arXiv subjects

Henrik Johansson

Publications and source records attributed to Henrik Johansson.

At least 55 records · Page 3Linked to original sources

arXiv2018

Heterotic and bosonic string amplitudes via field theory

Previous work has shown that massless tree amplitudes of the type I and IIA/B superstrings can be dramatically simplified by expressing them as double copies between field-theory amplitudes and scalar disk/sphere integrals, the latter containing all the $α'$-corrections. In this work, we pinpoint similar double-copy constructions for the heterotic and bosonic string theories using an $α'$-dependent field theory and the same disk/sphere integrals. Surprisingly, this field theory, built out of dimension-six operators such as $(D_μF^{μν})^2$, has previously appeared in the double-copy construction of conformal supergravity. We elaborate on the $α' \rightarrow \infty$ limit in this picture and derive new amplitude relations for various gauge-gravity theories from those of the heterotic string.

hep-th↗

arXiv2017

The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy

We use the recently developed generalized double-copy procedure to construct an integrand for the five-loop four-point amplitude of N=8 supergravity. This construction starts from a naive double copy of the previously computed corresponding amplitude of N=4 super-Yang-Mills theory. This is then systematically modified by adding contact terms generated in the context of the method of maximal unitarity cuts. For the simpler generalized cuts, whose corresponding contact terms tend to be the most complicated, we derive a set of formulas relating the contact contributions to the violations of the dual Jacobi identities in the relevant gauge-theory amplitudes. For more complex generalized unitarity cuts, which tend to have simpler contact terms associated with them, we use the method of maximal cuts more directly. The five-loop four-point integrand is a crucial ingredient towards future studies of ultraviolet properties of N=8 supergravity at five loops and beyond. We also present a nontrivial check of the consistency of the integrand, based on modern approaches for integrating over the loop momenta in the ultraviolet region.

hep-th↗

arXiv2017

Gauged supergravities and spontaneous SUSY breaking from the double copy

Supergravities with gauged R-symmetry and Minkowski vacua allow for spontaneous supersymmetry breaking and, as such, provide a framework for building supergravity models of phenomenological relevance. In this letter we initiate the study of double-copy constructions for these supergravities. We argue that, on general grounds, we expect their scattering amplitudes to be described by a double copy of the type: (Higgsed gauge theory) x (gauge theory with broken SUSY). We present a simple realization in which the resulting supergravity has U(1)_R gauge symmetry, spontaneously-broken N=2 supersymmetry, and massive gravitini. This is the first instance of a double-copy construction of a gauged supergravity and of a theory with spontaneously-broken supersymmetry. The construction extends in a straightforward manner to a large family of gauged Yang-Mills-Einstein supergravity theories with or without spontaneous gauge-symmetry breaking.

hep-th↗

arXiv2017

Two-loop supersymmetric QCD and half-maximal supergravity amplitudes

Using the duality between color and kinematics, we construct two-loop four-point scattering amplitudes in $\mathcal{N}=2$ super-Yang-Mills (SYM) theory coupled to $N_f$ fundamental hypermultiplets. Our results are valid in $D\le 6$ dimensions, where the upper bound corresponds to six-dimensional chiral $\mathcal{N}=(1,0)$ SYM theory. By exploiting a close connection with $\mathcal{N}=4$ SYM theory - and, equivalently, six-dimensional $\mathcal{N}=(1,1)$ SYM theory - we find compact integrands with four-dimensional external vectors in both the maximally-helicity-violating (MHV) and all-chiral-vector sectors. Via the double-copy construction corresponding $D$-dimensional half-maximal supergravity amplitudes with external graviton multiplets are obtained in the MHV and all-chiral sectors. Appropriately tuning $N_f$ enables us to consider both pure and matter-coupled supergravity, with arbitrary numbers of vector multiplets in $D=4$. As a bonus, we obtain the integrands of the genuinely six-dimensional supergravities with $\mathcal{N}=(1,1)$ and $\mathcal{N}=(2,0)$ supersymmetry. Finally, we extract the potential ultraviolet divergence of half-maximal supergravity in $D=5-2ε$ and show that it non-trivially cancels out as expected.

hep-th↗

arXiv2017

Complete construction of magical, symmetric and homogeneous N=2 supergravities as double copies of gauge theories

We show that scattering amplitudes in magical, symmetric or homogeneous N=2 Maxwell-Einstein supergravities can be obtained as double copies of two gauge theories, using the framework of color/kinematics duality. The left-hand-copy is N=2 super-Yang-Mills theory coupled to a hypermultiplet, whereas the right-hand-copy is a non-supersymmetric theory that can be identified as the dimensional reduction of a D-dimensional Yang-Mills theory coupled to P fermions. For generic D and P, the double copy gives homogeneous supergravities. For P=1 and D=7,8,10,14, it gives the magical supergravities. We compute explicit amplitudes, discuss their soft limit and study the UV-behavior at one loop.

