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arXiv 2012.13636hep-th
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非线性电动力学理论中的类$T\bar{T}$流和S-对偶

$T\bar{T}$-like Flows in Non-linear Electrodynamic Theories and S-duality

H. Babaei-Aghbolagh, Komeil Babaei Velni, Davood Mahdavian Yekta, H. Mohammadzadeh

备注：
24 pages, Minor corrections and new references, Accepted for publication in JHEP
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摘要：

本文研究了$D(=\!\!2n)$维时空中非线性电动力学理论的类$T\bar{T}$流。我们的分析仅限于变形问题的经典自由行动，采用建议的$T\bar{T}$运营商从一个简单的集成技术。我们表明，这个流动方程是兼容的$T\bar{T}$变形的标量场理论在$D\!=\!2$和非线性Born-Infeld型理论在$D\!=\!4$维。然而，我们的计算表明，这种$T\bar{T}$流在更高的维度是本质上不同于变形，已从AdS/CFT解释。事实上，可能作为这种有效玻恩-因费尔德作用量的全息对偶理论存在的引力不一定是AdS空间。作为$D\!=\!4$中的一个说明性研究，我们还将证明我们对$T\bar{T}$算子的构造保留了非超对称Born-Infeld理论的原始$SL(2,R)$对称性，以及$\mathcal{N}=2$超对称模型。结果表明，相应的$SL(2,R)$不变作用量确定了$D\!=\!4$中的$T\bar{T}$算符与能量动量张量二次型之间的关系.

英文摘要：

We investigate the $T\bar{T}$-like flows for non-linear electrodynamic theories in $D(=\!\!2n)$-dimensional spacetime. Our analysis is restricted to the deformation problem of the classical free action by employing the proposed $T\bar{T}$ operator from a simple integration technique. We show that this flow equation is compatible with $T\bar{T}$ deformation of a scalar field theory in $D\!=\!2$ and of a non-linear Born-Infeld type theory in $D\!=\!4$ dimensions. However, our computation discloses that this kind of $T\bar{T}$ flow in higher dimensions is essentially different from deformation that has been derived from the AdS/CFT interpretations. Indeed, the gravity that may be exist as a holographic dual theory of this kind of effective Born-Infeld action is not necessarily an AdS space. As an illustrative investigation in $D\!=\!4$, we shall also show that our construction for the $T\bar{T}$ operator preserves the original $SL(2,R)$ symmetry of a non-supersymmetric Born-Infeld theory, as well as $\mathcal{N}=2$ supersymmetric model. It is shown that the corresponding $SL(2,R)$ invariant action fixes the relationship between the $T\bar{T}$ operator and quadratic form of the energy-momentum tensor in $D\!=\!4$.

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