arXiv subjects

Gabriele Travaglini

Publications and source records attributed to Gabriele Travaglini.

At least 37 records · Page 2Linked to original sources

arXiv2019

A note on the absence of $R^2$ corrections to Newton's potential

We consider Einstein gravity with the addition of $R^2$ and $R^{μν} R_{μν}$ interactions in the context of effective field theory, and the corresponding scattering amplitudes of gravitons and minimally-coupled heavy scalars. First, we recover the known fact that graviton amplitudes are the same as in Einstein gravity. Then we show that all amplitudes with two heavy scalars and an arbitrary number of gravitons are also not affected by these interactions. We prove this by direct computations, using field redefinitions known from earlier applications in string theory, and with a combination of factorisation and power-counting arguments. Combined with unitarity, these results imply that, in an effective field theory approach, the Newtonian potential receives neither classical nor quantum corrections from terms quadratic in the curvature.

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arXiv2019

Dual conformal invariance for form factors

Form factors of the stress-tensor multiplet operator in $\mathcal{N}=4$ supersymmetric Yang-Mills reveal surprisingly simple structures similar to those appearing in scattering amplitudes. In this paper we show that, as for the case of amplitudes, they also enjoy dual conformal symmetry. We compute the dual conformal anomaly at one loop for an arbitrary number of particles and generic helicities, which matches the expression of the dual conformal anomaly of amplitudes, and perform explicit checks for MHV and NMHV one-loop form factors. In the NMHV case the realisation of dual conformal symmetry requires a delicate cancellation of offending terms arising from three-mass triangles, which we explicitly check in the case of the four-point NMHV form factor.

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arXiv2019

Complete Form Factors in Yang-Mills from Unitarity and Spinor Helicity in Six Dimensions

We present a systematic procedure to compute complete, analytic form factors of gauge-invariant operators at loop level in pure Yang-Mills. We consider applications to operators of the form $\mathrm{Tr}\, F^n$ where $F$ is the gluon field strength. Our approach is based on an extension to form factors of the dimensional reconstruction technique, in conjunction with the six-dimensional spinor-helicity formalism and generalised unitarity. For form factors this technique requires the introduction of additional scalar operators, for which we provide a systematic prescription. We also discuss a generalisation of dimensional reconstruction to any number of loops, both for amplitudes and form factors. Several novel results for one-loop minimal and non-minimal form factors of $\mathrm{Tr}\, F^n$ with $n>2$ are presented. Finally, we describe the \texttt{Mathematica} package \texttt{SpinorHelicity6D}, which is tailored to handle six-dimensional quantities written in the spinor-helicity formalism.

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arXiv2018

The SU(2|3) dynamic two-loop form factors

We compute two-loop form factors of operators in the $SU(2|3)$ closed subsector of $N=4$ supersymmetric Yang-Mills. In particular, we focus on the non-protected, dimension-three operators $\mathrm{Tr} (X[Y,Z])$ and $\mathrm{Tr} ( ψψ)$ for which we compute the four possible two-loop form factors, and corresponding remainder functions, with external states $\langle \bar{X} \bar{Y} \bar{Z}|$ and $\langle \barψ \barψ|$. Interestingly, the maximally transcendental part of the two-loop remainder of $\langle\bar{X} \bar{Y} \bar{Z}| \mathrm{Tr} (X[Y,Z]) |0\rangle$ turns out to be identical to that of the corresponding known quantity for the half-BPS operator $\mathrm{Tr} (X^3)$. We also find a surprising connection between the terms subleading in transcendentality and certain a priori unrelated remainder densities introduced in the study of the spin chain Hamiltonian in the SU(2) sector. Next, we use our calculation to resolve the mixing, recovering anomalous dimensions and eigenstates of the dilatation operator in the SU(2|3) sector at two loops. We also speculate on potential connections between our calculations in $N=4$ super Yang-Mills and Higgs + multi-gluon amplitudes in QCD in an effective Lagrangian approach.

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arXiv2018

Form factor recursion relations at loop level

We introduce a prescription to define form factor integrands at loop level in planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory. This relies on a periodic kinematic configuration that has been instrumental to describe form factors at strong coupling in terms of periodic Wilson loops. With this prescription, we are able to formulate loop-level recursion relations for planar form factor integrands, using a two-line (BCFW) and an all-line shift. We also point out important differences with the known recursion relations of integrands of planar loop amplitudes. We present a number of concrete one-loop examples to illustrate and validate our prescription for form factor integrands.