hep-th↗

arXiv2017

Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies

Color/kinematics duality and the double-copy construction have proved to be systematic tools for gaining new insight into gravitational theories. Extending our earlier work, in this paper we introduce new double-copy constructions for large classes of spontaneously-broken Yang-Mills-Einstein theories with adjoint Higgs fields. One gauge-theory copy entering the construction is a spontaneously-broken (super-)Yang-Mills theory, while the other copy is a bosonic Yang-Mills-scalar theory with trilinear scalar interactions that display an explicitly-broken global symmetry. We show that the kinematic numerators of these gauge theories can be made to obey color/kinematics duality by exhibiting particular additional Lie-algebraic relations. We discuss in detail explicit examples with N=2 supersymmetry, focusing on Yang-Mills-Einstein supergravity theories belonging to the generic Jordan family in four and five dimensions, and identify the map between the supergravity and double-copy fields and parameters. We also briefly discuss the application of our results to N=4 supergravity theories. The constructions are illustrated by explicit examples of tree-level and one-loop scattering amplitudes.

hep-th↗

arXiv2017

Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy

Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills+ϕ^3 theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism. Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. For the single-graviton case, we give amplitudes to any loop order and obtain, through gauge invariance, new loop-level amplitude relations for Yang-Mills theory.

hep-th↗

arXiv2017

Conformal Gravity from Gauge Theory

We use the duality between color and kinematics to obtain scattering amplitudes in non-minimal conformal N=0,1,2,4 (super)gravity theories. Generic tree amplitudes can be constructed from a double copy between (super-)Yang-Mills theory and a new gauge theory built entirely out of dimension-six operators. The latter theory is marginal in six dimensions and contains modes with a wrong-sign propagator, echoing the behavior of conformal gravity. The dimension-six Lagrangian is uniquely determined by demanding that its scattering amplitudes obey the color-kinematics duality. The conformal gravity amplitudes obtained from the double copy are compared with the Berkovits-Witten twistor string and shown to agree up to at least eight points in the MHV sector. Our construction can be generalized in a number of ways. Adding scalars to the dimension-six theory gives Maxwell-Weyl gravity, and further adding phi^3 self-interactions among these scalars gives Yang-Mills-Weyl gravity. The latter is identified with Witten's twistor string for maximal N=4 supersymmetry. Deforming the dimension-six theory by adding a Yang-Mills term, m^2 F^2, gives a gauge theory that interpolates between marginal D=6 and D=4 theories. The corresponding double copy gives an interpolation between conformal gravity and Einstein gravity.

hep-th↗

arXiv2017

Gravity Amplitudes as Generalized Double Copies

Whenever the integrand of a gauge-theory loop amplitude can be arranged into a form where the BCJ duality between color and kinematics is manifest, a corresponding gravity integrand can be obtained simply via the double-copy procedure. However, finding such gauge-theory representations can be challenging, especially at high loop orders. Here we show that we can instead start from generic gauge-theory integrands, where the duality is not manifest, and apply a modified double-copy procedure to obtain gravity integrands that include contact terms generated by violations of dual Jacobi identities. We illustrate this with three-, four- and five-loop examples in N=8 supergravity.

hep-th↗

arXiv2015

Color-Kinematics Duality for QCD Amplitudes

We show that color-kinematics duality is present in tree-level amplitudes of quantum chromodynamics with massive flavored quarks. Starting with the color structure of QCD, we work out a new color decomposition for n-point tree amplitudes in a reduced basis of primitive amplitudes. These primitives, with k quark-antiquark pairs and (n-2k) gluons, are taken in the (n-2)!/k! Melia basis, and are independent under the color-algebra Kleiss-Kuijf relations. This generalizes the color decomposition of Del Duca, Dixon, and Maltoni to an arbitrary number of quarks. The color coefficients in the new decomposition are given by compact expressions valid for arbitrary gauge group and representation. Considering the kinematic structure, we show through explicit calculations that color-kinematics duality holds for amplitudes with general configurations of gluons and massive quarks. The new (massive) amplitude relations that follow from the duality can be mapped to a well-defined subset of the familiar BCJ relations for gluons. They restrict the amplitude basis further down to (n-3)!(2k-2)/k! primitives, for two or more quark lines. We give a decomposition of the full amplitude in that basis. The presented results provide strong evidence that QCD obeys the color-kinematics duality, at least at tree level. The results are also applicable to supersymmetric and D-dimensional extensions of QCD.

hep-ph↗

arXiv2015

Pure Gravities via Color-Kinematics Duality for Fundamental Matter

We give a prescription for the computation of loop-level scattering amplitudes in pure Einstein gravity, and four-dimensional pure supergravities, using the color-kinematics duality. Amplitudes are constructed using double copies of pure (super-)Yang-Mills parts and additional contributions from double copies of fundamental matter, which are treated as ghosts. The opposite-statistics states cancel the unwanted dilaton and axion in the bosonic theory, as well as the extra matter supermultiplets in supergravities. As a spinoff, we obtain a prescription for obtaining amplitudes in supergravities with arbitrary non-self-interacting matter. As a prerequisite, we extend the color-kinematics duality from the adjoint to the fundamental representation of the gauge group. We explain the numerator relations that the fundamental kinematic Lie algebra should satisfy. We give nontrivial evidence supporting our construction using explicit tree and loop amplitudes, as well as more general arguments.

