Double-logarithms in $$ \mathcal{N} $$ = 8 supergravity: impact parameter description &amp; mapping to 1-rooted ribbon graphs

Vera, Agustín Sabio

doi:10.1007/jhep07(2019)080

Cited by 9 publications

(17 citation statements)

References 35 publications

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“…Notice that these power-like contributions are different from the most logarithmically enhanced terms discussed in [70,71]. In theories with only spin 1 particles, the dominant terms in the Regge limit are proportional to (log 2 (t/s)) ℓ at ℓ loops.…”

Section: Discussionmentioning

confidence: 88%

A tale of two exponentiations in N=8 supergravity

et al. 2019

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High-energy massless gravitational scattering in N = 8 supergravity was recently analyzed at leading level in the deflection angle, uncovering an interesting connection between exponentiation of infrared divergences in momentum space and the eikonal exponentiation in impact parameter space. Here we extend that analysis to the first non trivial sub-leading level in the deflection angle which, for massless external particles, implies going to two loops, i.e. to third post-Minkowskian (3PM) order. As in the case of the leading eikonal, we see that the factorisation of the momentum space amplitude into the exponential of the one-loop result times a finite remainder hides some basic simplicity of the impact parameter formulation. For the conservative part of the process, the explicit outcome is infrared (IR) finite, shows no logarithmic enhancement, and agrees with an old claim in pure Einstein gravity, while the dissipative part is IR divergent and should be regularized, as usual, by including soft gravitational bremsstrahlung. Finally, using recent threeloop results, we test the expectation that eikonal formulation accounts for the exponentiation of the lower-loop results in the momentum space amplitude. This passes a number of highly non-trivial tests, but appears to fail for the dissipative part of the process at all loop orders and sufficiently subleading order in ǫ, hinting at some lack of commutativity of the relevant infrared limits for each exponentiation.

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Section: Discussionmentioning

confidence: 88%

A tale of two exponentiations in N=8 supergravity

et al. 2019

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“…More recently, further confirmation of [20] has been found at three loops for N = 8 supergravity in [22]. The DL amplitudes in this theory have been investigated in impact parameter representation, together with their mapping to the problem of counting 1-rooted ribbon graphs, in [23].…”

Section: Jhep01(2020)163mentioning

confidence: 91%

“…As explained in [23], there is a rich history for the coefficients C (8) n . They are present in many body theory [32], as combinatoric weights in QED [33] and in calculations of the polaron Green's function in solid state physics [34].…”

Section: Double Logarithms In Perturbation Theorymentioning

confidence: 99%

“…1 This is a different approach to the asymptotic, and less accurate, one presented in [23] for the N = 8…”

Section: Jhep01(2020)163mentioning

confidence: 99%

“…case. Since the DL resummation is valid in the s −t = q 2 limit it is natural to constrain the integration in the eikonal phase to the region where q < √ s. A second improvement is to consider the t dependence in the argument of the logarithms, which was treated as a subleading effect in [23]. This allows for a better description of the interplay between impact parameter and energy in the quantities here investigated.…”

Section: Jhep01(2020)163mentioning

confidence: 99%

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Double logarithms in $$ \mathcal{N} $$ ≥ 4 supergravity: weak gravity and Shapiro’s time delay

Vera

2020

J. High Energ. Phys.

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A study of the double logarithmic in the center-of-mass energy, s, contributions to the four-graviton scattering amplitude is presented for four-dimensional N ≥ 4 supergravities. This includes a novel representation for the coefficients of the perturbative expansion based on exactly solvable recurrences. A review is given of the structure in the complex angular momentum plane for the t-channel partial wave singularities of the different amplitudes. Working in impact parameter representation, ρ, it is shown that the resummation of double logarithms makes gravity weaker in regions of small ρ and large s. This screening of the gravitational interaction at short distances in the double logarithmic sector of the amplitudes is more acute as the number of gravitinos in the theory increases. It brings corrections to the eikonal phase which can change the sign of the graviton's deflection angle and generate regions with repulsive interaction. For very small impact parameters there appears a constant negative shift in both the eikonal phase and Shapiro's time delay which is not large enough to generate causality violation.The AdS/CFT correspondence [1-3] and the physics program at the Large Hadron Collider (LHC) have revamped the interest in the calculation of scattering amplitudes. Being fundamental for the former and an interesting simplified model for the latter, N = 4 supersymmetric Yang-Mills theory has played a pivotal role in recent developments. A very interesting finding [4] has been the double-copy structure linking this theory to N = 8 supergravity [5,6].An interesting limit where to investigate scattering amplitudes in gravitational theories, of relevance in the work here presented, is that of multi-Regge kinematics. In this case the center-of-mass energy squared, s, is asymptotically larger than all other Mandelstam invariants and amplitudes factorize in terms of impact factors and reggeized gravitons exchanged in the t-channel [7,8]. For gravity, eikonal contributions are also relevant together with double-logarithmic in s (DL) terms [9][10][11]. Both can be studied using the high energy effective action derived by Lipatov [12]. In this framework the leading contributions to scattering amplitudes are generated by bunches of produced gravitons well separated in rapidity from each other. The regions in rapidity without radiation have their origin in the exchange of reggeized gravitons. These are created (annihilated) in the t-channel by A ++ (A −− ) fields, which are subject to the constraints ∂ ± A ±± = 0 in order to generate the rapidity gaps. The local and non-local (in rapidity) effective interactions which appear in this context are described by the action given in [12]. It contains the Einstein-Hilbert action together with a kinetic term for the reggeon fields plus induced contributions. Within this setup it is possible to calculate the graviton Regge trajectory and those effective vertices needed to produce inelastic amplitudes.Connecting with the double-copy structure of gravity [13], it is remarkable t...

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Two-Loop Five-Particle Scattering Amplitudes

Zoia

2022

Modern Analytic Methods for Computing Scattering Amplitudes

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I discuss the recent advances in the computation of two-loop scattering amplitudes for five-particle processes. The latter are fundamental ingredients to obtain predictions at the next-to-next-toleading order (NNLO) in QCD for many interesting LHC processes. I discuss the state-of-the-art technology for computing scattering amplitudes analytically, and present new results relevant for the LHC phenomenology.

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Double-logarithms in $$ \mathcal{N} $$ = 8 supergravity: impact parameter description & mapping to 1-rooted ribbon graphs

Cited by 9 publications

References 35 publications

A tale of two exponentiations in N=8 supergravity

A tale of two exponentiations in N=8 supergravity

Double logarithms in $$ \mathcal{N} $$ ≥ 4 supergravity: weak gravity and Shapiro’s time delay

Two-Loop Five-Particle Scattering Amplitudes

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