Construction of a crossing-simmetric, Regge-behaved amplitude for linearly rising trajectories

From S-matrix theory to strings: Scattering data and the commitment to non-arbitrariness

The early history of string theory is marked by a shift from strong interaction physics to quantum gravity. The first string models and associated theoretical framework were formulated in the late 1960s and early 1970s in the context of the S-matrix program for the strong interactions. In the mid-1970s, the models were reinterpreted as a potential theory unifying the four fundamental forces. This paper provides a historical analysis of how string theory was developed out of S-matrix physics, aiming to clarify how modern string theory, as a theory detached from experimental data, grew out of an S-matrix program that was strongly dependent upon observable quantities. Surprisingly, the theoretical practice of physicists already turned away from experiment before string theory was recast as a potential unified quantum gravity theory. With the formulation of dual resonance models (the "hadronic string theory"), physicists were able to determine almost all of the models' parameters on the basis of theoretical reasoning. It was this commitment to "non-arbitrariness", i.e., a lack of free parameters in the theory, that initially drove string theorists away from experimental input, and not the practical inaccessibility of experimental data in the context of quantum gravity physics. This is an important observation when assessing the role of experimental data in string theory.

Multiparticle Factorization and the Rigidity of String Theory

Is string theory uniquely determined by self-consistency? Causality and unitarity seemingly permit a multitude of putative deformations, at least at the level of two-to-two scattering. Motivated by this question, we initiate a systematic exploration of the constraints on scattering from higher-point factorization, which imposes extraordinarily restrictive sum rules on the residues and spectra defined by a given amplitude. These bounds handily exclude several proposed deformations of the string: the simplest "bespoke" amplitudes with tunable masses and a family of modified string integrands from "binary geometry." While the string itself passes all tests, our formalism directly extracts the three-point amplitudes for the low-lying string modes without the aid of worldsheet vertex operators.

Bruno Touschek and the Physics at Frascati at the Time of AdA and ADONE

The physics at Frascati in the years 60–70s is reviewed together with the role played by Bruno Touschek.

Unitarity and Low Energy Expansion of the Coon Amplitude

The Coon amplitude is a deformation of the Veneziano amplitude with logarithmic Regge trajectories and an accumulation point in the spectrum, which interpolates between string theory and field theory. With string theory, it is the only other solution to duality constraints explicitly known and it constitutes an important data point in the modern S-matrix bootstrap. Yet, its basics properties are essentially unknown. In this Letter, we fill this gap and derive the conditions of positivity and the low energy expansion of the amplitude. On the positivity side, we discover that the amplitude switches from a regime where it is positive in all dimensions to a regime with critical dimensions, which connects to the known d=26, 10 when the deformation is removed. Incidentally, we find that the Veneziano amplitude can be extended to massive scalars of masses up to m^{2}=1/3, where it has critical dimension 6.3. On the low-energy side, we compute the first few couplings of the theory in terms of q-deformed analogs of the standard Riemann zeta values of the string expansion. We locate their location in the EFT-hedron, and find agreement with a recent conjecture that theories with accumulation points populate this space. We also discuss their relation to low spin dominance. Finally, we comment on the length of the Coon parton.

Onset of Color Transparency in Holographic Light-Front QCD

The color transparency (CT) of a hadron, propagating with reduced absorption in a nucleus, is a fundamental property of QCD (quantum chromodynamics) reflecting its internal structure and effective size when it is produced at high transverse momentum, Q. CT has been confirmed in many experiments, such as semi-exclusive hard electroproduction, eA→e′πX, for mesons produced at Q2>3GeV2. However, a recent JLab (Jefferson Laboratory) measurement for a proton electroproduced in carbon eC→e′pX, where X stands for the inclusive sum of all produced final states, fails to observe CT at Q2 up to 14.2 GeV2. In this paper, the onset of CT is determined by comparing the Q2-dependence of the hadronic cross sections for the initial formation of a small color-singlet configuration using the generalized parton distributions from holographic light-front QCD. A critical dependence on the hadron’s twist, τ, the number of hadron constituents, is found for the onset of CT, with no significant effects from the nuclear medium. This effect can explain the absence of proton CT in the present kinematic range of the JLab experiment. The proton is predicted to have a “two-stage” color transparency with the onset of CT differing for the spin-conserving (twist-3, τ=3) Dirac form factor with a higher onset in Q2 for the spin-flip Pauli (twist-4) form factor. In contrast, the neutron is predicted to have a “one-stage” color transparency with the onset at higher Q2 because of the dominance of its Pauli form factor. The model also predicts a strong dependence at low energies on the flavor of the quark current coupling to the hadron.

Reverse Bootstrapping: IR Lessons for UV Physics

S-matrix bootstrap and positivity bounds are usually viewed as constraints on low-energy theories imposed by the requirement of a standard UV completion. By considering graviton-photon scattering in the standard model, we argue that the low-energy theory can be used to put constraints on the UV behavior of the gravitational scattering amplitudes.

