The structure of scattering amplitudes in supergravity theories continues to be of interest. Recently, the amplitude for $2\rightarrow 2$ scattering in ${\cal N}=8$ supergravity was presented at three-loop order for the first time. The result can be written in terms of an exponentiated one-loop contribution, modulo a remainder function which is free of infrared singularities, but contains leading terms in the high energy Regge limit. We explain the origin of these terms from a well-known, unitarity-restoring exponentiation of the high-energy gravitational $S$-matrix in impact-parameter space. Furthermore, we predict the existence of similar terms in the remainder function at all higher loop orders. Our results provide a non-trivial cross-check of the recent three-loop calculation, and a necessary consistency constraint for any future calculation at higher loops.
High-energy massless gravitational scattering in ${\cal N}=8$ 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 am…
We construct the on-shell double copy for linearised four-dimensional ${\cal N}=2$ supergravity coupled to one vector multiplet with a quadratic prepotential. We apply this dictionary to the weak-field approximation of dyonic BPS black holes in this theory.
A rectangular Wilson loop centered at the origin, with sides parallel to space and time directions and length $2L$ and $2T$ respectively, is perturbatively evaluated ${\cal O}(g^4)$ in Feynman gauge for Yang--Mills theory in $1+(D-1)$ dimensions. When $D>2$, there is a dependence on the dimensionless ratio $L/T$, besides the area. In the limit $T \to \infty$, keeping $D>2$, the leading expression of the loop involves only the Casimir constant $C_F$ of the fundamental representation and is thereby in agreement with the expected Abelian-like time exponentiation (ALTE). At $D= 2$ the result depen…
We approach the issue of exponentiation of soft gauge boson corrections to scattering amplitudes from a path integral point of view. We show that if one represents the amplitude as a first quantized path integral in a mixed coordinate-momentum space representation, a charged particle interacting with a soft gauge field is represented as a Wilson line for a semi-infinite line segment, together with calculable fluctuations. Combining such line segments, we show that exponentiation in an abelian field theory follows immediately from standard path-integral combinatorics. In the non-abelian case, w…
Recently, a careful canonical quantisation of the theory of closed bosonic tensionless strings has resulted in the discovery of three separate vacua and hence three different quantum theories that emerge from this single classical tensionless theory. In this note, we perform lightcone quantisation with the aim of determination of the critical dimension of these three inequivalent quantum theories. The satisfying conclusion of a rather long and tedious calculation is that one of vacua does not lead to any constraint on the number of dimensions, while the other two give $D=26$. This implies that…
I review the recent progress in studying long-distance singularities in gauge-theory scattering amplitudes in terms of Wilson lines. The non-Abelian exponentiation theorem, which has been recently generalised to the case of multi-leg amplitudes, states that diagrams exponentiate such that the colour factors in the exponent are fully connected. After a brief review of the diagrammatic approach to soft gluon exponentiation, I sketch the method we used to prove the theorem and illustrate how connected colour factors emerge in the exponent in webs that are formed by sets of multiple-gluon-exchange…
In light of the strong advances in understanding the mathematical structure of scattering amplitudes, we discuss the Regge limit of QCD and of the ${\cal N}=4$ Super Yang-Mills theory.
