Amplitude relations in non-linear sigma model

140

221

In this paper we derive the tree-level S-matrix of the effective theory of Goldstone bosons known as the non-linear sigma model (NLSM) from string theory. This novel connection relies on a recent realization of tree-level open-superstring S-matrix predictions as a double copy of super-Yang-Mills theory with Z-theory -the collection of putative scalar effective field theories encoding all the α ′ -expansion of the open superstring. Here we identify the color-ordered amplitudes of the NLSM as the low-energy limit of abelian Z-theory. This realization also provides natural higher-derivative corrections to the NLSM amplitudes arising from higher powers of α ′ in the abelian Z-theory amplitudes, and through double copy also to Born-Infeld and Volkov-Akulov theories. The amplitude relations due to Kleiss-Kuijf as well as Bern, Johansson and one of the current authors obeyed by Z-theory amplitudes thereby apply to all α ′ -corrections of the NLSM. As such we naturally obtain a cubic-graph parameterization for the abelian Z-theory predictions whose kinematic numerators obey the duality between color and kinematics to all orders in α ′ .

Section: Jhep06(2017)093mentioning

confidence: 99%

Section: Jhep06(2017)093mentioning

confidence: 99%

Section: Jhep06(2017)093mentioning

confidence: 99%

See 1 more Smart Citation

Abelian Z-theory: NLSM amplitudes and α ′ -corrections from the open string

Carrasco

Mafra

Schlotterer

2017

140

221

“…This indeed suggests their uniqueness, and though of completely different nature, it hints to deeper connections with gauge theory and gravity. It is probably one of the main motivation behind the recent increase of activities in studying theoretical properties of NLSM: [21][22][23][24][25][26][27][28][29][30][31][32][33]. This effort demonstrates the importance of NLSM; however, these studies mainly concentrated only on the leading, two-derivative (O(p 2 )) order.…”

Section: Contentsmentioning

confidence: 99%

Higher-order tree-level amplitudes in the nonlinear sigma model

Bijnens

Kampf

Sjö

2019

We present a generalisation of the flavour-ordering method applied to the chiral nonlinear sigma model with any number of flavours. We use an extended Lagrangian with terms containing any number of derivatives, organised in a power-counting hierarchy. The method allows diagrammatic computations at tree-level with any number of legs at any order in the power-counting. Using an automated implementation of the method, we calculate amplitudes ranging from 12 legs at leading order, O(p 2 ), to 6 legs at next-tonext-to-next-to-leading order, O(p 8 ). In addition to this, we generalise several properties of amplitudes in the nonlinear sigma model to higher orders. These include the double soft limit and the uniqueness of stripped amplitudes.

“…There is a dictionary for the squaring relations between amplitudes in lower supersymmetric theories with different matter content (see e.g. [76]) and even for some effective field theories [77].…”

Section: Gravity From Yang-millsmentioning

confidence: 99%

Gravity on-shell diagrams

Herrmann

Trnka

2016

We study on-shell diagrams for gravity theories with any number of supersymmetries and find a compact Grassmannian formula in terms of edge variables of the graphs. Unlike in gauge theory where the analogous form involves only d log-factors, in gravity there is a non-trivial numerator as well as higher degree poles in the edge variables. Based on the structure of the Grassmannian formula for N = 8 supergravity we conjecture that gravity loop amplitudes also possess similar properties. In particular, we find that there are only logarithmic singularities on cuts with finite loop momentum and that poles at infinity are present, in complete agreement with the conjecture presented in [1].