String amplitudes from field-theory amplitudes and vice versa

M2 to D2 and vice versa by 3-Lie and Lie bialgebra

Using the concept of 3-Lie bialgebra, which has recently been defined in arXiv:1604.04475, we construct Bagger-Lambert-Gustavson (BLG) model for M2-brane on Manin triple of a special 3-Lie bialgebra. Then by using the correspondence and relation between those 3-Lie bialgebra with Lie bialgebra, we reduce this model to an $N=(4,4)$ WZW model (D2-brane), such that, its algebraic structure is a Lie bialgebra with one 2-cocycle. In this manner by using correspondence of 3-Lie bialgebra and Lie bialgebra (for this special 3-Lie algebra) one can construct M2-brane from a D2-brane and vice versa.

3-Leibniz bialgebra in $N=6$ Chern-Simons gauge theories, multiple M2 to D2 branes and vice versa

Constructing M2-brane and its boundary conditions from D2-brane and the related boundary conditions and vice versa has been possible in our recent work by using 3-Lie bialgebra for BLG model with N = 8 supersymmetry. This could be generalized for BL model with N = 6 by the concept of the 3-Leibniz bialgebra. The 3-Lie bialgebra is an especial case of 3-Leibniz bialgebra, then more comprehensive information will be obtained in this work. Consequently, according to the correspondence of these 3-Leibniz bialgebras with Lie bialgebras, we reduce to D2-brane such that with some restrictions on the …

Effect of the Gribov horizon on the Polyakov loop and vice versa

We consider finite temperature SU(2) gauge theory in the continuum formulation, which necessitates the choice of a gauge fixing. Choosing the Landau gauge, the existing gauge copies are taken into account by means of the Gribov-Zwanziger (GZ) quantization scheme, which entails the introduction of a dynamical mass scale (Gribov mass) directly influencing the Green functions of the theory. Here, we determine simultaneously the Polyakov loop (vacuum expectation value) and Gribov mass in terms of temperature, by minimizing the vacuum energy w.r.t. the Polyakov loop parameter and solving the Gribov…

违反CPT不会导致违反洛伦兹不变性，反之亦然

CPT Violation Does Not Lead to Violation of Lorentz Invariance and Vice Versa

提出了一类相互作用非定域量子场论，其中CPT不变性被破坏而Lorentz不变性存在。这一结果排除了文献中以前的主张，CPT违反意味着违反洛伦兹不变性。此外，存在这个定理的倒数，即洛伦兹不变性的破坏不会导致CPT破坏，只要洛伦兹不变性的剩余对称性允许粒子的适当表示理论。后者发生在非对易时空上的量子场论的情况下，它取代了破缺的洛伦兹对称性，拥有扭曲的庞加莱不变性。利用这种CPT违反交互和C违反的添加（例如，在弱相互作用中，由于组合相互作用引起的量子校正可能导致粒子和反粒子的不同性质，包括它们的质量。

吸引力与排斥力的交叉

Crossover from Attractive to Repulsive Casimir Forces and Vice Versa

系统描述的O（n）对称$ϕ^4$哈密顿被认为是在$d$维膜几何在其体临界点。薄膜的边界平面$\mathfrak{B}_j, j=1,2$之间的临界Casimir力，作为一般的保密边界条件$\partial_n\bmϕ=\mathring{c}_j\bmϕ$的薄膜厚度$L$的函数进行了研究。当$d<4$，其中$c_i$是与变量$\mathring{c}_i$相关的标度场，$Φ$是表面交叉指数时，单位横截面积的减少的过量自由能的$L$依赖部分采用标度形式$f_{\text{res}}\approx D(c_1L^{Φ/ν},c_2L^{Φ/ν})/L^{d-1}$。给出了在$d=4-ε$维下函数$D(\mathsf{c}_1,\mathsf{c}_2)$的显式双圈重整化群结果。这些结果表明：（i）Casimir力可以有任何一个符号，这取决于$\mathsf{c}_1$和$\mathsf{c}_2$，（ii）对于适当选择的增强$\mathring{c}_j$，从吸引到排斥的交叉，反之亦然，随着$L$的增加。

洛伦兹时空几何的扩展：从芬斯勒到嘉当，反之亦然

Extensions of Lorentzian spacetime geometry: From Finsler to Cartan and vice versa

我们简要地回顾了两个最近发展的时空洛伦兹几何的扩展，并证明它们实际上是密切相关的。第一个是观察者空间的概念，它概括了洛伦兹观察者的空间，即，未来的单位时间向量，使用嘉当几何。第二个是芬斯勒时空的概念，它将广义相对论的洛伦兹度规推广到依赖于爱因斯坦的芬斯勒度规。我们表明，每一个芬斯勒时空拥有一个定义良好的观察者空间，可以自然地配备了一个嘉当几何。相反，我们推导出条件下，观察者空间的嘉当几何产生芬斯勒时空。我们进一步表明，这两个结构是相辅相成的。最后，我们将我们的结构应用到两个引力理论，观察者空间上的MacDowell-Mandarin引力和Finsler引力，并将它们的作用从一个几何转换到另一个几何。