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arXiv2018

$\text{Tr}(F^3)$ supersymmetric form factors and maximal transcendentality Part II: $0<\mathcal{N}<4$ super Yang-Mills

The study of form factors has many phenomenologically interesting applications, one of which is Higgs plus gluon amplitudes in QCD. Through effective field theory techniques these are related to form factors of various operators of increasing classical dimension. In this paper we extend our analysis of the first finite top-mass correction, arising from the operator ${\rm Tr} (F^3)$, from $\mathcal{N}=4$ super Yang-Mills to theories with $\mathcal{N}<4$, for the case of three gluons and up to two loops. We confirm our earlier result that the maximally transcendental part of the associated Catani remainder is universal and equal to that of the form factor of a protected trilinear operator in the maximally supersymmetric theory. The terms with lower transcendentality deviate from the $\mathcal{N}=4$ answer by a surprisingly small set of terms involving for example $ζ_2$, $ζ_3$ and simple powers of logarithms, for which we provide explicit expressions.

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arXiv2018

$\text{Tr}(F^3)$ supersymmetric form factors and maximal transcendentality Part I: $\mathcal{N}=4$ super Yang-Mills

In the large top-mass limit, Higgs plus multi-gluon amplitudes in QCD can be computed using an effective field theory. This approach turns the computation of such amplitudes into that of form factors of operators of increasing classical dimension. In this paper we focus on the first finite top-mass correction, arising from the operator ${\rm Tr}(F^3)$, up to two loops and three gluons. Setting up the calculation in the maximally supersymmetric theory requires identification of an appropriate supersymmetric completion of ${\rm Tr}(F^3)$, which we recognise as a descendant of the Konishi operator. We provide detailed computations for both this operator and the component operator ${\rm Tr}(F^3)$, preparing the ground for the calculation in $\mathcal{N}<4$, to be detailed in a companion paper. Our results for both operators are expressed in terms of a few universal functions of transcendental degree four and below, some of which have appeared in other contexts, hinting at universality of such quantities. An important feature of the result is a delicate cancellation of unphysical poles appearing in soft/collinear limits of the remainders which links terms of different transcendentality. Our calculation provides another example of the principle of maximal transcendentality for observables with non-trivial kinematic dependence.

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arXiv2018

All rational one-loop Einstein-Yang-Mills amplitudes at four points

All four-point mixed gluon-graviton amplitudes in pure Einstein-Yang-Mills theory with at most one state of negative helicity are computed at one-loop order and maximal powers of the gauge coupling using D-dimensional generalized unitarity. The resulting purely rational expressions take very compact forms. We comment on the color-kinematics duality picture and a relation to collinear limits of pure gluon amplitudes.

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arXiv2017

Higgs amplitudes from $\mathcal{N}=4$ super Yang-Mills theory

Higgs plus multi-gluon amplitudes in QCD can be computed in an effective Lagrangian description. In the infinite top-mass limit, an amplitude with a Higgs and $n$ gluons is computed by the form factor of the operator ${\rm Tr}\, F^2$. Up to two loops and for three gluons, its maximally transcendental part is captured entirely by the form factor of the protected stress tensor multiplet operator $\mathcal{T}_2$ in $\mathcal{N}=4$ supersymmetric Yang-Mills theory. The next order correction involves the calculation of the form factor of the higher-dimensional, trilinear operator ${\rm Tr}\, F^3$. We present explicit results at two loops for three gluons, including the subleading transcendental terms derived from a particular descendant of the Konishi operator that contains ${\rm Tr}\, F^3$. These are expressed in terms of a few universal building blocks already identified in earlier calculations. We show that the maximally transcendental part of this quantity, computed in non-supersymmetric Yang-Mills theory, is identical to the form factor of another protected operator, $\mathcal{T}_3$, in the maximally supersymmetric theory. Our results suggest that the maximally transcendental part of Higgs amplitudes in QCD can be entirely computed through $\mathcal{N}=4$ super Yang-Mills.

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arXiv2016

The connected prescription for form factors in twistor space

We propose a connected prescription formula in twistor space for all tree-level form factors of the stress tensor multiplet operator in $\mathcal{N}=4$ super Yang-Mills, which is a generalisation of the expression of Roiban, Spradlin and Volovich for superamplitudes. By introducing link variables, we show that our formula is identical to the recently proposed four-dimensional scattering equations for form factors. Similarly to the case of amplitudes, the link representation of form factors is shown to be directly related to BCFW recursion relations, and is considerably more tractable than the scattering equations. We also discuss how our results are related to a recent Grassmannian formulation of form factors, and comment on a possible derivation of our formula from ambitwistor strings.

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arXiv2015

One-Loop Soft Theorems via Dual Superconformal Symmetry

We study soft theorems at one loop in planar N=4 super Yang-Mills theory through finite order in the infrared regulator and to subleading order in the soft parameter δ. In particular, we derive a universal constraint from dual superconformal symmetry, which we use to bootstrap subleading log δ behaviour. Moreover, we determine the complete infrared-finite subleading soft contribution of n-point MHV amplitudes using momentum twistors. Finally, we compute the subleading log δ behaviour of one-loop NMHV ratio functions at six and seven points, finding that universality holds within but not between helicity sectors.

