GSY孤子的超对称化
Supersymmetrising the GSY Soliton
摘要：
我们超对称的Hopfion研究在以前的工作。这个孤子代表了$U(1)$规范理论中的封闭半局域涡弦。它带有非零的霍普夫数，由于额外的绕组的相位模量，因为一个沿着封闭的字符串移动。我们研究了$\mathcal{N}= 2$超对称QED中的两种味解。作为一个初步的练习，我们紧致一个空间维，并考虑一个直涡周期性边界条件。结果是1/2-BPS饱和。可以引入沿着弦的额外缠绕，并且它不会破坏物体的BPS性质。接下来，我们考虑一个环状的旋涡在一个非紧的空间，并表明，周长的环$L$可以稳定，一旦前面提到的绕组沿字符串被引入。当然，环状涡旋不是BPS，但如果$L$很大，它的能量就会接近BPS的边界，这在角动量$J$很大的情况下是可以保证的。由此我们得到了渐近BPS饱和孤子的概念。在极限$J\rightarrow \infty$中实现BPS饱和。
英文摘要：
We supersymmetrise the Hopfion studied in a previous work. This soliton represents a closed semilocal vortex string in $U(1)$ gauge theory. It carries nonzero Hopf number due to the additional winding of a phase modulus as one moves along the closed string. We study this solution in $\mathcal{N}= 2$ supersymmetric QED with two flavours. As a preliminary exercise we compactify one space dimension and consider a straight vortex with periodic boundary conditions. It turns out to be 1/2-BPS saturated. An additional winding along the string can be introduced and it does not spoil the BPS nature of the object. Next, we consider a ring-like vortex in a non-compact space and show that the circumference of the ring $L$ can be stabilised once the previously mentioned winding along the string is introduced. Of course the ring-like vortex is not BPS but its energy becomes close to the BPS bound if $L$ is large, which can be guaranteed in the case that we have a large value of the angular momentum $J$. Thus we arrive at the concept of asymptotically BPS-saturated solitons. BPS saturation is achieved in the limit $J\rightarrow \infty$.
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