On three-algebra and bi-fundamental matter amplitudes and integrability of supergravity

140

232

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%

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

Carrasco

Mafra

Schlotterer

2017

140

232

“…One may choose the numerator factor of such a graph in at least two different ways. On the one hand one can use these relations to simplify all products of orbifold group elements and simply read off the coefficient of 12 This identity can be proven using (2.3) to show that gT A g † = g AB T B and expressing the structure constants asf…”

Section: Loop-level Amplitudesmentioning

confidence: 99%

“…Its scattering amplitudes have been extensively studied. The formulation of color/kinematics duality, discussed and explored in [11,12], was aided by the three-algebra formulation of this theory, in which all propagating fields formally carry a single (adjoint-like) color index.…”

Section: Jhep01(2014)152 1 Introductionmentioning

confidence: 99%

Color/kinematics duality for general abelian orbifolds of $ \mathcal{N} $ = 4 super Yang-Mills theory

Chiodaroli

Jin

Roiban

2014

138

To explore color/kinematics duality for general representations of the gauge group we formulate the duality for general abelian orbifolds of the SU(N ), N = 4 super Yang-Mills theory in four dimensions, which have fields in the bi-fundamental representation, and use it to construct explicitly complete four-vector and four-scalar amplitudes at one loop. For fixed number of supercharges, graph-organized L-loop n-point integrands of all orbifold theories are given in terms of a fixed set of polynomials labeled by L representations of the orbifold group. In contrast to the standard duality-satisfying presentation of amplitudes of the N = 4 super Yang-Mills theory, each graph may appear several times with different internal states. The color and R-charge flow provide a way to deform the amplitudes of orbifold theories to those of more general quiver gauge theories which do not necessarily exhibit color/kinematics duality on their own.Based on the organization of amplitudes required by the duality between color and kinematics in orbifold theories we show how the amplitudes of certain non-factorized mattercoupled supergravity theories can be found through a double-copy construction.We also carry out a comprehensive search for theories with fields solely in the adjoint representation of the gauge group and amplitudes exhibiting color/kinematics duality for all external states and find an interesting relation between supersymmetry and existence of the duality.

“…Such a framework, in which both the kinematic and color part of an amplitude are treated symmetrically (and are given by instanton sums), is reminiscent of color/kinematics duality [42]. The kinematic part however exhibits localization on instantons of fixed degree; since a similar localization does seem to occur for the color-fermions, this may be a possible explanation for the absence of the duality for ABJ(M) amplitudes [43]. It would be interesting to explore whether the duality is restored if one restricts the "color instantons" to have the same degree as the "kinematic instantons".…”

Section: Jhep06(2014)088mentioning

confidence: 99%

A twistor string for the ABJ(M) theory

Engelund

Roiban

2014

Abstract:We construct an open string theory whose single-trace part of the tree-level Smatrix reproduces the S-matrix of the ABJ(M) theory with a unitary gauge group. We also demonstrate that the multi-trace part of the string theory tree-level S-matrix -which has no counterpart in the pure N = 6 super-Chern-Simons theory -is due to conformal supergravity interactions and identify certain Lagrangian interaction terms. Our construction suggests that there exists a higher dimensional theory which can be dimensionally-reduced, in a certain sense, to the ABJ(M) theory. It also suggests a generalization of this theory to product gauge groups with more than two factors.