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arXiv2015

On Yangian symmetry of scattering amplitudes and the dilatation operator in N=4 super Yang-Mills

It is known that the Yangian of PSU(2,2|4) is a symmetry of the tree-level S-matrix of N=4 super Yang-Mills. On the other hand, the complete one-loop dilatation operator in the same theory commutes with the level-one Yangian generators only up to certain boundary terms found by Dolan, Nappi and Witten. Using a result by Zwiebel, we show how the Yangian symmetry of the tree-level S-matrix of N=4 super Yang-Mills implies precisely the Yangian invariance, up to boundary terms, of the one-loop dilatation operator.

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arXiv2015

Integrability and unitarity

We show how generalised unitarity can be used to determine the one-loop dilatation operator in N=4 super Yang-Mills. Our analysis focuses on two sectors, namely the bosonic SO(6) sector and the SU(2|3) sector. The calculation is performed on shell, with no off-shell information introduced at any stage. In this way, we establish a direct connection between scattering amplitudes and the dilatation operator of the N=4 theory.

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arXiv2015

Double-Soft Limits of Gluons and Gravitons

The double-soft limit of gluon and graviton amplitudes is studied in four dimensions at tree level. In general this limit is ambiguous and we introduce two natural ways of taking it: A consecutive double-soft limit where one particle is taken soft before the other and a simultaneous limit where both particles are taken soft uniformly. All limits yield universal factorisation formulae which we establish by BCFW recursion relations down to the subleading order in the soft momentum expansion. These formulae generalise the recently discussed subleading single-soft theorems. While both types of limits yield identical results at the leading order, differences appear at the subleading order. Finally, we discuss double-scalar emission in $\mathcal{N}=4$ super Yang-Mills theory. These results should be of use in establishing the algebraic structure of potential hidden symmetries in the quantum gravity and Yang-Mills S-matrix.

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arXiv2015

Integrability and MHV diagrams in N=4 supersymmetric Yang-Mills theory

We apply MHV diagrams to the derivation of the one-loop dilatation operator of N=4 super Yang-Mills in the SO(6) sector. We find that in this approach the calculation reduces to the evaluation of a single MHV diagram in dimensional regularisation. This provides the first application of MHV diagrams to an off-shell quantity. We also discuss other applications of the method and future directions.

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arXiv2014

On super form factors of half-BPS operators in N=4 super Yang-Mills

We compute form factors of half-BPS operators in N=4 super Yang-Mills dual to massive Kaluza-Klein modes in supergravity. These are appropriate supersymmetrisations T_k of the scalar operators Tr(ϕ^k) for any k, which for k=2 give the chiral part of the stress-tensor multiplet operator. Using harmonic superspace, we derive simple Ward identities for these form factors, which we then compute perturbatively at tree level and one loop. We propose a novel on-shell recursion relation which links form factors with different numbers of fields. Using this, we conjecture a general formula for the n-point MHV form factors of T_k for arbitrary k and n. Finally, we use supersymmetric generalised unitarity to derive compact expressions for all one-loop MHV form factors of T_k in terms of one-loop triangles and finite two-mass easy box functions.

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arXiv2014

The last of the simple remainders

We compute the n-point two-loop form factors of the half-BPS operators Tr(phi_{AB}^n) in N=4 super Yang-Mills for arbitrary n >2 using generalised unitarity and symbols. These form factors are minimal in the sense that the n^{th} power of the scalar field in the operator requires the presence of at least n on-shell legs. Infrared divergences are shown to exponentiate as for amplitudes, reproducing the known cusp and collinear anomalous dimensions at two loops. We define appropriate infrared-finite remainder functions and compute them analytically for all n. The results obtained by using the known expressions of the integral functions involve complicated combinations of Goncharov multiple polylogarithms, but we show that much simpler expressions can in fact be derived using the symbol of transcendental functions. For n=3 we find a very compact remainder function expressed in terms of classical polylogarithms only. For arbitrary n>3 we are able to write all the remainder functions in terms of a single compact building block, expressed as a sum of classical polylogarithms augmented by two multiple polylogarithms. The decomposition of the symbol into specific components is crucial in order to single out a natural combination of multiple polylogarithms. Finally, we analyse in detail the behaviour of these minimal form factors in collinear and soft limits, which deviates from the usual behaviour of amplitudes and non-minimal form factors.

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arXiv2014

Simplifying instanton corrections to N=4 SYM correlators

We compute instanton corrections to non-minimal correlation functions of chiral primary operators in the N=4 super Yang-Mills super-current multiplet. Using a representation in terms of Mellin integrals, we find that these corrections can be written as conformal integrals in AdS_5 times certain "kinematic" prefactors that are independent of the instanton moduli. We then consider the consecutive, pairwise light-like limit x_{i, i+1}^2 -> 0 of such correlators, and prove that the ratio between the instanton contribution and the corresponding tree-level expression vanishes in this limit. We also speculate on the extension to the non-perturbative level of the proposed duality with polygonal Wilson loops and briefly discuss its potential implications for scattering amplitudes.

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