论文标题
小耦合处的气缸量子场理论
Cylinder quantum field theories at small coupling
论文作者
论文摘要
我们表明，在小耦合极限的情况下，在圆柱体上压缩的任何2D标量场理论都等效于涉及潜在$ V $中的无质量粒子的一维理论，而无限巨大的巨大质量巨大的巨大质量巨大的kaluza-klein（kkk）模式是等效的。稍微远离深度IR区域的效果是开关零模式与KK模式之间的相互作用，其强度受耦合的力量控制，从而使相互作用越来越抑制。我们以Liouville Field理论为著名的例子，从其全球版本开始，我们以耦合常数的触及扰动来计算圆环（一环）分区函数。在t偶数转换下，领先顺序的分区函数是不变的，该函数将圆柱体的半径映射到其反向，并通过圆柱体的Schwinger参数的平方重新升级。我们表明，这种行为是气缸QFT的通用特征。
We show that any 2D scalar field theory compactified on a cylinder and with a Fourier expandable potential $V$ is equivalent, in the small coupling limit, to a 1D theory involving a massless particle in a potential $V$ and an infinite tower of free massive Kaluza-Klein (KK) modes. Moving slightly away from the deep IR region has the effect of switching on interactions between the zero mode and the KK modes, whose strength is controlled by powers of the coupling, hence making the interactions increasingly suppressed. We take the notable example of Liouville field theory and, starting from its worldline version, we compute the torus (one-loop) partition function perturbatively in the coupling constant. The partition function at leading order is invariant under a T-duality transformation that maps the radius of the cylinder to its inverse and rescales it by the square of the Schwinger parameter of the cylinder. We show that this behavior is a universal feature of cylinder QFTs.
