arXiv 1905.093132019-05-30hep-thgr-qc

Noether恒等式、$β$ -函数和DFT中的对称性

Noether Identities, $β$-functions and symmetries in DFT

J. Antonio García, R. Abraham Sánchez-Isidro

备注：: Latex 16 pages, v2 references added

摘要：

给定封闭弦σ模型的$β$函数，直到$α'$中的一个循环，有效作用量实现条件$β=0$以保持量子水平的共形对称性。弦论的一个更有力、更引人注目的结果是，这种有效作用量包含了爱因斯坦引力作为时空中涌现的动力学。本文从$β$函数及其与有效作用量运动方程的关系出发，证明了微分恒等式[1]是与有效作用量及其规范对称性有关的Noether恒等式。从这里，我们重建规范和时空对称性的有效作用量。进而证明了微分恒等式是场强$H$和黎曼张量$R$的压缩Bianchi恒等式。接下来，我们将同样的思想应用于DFT。以DFT中的广义$β$函数与运动方程成正比为出发点，构造了DFT中的广义微分恒等式。将Noether恒等式与DFT的压缩Bianchi恒等式联系起来，我们能够重建广义规范和时空对称性。最后，我们恢复原来的$β$功能，有效的行动，微分身份，和对称性时，我们关闭的$\tilde x$从DFT的时空坐标。

英文摘要：

Given the $β$ functions of the closed string sigma model up to one loop in $α'$, the effective action implement the condition $β=0$ to preserve conformal symmetry at quantum level. One of the more powerful and striking results of string theory is that this effective action contains Einstein gravity as an emergent dynamics in space-time. We show from the $β$ functions and its relation with the equations of motion of the effective action, that the differential identities [1] are the Noether identities associated with the effective action and its gauge symmetries. From here, we reconstruct the gauge and space time symmetries of the effective action. In turn, we can show that the differential identities are the contracted Bianchi identities of the the field strength $H$ and Riemann tensor $R$. Next, we apply the same ideas to DFT. Taking as starting point that the generalized $β$ functions in DFT are proportional to the equations of motion, we construct the generalized differential identities in DFT. Relating the Noether identities with the contracted Bianchi identities of DFT, we were able to reconstruct the generalized gauge and space time symmetries. Finally, we recover the original $β$ functions, effective action, differential identities, and symmetries when we turn off the $\tilde x$ space time coordinates from DFT.

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