论文标题
$ \ mathrm {t} \ bar {\ mathrm {t}} - $喜欢在任意维度中的变形的公制方法
Metric approach to a $\mathrm{T}\bar{\mathrm{T}}-$like deformation in arbitrary dimensions
论文作者
论文摘要
我们考虑一个单参数的复合场家族 - 在应力 - 能量张量的组件中的双线性 - 概括了$ \ mathrm {t} \ bar {\ mathrm {t}} $ operator operator to to nutary Appion dimension $ d \ geq 2 $。我们表明，根据特定的流动方程，它们诱导了与磁场依赖的磁场依赖性修改相同的经典作用的变形。即使起点是平坦的空间，对于任何$ d> 2 $，通常对变形度量弯曲，因此表明相应的变形不能解释为坐标转换。本文的中心部分致力于开发递归算法，以计算溶液扩展到度量流程方程的功率系列的系数。我们表明，在对应力 - 能量张量的一些相当限制的假设下，功率系列产生了精确的解决方案。最后，我们考虑了$ d = 4 $中的一类理论，其压力能量张量符合上述假设，即$ d = 4 $的阿贝里安仪表理论家族。对于这些理论，我们获得了变形度量和维尔贝因的确切表达。特别是，后者的结果意味着，在特定弯曲空间中的Modmax理论在动态上等同于其在平坦空间中的出生攻击样延伸。我们还讨论了后者理论从$ d = 4 $减少到$ d = 2 $，其中出现了有趣的边缘变形$ d = 2 $ field理论。
We consider a one-parameter family of composite fields -- bi-linear in the components of the stress-energy tensor -- which generalise the $\mathrm{T}\bar{\mathrm{T}}$ operator to arbitrary space-time dimension $d\geq 2$. We show that they induce a deformation of the classical action which is equivalent -- at the level of the dynamics -- to a field-dependent modification of the background metric tensor according to a specific flow equation. Even though the starting point is the flat space, the deformed metric is generally curved for any $d>2$, thus implying that the corresponding deformation can not be interpreted as a coordinate transformation. The central part of the paper is devoted to the development of a recursive algorithm to compute the coefficients of the power series expansion of the solution to the metric flow equation. We show that, under some quite restrictive assumptions on the stress-energy tensor, the power series yields an exact solution. Finally, we consider a class of theories in $d=4$ whose stress-energy tensor fulfils the assumptions above mentioned, namely the family of abelian gauge theories in $d=4$. For such theories, we obtain the exact expression of the deformed metric and the vierbein. In particular, the latter result implies that ModMax theory in a specific curved space is dynamically equivalent to its Born-Infeld-like extension in flat space. We also discuss a dimensional reduction of the latter theories from $d=4$ to $d=2$ in which an interesting marginal deformation of $d=2$ field theories emerges.
