang-Mills theory has actually no sign problem and that the flat directions are lifted and thus stabilized by quantum corrections. Only the bare mass of the scalars experience a finite additive renormalization in this finite theory. On various lattices with different lattice constants we determine the scalar masses and hopping parameters for which the supersymmetry violating terms are minimal. By studying four Ward identities and by monitoring the $π$-mass we show that supersymmetry is indeed restored in the continuum limit. In the second part we calculate the masses of the low-lying bound states. We find that in the infinite-volume and supersymmetric continuum limit the Veneziano-Yankielowicz super-multiplet becomes massless and the Farrar-Gabadadze-Schwetz super-multiplet decouples from the theory. In addition, we estimate the masses of the excited mesons in the Veneziano-Yankielowicz multiplet. We observe that the gluino-glueballs have comparable masses to the excited mesons.
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