标题： 拓扑电弱相变 显示英文标题

标题： Topological Electroweak Phase Transition

摘要： 在这项工作中，我们将研究非平凡拓扑对标准模型有效势的影响。具体来说，我们将假设时空拓扑为$S^1\times R^3$，并计算这种拓扑时空下的标准模型有效势。 正如我们所展示的，对于紧致维度半径的较小值，电弱对称性未被破坏，但在临界长度及更大时，电弱对称性会被破坏，因为与原点处的最小值相比，Higgs场的构型空间中包含了一个额外的能量更有利的最小值。这两个最小值由一个势垒分隔开，因此可以通过量子隧穿发生相变，这模仿了一阶相变。 这是一种非热相变，类似于可能的量子霍尔拓扑相变，因此在这种情景下，电弱对称性的破缺不需要高温即可发生。当前情景并不依赖于暴胀时代的出现，仅依赖于宇宙的膨胀；然而，如果暴胀确实发生了，我们简要讨论了$S^1\times R^3$时空中的超视界项冻结问题。 我们还研究了由于非平凡拓扑导致的引力势的大尺度差异。最后，我们简要提到由于非平凡拓扑而可能存在的不同且不等价的拓扑场构型，这些构型由第一斯蒂弗尔类分类，在此情况下为$H^{1}(S^{1}{\times R}^{3},Z_{\widetilde{2}})=Z_2$，因此可以存在偶数和奇数元素。 我们还简要定性地讨论了由拓扑诱导的电弱相变如何产生原初引力波。 显示英文摘要

摘要： In this work we shall consider the effects of a non-trivial topology on the effective potential of the Standard Model. Specifically we shall assume that the spacetime topology is $S^1\times R^3$ and we shall calculate the Standard Model effective potential for such a topological spacetime. As we demonstrate, for small values of the compact dimension radius, the electroweak symmetry is unbroken, but for a critical length and beyond, the electroweak symmetry is broken, since the configuration space of the Higgs field contains an additional energetically favorable minimum, compared to the minimum at the origin. The two minima are separated by a barrier, thus a phase transition can occur, via quantum tunnelling, which mimics a first order phase transition. This is a non-thermal phase transition, similar possibly to quantum Hall topological phase transitions, hence in the context of this scenario, the electroweak symmetry breaking does not require a high temperature to occur. The present scenario does not rely on the occurrence of the inflationary era, only on the expansion of the Universe, however we briefly discuss the freezing of the superhorizon terms in $S^1\times R^3$ spacetime, if inflation occurred. We also investigate the large scale differences of the gravitational potential due to the non-trivial topology. Finally, we briefly mention the distinct inequivalent topological field configurations that can exist due to the non-trivial topology, which are classified by the first Stieffel class which in the case at hand is $H^{1}(S^{1}{\times R}^{3},Z_{\widetilde{2}})=Z_2$, so even and odd elements can exist. We also briefly qualitatively discuss how a topologically induced electroweak phase transition can yield primordial gravitational waves.