This Ph.D. thesis reaches two main results. The first one is represented by a detailed study, in Feynman gauge, of the perturbative ${\cal O}(g^4)$ contribution to a space-time Wilson loop, with respect to its (expected) Abelian-like time exponentiation when the temporal side goes to infinity. As soon as we are in dimensions greater than two, the expected behavior is found. But if we proceed first to the dimensional limit $D \to 2$, the exponentiation is not recovered. The limits $T \to \infty$ and $D \to 2$ do not commute. The other result is the computation in dimensions $D=2+ε$ and in light…
(abbreviated) I will describe my work on proton Compton scattering in a Unified Proton-Delta theory and on the computation of scattering amplitudes in Yang-Mills theory. We study proton Compton scattering in the first resonance region in an effective field theory approach with adviser Dr. Konstantin G. Savvidy. Proton and $Δ^+$ are naturally unified in the generalized Rarita-Schwinger theory proposed by Savvidy. We introduce six non-minimal electromagnetic interactions--with their coefficients being called "form factors"--and bare polarizabilities in an effective Lagrangian. We express proton …
There is an apparent discrepancy in the literature with regard to the quasinormal mode frequencies of Schwarzschild-de Sitter black holes in the degenerate-horizon limit. On the one hand, a Poschl-Teller-inspired method predicts that the real part of the frequencies will depend strongly on the orbital angular momentum of the perturbation field whereas, on the other hand, the degenerate limit of a monodromy-based calculation suggests there should be no such dependence (at least, for the highly damped modes). In the current paper, we provide a possible resolution by critically re-assessing the l…
We use $\mathcal N=8$ supergravity as a toy model for understanding the dynamics of black hole binary systems via the scattering amplitudes approach. We compute the conservative part of the classical scattering angle of two extremal (half-BPS) black holes with minimal charge misalignment at $\mathcal O(G^3)$ using the eikonal approximation and effective field theory, finding agreement between both methods. We construct the massive loop integrands by Kaluza-Klein reduction of the known $D$-dimensional massless integrands. To carry out integration we formulate a novel method for calculating the …
We point out that the states required by the Lattice Weak Gravity Conjecture, along with certain genericity conditions, imply the existence of non-vanishing kinetic mixing between massless Abelian gauge groups in the low-energy effective theory. We carry out a phenomenological estimate using a string-inspired probability distribution for the masses of superextremal states and compare the results to expectations from string theory and field theory, estimating the magnitude of kinetic mixing in each case. In the string case, we compute the kinetic mixing in an ensemble of 1858 MSSM-like heteroti…
We introduce a novel framework to study high-order gravitational effects on a binary from the scattering of its emitted gravitational radiation. Here we focus on the radiation-reaction due to the background of the binary's gravitational potential, namely on the so-called tail effects, as the starting point to this type of scattering effects. We start from the effective field theory of a binary composite-particle. Through multi-loop and generalized-unitarity methods, we derive the causal effective actions of the dynamical multipoles, the energy spectra, and the observable flux, due to these eff…
For a field theory that is invariant under diffeomorphisms there is a subtle interplay between symmetries, conservation laws and the phase space of the theory. The natural language for describing these ideas is that of differential forms and both differential forms on space-time and differential forms on the infinite dimensional space of solutions of the equations of motion of the field theory play an important role. There are exterior derivatives on both spaces and together they weave a double differential complex which captures the cohomology of the theory. This is important in the definitio…
We consider the recently developed diagrammatic approach to soft-gluon exponentiation in multiparton scattering amplitudes, where the exponent is written as a sum of webs - closed sets of diagrams whose colour and kinematic parts are entangled via mixing matrices. A complementary approach to exponentiation is based on the multiplicative renormalizability of intersecting Wilson lines, and their subsequent finite anomalous dimension. Relating this framework to that of webs, we derive renormalization constraints expressing all multiple poles of any given web in terms of lower-order webs. We exami…
We study an alternative to dimensional regularisation of planar scattering amplitudes in N=4 super Yang-Mills theory by going to the Coulomb phase of the theory. The infrared divergences are regulated by masses obtained from a Higgs mechanism, allowing us to work in four dimensions. The corresponding string theory set-up suggests that the amplitudes have an exact dual conformal symmetry. The latter acts on the kinematical variables of the amplitudes as well as on the Higgs masses in an effectively five dimensional space. We confirm this expectation by an explicit calculation in the gauge theor…
Brane tilings, sometimes called dimer models, are a class of bipartite graphs on a torus which encode the gauge theory data of four-dimensional SCFTs dual to D3-branes probing toric Calabi--Yau threefolds. An efficient way of encoding this information exploits the theory of dessin d'enfants, expressing the structure in terms of a permutation triple, which is in turn related to a Belyi pair, namely a holomorphic map from a torus to a P^1 with three marked points. The procedure of a-maximization, in the context of isoradial embeddings of the dimer, also associates a complex structure to the toru…
I discuss the state-of-the-art knowledge of long-distance singularities in multi-leg gauge-theory scattering amplitudes and report on an on-going calculation of the three-loop soft anomalous dimension through the renormalization of correlators of semi-infinite Wilson lines. I also discuss the non-Abelian exponentiation theorem that has been recently generalised to multiple Wilson lines and demonstrate its application in computing the soft anomalous dimension. Finally, I present recent results for multiple-gluon-exchange webs and discuss their analytic structure.
The two-loop four-point amplitude of two massless SU(N) colored scalars and two color singlet operators with different virtuality described by a half-BPS and Konishi operators is calculated analytically in maximally supersymmetric Yang-Mills theory. We verify the ultraviolet behaviour of the unprotected composite operator and exponentiation of the infrared divergences with correct universal values of the anomalous dimensions in the modified dimensional reduction scheme. The amplitude is found to contain lower transcendental weight terms in addition to the highest ones and the latter has no sim…
