Anomalous Thresholds for the S-matrix of Unstable Particles
While the modern S-matrix bootstrap has led to tremendous progress, the processes in question often involve states that are not stable. In this talk, we will discuss the analytic properties of S-matrix for unstable particles by defining them as the residues on the unphysical sheets where unstable poles reside, and show that anomalous thresholds associated with UV physics are unavoidable for unstable particles. As a result, any dispersive representation for the amplitude will involve contributions from these thresholds, violating the general positivity bound even for non-gravitational theories.
Bootstrap Principle for the Spectrum and Scattering of Strings
Quantum Gravity S-matrix Bootstrap
The goal of the S-matrix Bootstrap program is to use the constraints of causality, crossing, and unitarity to explore the space of physical scattering amplitudes and look for interesting corners. In this talk, I will discuss the Bootstrap of graviton scattering amplitudes in maximally supersymmetric theories in dimensions greater or equal than nine. In doing so, I will review the numerical setup, and show the numerical results obtained, providing evidence for the uniqueness of String Theory. I will conclude by mentioning the possibility of extending and improving these studies by performing more sophisticated numerical analysis.
Scattering Amplitudes at the Precision Frontier
The increasing accuracy of experimental data from the past, current and future LHC runs, will require theoretical predictions to be computed at the highest possible accuracy. Within the framework of perturbative QCD, one of the precision calculation frontiers is the 2->3 scattering process. I will briefly showcase the state-of-the-art theoretical predictions for the 2->3 scattering process studied at the LHC and discuss in detail modern methods to compute two-loop multi-leg scattering amplitudes.
Exploring amplitude criteria for weak gravity: phenomenological perspectives
Various connections between amplitude positivity in gravity theories and weak gravity conjecture have been observed in the past years. In this talk I would like to explore this connection further with an emphasis on phenomenological perspectives. In particular I will discuss phenomenological motivation in asking how much a hidden sector can be decoupled from our sector, e.g., in the context of dark sector physics and inflation. Then, I will discuss a possible application of amplitude positivity and weak gravity to this problem, summarizing the status and future issues in the theory side as well.
From massive higher spins to Kerr black holes
I will review some recent developments in massive higher-spin theory, namely, Zinoviev's massive gauge symmetry and the new chiral-field approach. I will discuss the applications of massive higher-spin scattering amplitudes to classical gravitational dynamics of rotating black holes, in particular, the so-called gravitational Compton amplitude.
To be announced
Spin magnitude change and uplifting spin supplementary condition in conservative orbital motion
In conventional world-line formalism for spinning binaries in general relativity, one assumes that the dynamical degrees of freedom for spin are completely captured by the rest frame canonical spin. A spin supplementary condition (SSC) is then necessary to remove redundancies. We study this problem from an amplitude-based field theory perspective. In higher spin field theories, it is notoriously difficult to impose transverse and traceless conditions when interactions are included. We take an alternative approach and keep the additional degrees of freedom. We see that for generic Wilson coefficients, we obtain a system with a dynamical mass dipole that has physical effect starting at the quadrupole level. It will decouple when we choose special values for Wilson coefficients, and we land back on the dynamics of conventional spinning binaries. The situation is very similar to a symmetry breaking in the classical limit. We also construct a world-line Lagrangian and a classical effective Hamiltonian that completely match the physics mentioned above. Thus our approach can naturally incorporate a dynamical mass dipole and thus be more generic than the conventional formalism. The mass dipole has physical effects, and its significance is a question for phenomenology. Alternatively, our formalism simplifies the calculation for conventional spinning binaries, as the SSC constraint is relaxed.
Jiang-Hao Yu (Download the file)
Effective Field Theories from IR Amplitudes to UV Physics
Effective Field Theories systematically parametrize high energy effects using low energy degree of freedom, by writing down effective operators order by order. We construct generic operator bases up to any order using the on-shell scattering amplitudes and Young tensor technique, and apply to the dimension-8 standard model effective field theory, gravity effective theory etc. Then we discuss the chiral effective theory for strong and weak dynamics by decomposing the massive on-shell amplitudes. Finally we discuss all possible UV resonance completions of the SMEFT operators by generalized partial wave analysis, which provides a new strategy of searching new physics at future colliders.
Christian Jepsen (Download the file)
Scattering on the Worldvolume
Since early dual model days, it has been known how to dimensionally generalize the tachyonic Virasoro-Shapiro amplitude by uplifting the Koba-Nielsen integral to a d-dimensional conformally invariant integral. In this talk, we will revisit this construction and uncover a number of new properties. By using conformal transformations, we can decompose the higher-d amplitudes into partial amplitudes and derive the dimensional continuation of the Veneziano amplitude. These generalized partial amplitudes satisfy an infinite set of identities that generalize the KLT relation. For spacetimes below suitable d-dependent critical dimensions, the higher-d four-point amplitudes satisfy the positivity conditions mandated by unitarity.
Suro Kim (Download the file)
Constraining constraining millicharged dark matter with gravitational positivity bounds
Positivity bound is one of the UV-IR consistency conditions which can be derived from fundamental principles such as unitarity and causality. Recently, it has been studied to incorporate gravity effects to the positivity constraints and apply them to various phenomenologies. In this talk, we study the implications of the gravitational positivity bound for dark matter. In particular, we focus on the millicharged dark matter and constrain their parameter spaces.