hep-th↗

arXiv2015

Cross-Order Integral Relations from Maximal Cuts

We study the ABDK relation using maximal cuts of one- and two-loop integrals with up to five external legs. We show how to find a special combination of integrals that allows the relation to exist, and how to reconstruct the terms with one-loop integrals squared. The reconstruction relies on the observation that integrals across different loop orders can have support on the same generalized unitarity cuts and can share global poles. We discuss the appearance of nonhomologous integration contours in multivariate residues. Their origin can be understood in simple terms, and their existence enables us to distinguish contributions from different integrals. Our analysis suggests that maximal and near-maximal cuts can be used to infer the existence of integral identities more generally.

hep-th↗

arXiv2015

Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity

We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N=2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian and Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which through the double copy are responsible for the non-abelian vector interactions in the supergravity theory. As a demonstration of the power of this structure, we present explicit computations at tree-level and one loop. The double-copy construction allows us to obtain compact expressions for the supergravity superamplitudes which are naturally organized as polynomials in the gauge coupling constant.

hep-th↗

arXiv2013

Color-Kinematics Duality in Multi-Regge Kinematics and Dimensional Reduction

In this note we study the applicability of the color-kinematics duality to the scattering of two distinguishable scalar matter particles with gluon emission in QCD, or graviton emission in Einstein gravity. Previous analysis suggested that direct use of the Bern-Carrasco-Johansson double-copy prescription to matter amplitudes does not reproduce the gravitational amplitude in multi-Regge kinematics. This situation, however, can be avoided by extensions to the gauge theory, while maintaning the same Regge limit. Here we present two examples of these extensions: the introduction of a scalar contact interaction and the relaxation of the distinguishability of the scalars. In both cases new diagrams allow for a full reconstruction of the correct Regge limit on the gravitational side. Both modifications correspond to theories obtained by dimensional reduction from higher-dimensional gauge theories.

hep-th↗

arXiv2013

Color-kinematics duality and dimensional reduction for graviton emission in Regge limit

In this talk we review the work in [1,2,3] where we have studied the applicability of the color-kinematics duality to the scattering of two distinguishable scalar matter particles with one gluon emission in QCD, or one graviton emission in Einstein gravity. We have shown that the duality works well in the Regge limit under two different extensions of the gauge theory: the introduction of a new scalar contact interaction and the relaxation of the distinguishability of the scalars. Both modifications correspond to theories obtained by dimensional reduction from higher-dimensional pure gauge theories.

hep-th↗

arXiv2013

On Three-Algebra and Bi-Fundamental Matter Amplitudes and Integrability of Supergravity

We explore tree-level amplitude relations for SU(N)xSU(M) bi-fundamental matter theories. Embedding the group-theory structure in a Lie three-algebra, we derive Kleiss-Kuijf-like relations for bi-fundamental matter theories in general dimension. We investigate the three-algebra color-kinematics duality for these theories. Unlike the Yang-Mills two-algebra case, the three-algebra Bern-Carrasco-Johansson relations depend on the spacetime dimension and on the detailed symmetry properties of the structure constants. We find the presence of such relations in three and two dimensions, and absence in D>3. Surprisingly, beyond six point, such relations are absent in the Aharony-Bergman-Jafferis-Maldacena theory for general gauge group, while the Bagger-Lambert-Gustavsson theory, and its supersymmetry truncations, obey the color-kinematics duality like clockwork. At four and six points the relevant partial amplitudes of the two theories are bijectively related, explaining previous results in the literature. In D=2 the color-kinematics duality gives results consistent with integrability of two-dimensional $\mathcal{N}=16$ supergravity: The four-point amplitude satisfies a Yang-Baxter equation; the six- and eight-point amplitudes vanish for certain kinematics away from factorization channels, as expected from integrability.

hep-th↗

arXiv2013

Equivalent D=3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories

We show that three-dimensional supergravity amplitudes can be obtained as double copies of either three-algebra super-Chern-Simons matter theory or that of two-algebra super-Yang-Mills theory, when either theory is organized to display the color-kinematics duality. We prove that only helicity-conserving four-dimensional gravity amplitudes have nonvanishing descendants when reduced to three dimensions; implying the vanishing of odd-multiplicity S-matrix elements, in agreement with Chern-Simons matter theory. We explicitly verify the double-copy correspondence at four and six points for N=12,10,8 supergravity theories and discuss its validity for all multiplicity.

hep-th↗

arXiv2012

An Overview of Maximal Unitarity at Two Loops

We discuss the extension of the maximal-unitarity method to two loops, focusing on the example of the planar double box. Maximal cuts are reinterpreted as contour integrals, with the choice of contour fixed by the requirement that integrals of total derivatives vanish on it. The resulting formulae, like their one-loop counterparts, can be applied either analytically or numerically.

hep-th↗