Four-graviton couplings in the low energy effective action of type II string vacua compactified on tori are strongly constrained by supersymmetry and U-duality. While the $R^4$ and $D^4 R^4$ couplings are known exactly in terms of Langlands-Eisenstein series of the U-duality group, the $D^6 R^4$ couplings are not nearly as well understood. Exploiting the coincidence of the U-duality group in $D=6$ with the T-duality group in $D=5$, we propose an exact formula for the $D^6 R^4$ couplings in type II string theory compactified on $T^4$, in terms of a genus-two modular integral plus a suitable Eisenstein series. The same modular integral computes the two-loop correction to $D^6 R^4$ in 5 dimensions, but here provides the non-perturbative completion of the known perturbative terms in $D=6$. This proposal hinges on a systematic re-analysis of the weak coupling and large radius of the $D^6 R^4$ in all dimensions $D\geq 3$, which fills in some gaps and resolves some inconsistencies in earlier studies.
We provide a systematic method to compute tree-level scattering amplitudes with spinning external states from amplitudes with scalar external states in arbitrary spacetime dimensions. We write down analytic answers for various scattering amplitudes, including the four graviton amplitude due to the massive spin $J$ exchange. We verify the results by computing angular distributions in 3 + 1 dimensions using various identities involving Jacobi polynomials.
Automorphic properties of low energy string amplitudes in various dimensions
本文研究了d-环面上紧化的最大超对称弦论的四引力子振幅的低能展开中出现的高阶导数相互作用的模依赖系数。这些自守函数是通过施加各种相容性条件来确定的，对于D ^6 R ^4阶以下的项和不同的d值。它们满足拉普拉斯本征值方程，有或没有源项，其解决方案给出的爱森斯坦级数，或更一般的自守函数，某些抛物子群的相关U-对偶群。尽管弦论的表达式是有限的，但相应的超引力场论极限的紫外发散被编码在不同的符号中。这个分析包括有趣的SL（d）和SO（d，d）爱森斯坦级数的超环面紧化的单圈和双圈弦和超重力振幅的表示。
The field of scattering amplitudes plays a central role in elementary-particle physics. This includes various problems of broader interest for collider physics, gravitational physics, and fundamental principles underlying quantum field theory. We describe various applications and theoretical advances pointing towards novel descriptions of quantum field theories. Comments on future prospects are included.
A conjecture made by Bern, Dixon, Dunbar, and Kosower asserts a simple dimension-shifting relationship between the one-loop structure of N = 4 MHV amplitudes and all-plus helicity amplitudes in pure Yang-Mills theory. We prove this conjecture to all orders in dimensional regularisation using unitarity cuts, and evaluate the form of these simplest one-loop amplitudes using a generalised D-dimensional unitarity technique which captures the full amplitude to all multiplicities.
We compute the normalization of the D-instanton amplitudes in type 0B string theory in two dimensions and find perfect agreement with the dual matrix model result.
The recently introduced anomaly-free twistor string in 4 dimensions is further explored. The spectrum based on the physical states and its Minkowski interpretation are examined. Scattering amplitudes with vertex operators involving gravitons and fermions are computed and are compared with Einstein-Yang-Mills amplitudes. Tree and one-loop scattering amplitudes are shown to have proper unitary factorization properties. Finally a string field theory is proposed.
The recursive expansion of tree level multitrace Einstein-Yang-Mills (EYM) amplitudes induces a refined graphic expansion, by which any tree-level EYM amplitude can be expressed as a summation over all possible refined graphs. Each graph contributes a unique coefficient as well as a proper combination of color-ordered Yang-Mills (YM) amplitudes. This expansion allows one to evaluate EYM amplitudes through YM amplitudes, the latter have much simpler structures in four dimensions than the former. In this paper, we classify the refined graphs for the expansion of EYM amplitudes into $\text{N}^{\,…
Positivity of the Veneziano Amplitude in Ten Dimensions
Mani L. Bhaumik Institute for Theoretical Physics Department of Physics and Astronomy University of California, Los Angeles（加州大学洛杉矶分校曼尼·L·巴乌米克理论物理学院物理与天文学系）
In four dimensions, a tree-level double-trace Einstein-Yang-Mills (EYM) amplitude with two negative-helicity gluons (the $(g^-,g^-)$-configuration) satisfies a symmetric spanning forest formula, which was derived from the graphic expansion rule. On another hand, in the framework of Cachazo-He-Yuan (CHY) formula, the maximally-helicity-violating (MHV) amplitudes are supported by the MHV solution of scattering equations. The relationship between the symmetric formula for double-trace amplitudes, and the MHV sector of Cachazo-He-Yuan (CHY) formula in four dimensions is still not clear. In this no…
We investigate properties of four point colour ordered scattering amplitudes in D=6 fishnet CFT. We show that such amplitudes are related via very simple relation to their D=4 counterparts considered previously in the literature. Exploiting this relation we obtain closed expression for such amplitudes and investigate its behaviour at weak and strong coupling. As by product of this investigation we also obtain generating function for on-shell D=6 Box ladder diagrams with l rungs.