Arpita Mitra (Download the file)
Celestial Eikonal Amplitudes in the Near-Horizon Region
Infrared properties of scattering processes in relation to asymptotic symmetries have given rise to a promising version of flat space holography known as celestial conformal field theory framework, where bulk scattering amplitudes in boost eigenstate basis are dual to correlators of conformal field theories residing on celestial spheres at null infinity. We have constructed a celestial conformal field theory on the horizon corresponding to a non-perturbative eikonal scattering amplitude involving two massless scalars mediated by soft gravitons in the near-horizon region of a large eternal Schwarzschild black hole. From the known two-dimensional near-horizon scattering amplitude computed within the effective field theory framework, we first construct a four-dimensional amplitude involving two external s-wave legs in a flat spacetime frame around the bifurcation sphere strictly in a small angle approximation limit by resumming over the spherical harmonics. While the kinematics of external particles in this frame at leading order are analogous to a Minkowski spacetime, the eikonal amplitude differs from those about flat spacetime due to the near-horizon scattering potential. We derive a celestial correlator following a Mellin transform that provides an all loop order result, with a universal leading ultraviolet (UV) soft scaling behavior of the conformally invariant cross-ratio, and an infrared (IR) pole for the scaling dimension at each loop order. We argue these properties manifest soft graviton exchanges in the near-horizon region and, consequently, the soft UV behavior of the amplitude.
Justinas Rumbutis (Download the file)
S-Matrix bootstrap for particles with color
S-Matrix bootstrap is a powerful technique of bounding low energy EFT coefficients by imposing UV consistency conditions. Recently there has been a lot of progress in applying these bounds to gravitational EFTs using techniques developed by Caron-Huot, et al. 2021. In this work we derive the bounds for gauge theories coupled to gravity and investigate their dependance on the rank of the gauge group. In particularly we look at the four point amplitudes of external colored scalar particles and use numerical optimization to bound several EFT couplings.
Fumiya Sano (Download the file)
Analytic Formulae for Inflationary Correlators with Dynamical Mass
Massive fields can imprint unique oscillatory features on primordial correlation functions or inflationary correlators, which is dubbed the cosmological collider signal. In this work, we analytically investigate the effects of a time-dependent mass of a scalar field on inflationary correlators, extending previous numerical studies and implementing techniques developed in the cosmological bootstrap program. The time-dependent mass is in general induced by couplings to the slow-roll inflaton background, with particularly significant effects in the case of non-derivative couplings. By linearly approximating the time dependence, the mode function of the massive scalar is computed analytically, on which we derive analytic formulae for two-, three-, and four-point correlators with the tree-level exchange of the massive scalar. The obtained formulae are utilized to discuss the phenomenological impacts on the power spectrum and bispectrum, and it is found that the scaling behavior of the bispectrum in the squeezed configuration, i.e., the cosmological collider signal, is modified from a time-dependent Boltzmann suppression. By investigating the scaling behavior in detail, we are in principle able to determine the non-derivative couplings between the inflaton and the massive particle.
Junsei Tokuda (Download the file)
String loops and gravitational positivity bounds
We study loop corrections to positivity bounds on effective field theories in the context of 2→2 scattering in gravitational theories, in the presence of light particles. It has been observed that certain negative contributions at low energies are enhanced by inverse powers of a small mass m and are nontrivial to cancel against other low-energy contributions. These originate from near the forward limit of diagrams involving graviton exchange. We observe that scattering in this kinematics domain remains infrared-sensitive even at high center-of-mass energy. By considering a string-inspired model in which high-energy loops can be calculated using unitarity and Regge behavior of tree amplitudes, we uncover a natural mechanism through which 1/m-enhanced terms perfectly cancel between low and high energy contributions. This concretely explains possible positivity violations in the presence of gravity from the high-energy viewpoint.
Dynamics of Spinning Binary at 2PM
We consider the covariant proposal for the gravitational Compton amplitude for a Kerr black hole. Employing the covariant three- and four-point Compton amplitudes, we assemble the classical one-loop integrand on the maximal cut at all orders in spin, utilizing the method of unitarity. Expanding in powers of spin, we evaluate the one-loop amplitude up to $\mathcal O(G^2 a^8)$. Supplemented with extra contact contributions derived from the far-zone data of the Teukolsky solutions, the one-loop amplitude is in agreement with results available in the literature. In the aligned-spin case, we develop a method for evaluating the tensor tensor integral generating functions which allows us to compute the spin-resummed 2PM eikonal numerically.
Gauged Soft Recursion Relation for Chiral Perturbation Theory
We establish a systematic construction of the on-shell amplitude/operator basis for Chiral Perturbation Theory (ChPT) in D = 4 spacetime dimensions and with an arbitrary number of flavors N_f. For kinematic factors, we employ spinor-helicity variables to construct the soft blocks, which are local amplitudes satisfying the Adler’s zero condition. Then we derive the recursion relation for the tree level amplitudes in ChPT, which divided by the soft factors coming from the Adler's zero condition to reduce the large-z behavior in the usual EFTs. Moreover, the constructed amplitudes can contain a finite number of gauge bosons, and we discuss the criteria for on-shell constructibility.