We consider UV divergences for the on-shell planar gluon-gluon scattering amplitudes in the gauge theory in arbitrary D-dimensions in the one-loop order. The amplitudes are evaluated using the standard Feynman diagram technique for several choices of external gluon polarizations. Using the Passarino - Veltman reduction, the expansion in terms of the scalar master integrals is constructed and their calculation is performed within dimensional regularization. The resulting expressions are confronted with existing results for various cases, including maximally supersymmetric theories in D=4, 6, 8,…
We derive the static Schwarzschild-Tangherlini metric by extracting the classical contributions from the multi-loop vertex functions of a graviton emitted from a massive scalar field. At each loop orders the classical contribution is proportional to a unique master integral given by the massless sunset integral. By computing the scattering amplitudes up to three-loop order in general dimension, we explicitly derive the expansion of the metric up to the fourth post-Minkowskian order $O(G_N^4)$ in four, five and six dimensions. There are ultraviolet divergences that are cancelled with the introd…
The analyticity properties of the scattering amplitude for a massive scalar field is reviewed in this article where the spacetime geometry is $R^{3,1}\otimes S^1$ i.e. one spatial dimension is compact. Khuri investigated the analyticity of scattering amplitude in a nonrelativitstic potential model in three dimensions with an additional compact dimension. He showed that, under certain circumstances, the forward amplitude is nonanalytic. He argued that in high energy scattering if such a behaviour persists it would be in conflicts with the established results of quantum field theory and LHC migh…
D-instanton amplitudes suffer from various infrared divergences associated with tachyonic or massless open string modes, leading to ambiguous contribution to string amplitudes. It has been shown previously that string field theory can resolve these ambiguities and lead to unambiguous expressions for D-instanton contributions to string amplitudes, except for an overall normalization constant that remains undetermined. In this paper we show that string field theory, together with the world-sheet description of the amplitudes, can also fix this normalization constant. We apply our analysis to the…
To our best knowledge, the leading non-perturbative stringy interaction between an NS brane and a Dp brane remains unknown. We here present the non-perturbative stringy amplitudes for a system of an F-string and a Dp brane and a system of an NS 5 brane and a Dp brane for $0 \le p \le 6$. In either case, the F or NS5 and the Dp are placed parallel at a separation. We obtain the respective amplitudes, starting from the amplitude for a system of a D1 and a D3 for the former and that for a system of a D5 and a D3 system for the latter, based on the IIB S-duality and various T-dualities plus the co…
We prove the conjecture made by Bern, Dixon, Dunbar, and Kosower that describes a simple dimension shifting relationship between the one-loop structure of N = 4 MHV amplitudes and all-plus helicity amplitudes in pure Yang-Mills theory. The proof captures all orders in dimensional regularisation using unitarity cuts, by combining massive spinor-helicity with Coulomb-branch supersymmetry. The form of these amplitudes can be given in terms of pentagon and box integrals using a generalised D-dimensional unitarity technique which captures the full amplitude to all multiplicities.
We explore how various topics in modern scattering amplitudes research find application in the description of collider physics processes. After a brief review of experimentally measured quantities and how they are related to amplitudes, we summarise recent developments in perturbative QFT, and how they have impacted our ability to do precision physics with colliders. Next, we explain how the study of (next-to-)soft radiation is directly relevant to increasing theoretical precision for key processes at the LHC and related experiments. Finally, we describe the various techniques that are used to…
On-shell amplitude methods allow to derive one-loop renormalization effects from just tree-level amplitudes, with no need of loop calculations. We derive a simple formula to obtain the anomalous dimensions of higher-dimensional operators from a product of tree-level amplitudes. We show how this works for dimension-6 operators of the Standard Model, providing explicit examples of the simplicity, elegance and efficiency of the method. Many anomalous dimensions can be calculated from the same Standard Model tree-level amplitude, displaying the attractive recycling aspect of the on-shell method. W…
This article discusses a prescription to compute polarized dimensionally regularized amplitudes, providing a recipe for constructing simple and general polarized amplitude projectors in D dimensions that avoids conventional Lorentz tensor decomposition and avoids also dimensional splitting. Because of the latter, commutation between Lorentz index contraction and loop integration is preserved within this prescription, which entails certain technical advantages. The usage of these D-dimensional polarized amplitude projectors results in helicity amplitudes that can be expressed solely in terms of…