Amplitudes and the Riemann Zeta Function

Physical properties of scattering amplitudes are mapped to the Riemann zeta function. Specifically, a closed-form amplitude is constructed, describing the tree-level exchange of a tower with masses m_{n}^{2}=μ_{n}^{2}, where ζ(1/2±iμ_{n})=0. Requiring real masses corresponds to the Riemann hypothesis, locality of the amplitude to meromorphicity of the zeta function, and universal coupling between massive and massless states to simplicity of the zeros of ζ. Unitarity bounds from dispersion relations for the forward amplitude translate to positivity of the odd moments of the sequence of 1/μ_{n}^{2}.

Superstring Loop Amplitudes from the Field Theory Limit

We propose a procedure to determine the moduli-space integrands of loop-level superstring amplitudes for massless external states in terms of the field theory limit. We focus on the type II superstring. The procedure is to (i) take a supergravity loop integrand written in a BCJ double-copy representation, (ii) use the loop-level scattering equations to translate that integrand into the ambitwistor string moduli-space integrand, localised on the nodal Riemann sphere, and (iii) uplift that formula to one on the higher-genus surface valid for the superstring, guided by modular invariance. We show how this works for the four-point amplitude at two loops, where we reproduce the known answer, and at three loops, where we present a conjecture that is consistent with a previous proposal for the chiral measure. Useful supergravity results are currently known up to five loops.

Local Zeta Functions and Koba–Nielsen String Amplitudes

This article is a survey of our recent work on the connections between Koba–Nielsen amplitudes and local zeta functions (in the sense of Gel’fand, Weil, Igusa, Sato, Bernstein, Denef, Loeser, etc.). Our research program is motivated by the fact that the p-adic strings seem to be related in some interesting ways with ordinary strings. p-Adic string amplitudes share desired characteristics with their Archimedean counterparts, such as crossing symmetry and invariance under Möbius transformations. A direct connection between p-adic amplitudes and the Archimedean ones is through the limit p→1. Gerasimov and Shatashvili studied the limit p→1 of the p-adic effective action introduced by Brekke, Freund, Olson and Witten. They showed that this limit gives rise to a boundary string field theory, which was previously proposed by Witten in the context of background independent string theory. Explicit computations in the cases of 4 and 5 points show that the Feynman amplitudes at the tree level of the Gerasimov–Shatashvili Lagrangian are related to the limit p→1 of the p-adic Koba–Nielsen amplitudes. At a mathematical level, this phenomenon is deeply connected with the topological zeta functions introduced by Denef and Loeser. A Koba–Nielsen amplitude is just a new type of local zeta function, which can be studied using embedded resolution of singularities. In this way, one shows the existence of a meromorphic continuations for the Koba–Nielsen amplitudes as functions of the kinematic parameters. The Koba–Nielsen local zeta functions are algebraic-geometric integrals that can be defined over arbitrary local fields (for instance R, C, Qp, Fp((T))), and it is completely natural to expect connections between these objects. The limit p tends to one of the Koba–Nielsen amplitudes give rise to new amplitudes which we have called Denef–Loeser amplitudes. Throughout the article, we have emphasized the explicit calculations in the cases of 4 and 5 points.

Single-Valued Integration and Superstring Amplitudes in Genus Zero

We study open and closed string amplitudes at tree-level in string perturbation theory using the methods of single-valued integration which were developed in the prequel to this paper (Brown and Dupont in Single-valued integration and double copy, 2020). Using dihedral coordinates on the moduli spaces of curves of genus zero with marked points, we define a canonical regularisation of both open and closed string perturbation amplitudes at tree level, and deduce that they admit a Laurent expansion in Mandelstam variables whose coefficients are multiple zeta values (resp. single-valued multiple zeta values). Furthermore, we prove the existence of a motivic Laurent expansion whose image under the period map is the open string expansion, and whose image under the single-valued period map is the closed string expansion. This proves the recent conjecture of Stieberger that closed string amplitudes are the single-valued projections of (motivic lifts of) open string amplitudes. Finally, applying a variant of the single-valued formalism for cohomology with coefficients yields the KLT formula expressing closed string amplitudes as quadratic expressions in open string amplitudes.

On the asymptotic properties of a canonical diffraction integral

We introduce and study a new canonical integral, denoted I + - ε , depending on two complex parameters α ₁ and α ₂. It arises from the problem of wave diffraction by a quarter-plane and is heuristically constructed to capture the complex field near the tip and edges. We establish some region of analyticity of this integral in C 2 , and derive its rich asymptotic behaviour as |α ₁ | and |α ₂ | tend to infinity. We also study the decay properties of the function obtained from applying a specific double Cauchy integral operator to this integral. These results allow us to show that this integral shares all of the asymptotic properties expected from the key unknown function G _+- arising when the quarter-plane diffraction problem is studied via a two-complex-variables Wiener-Hopf technique (see Assier & Abrahams, SIAM J. Appl. Math., in press). As a result, the integral I + - ε can be used to mimic the unknown function G _+- and to build an efficient 'educated' approximation to the quarter-plane problem.

Finite Quantum Gravity Amplitudes: No Strings Attached

We study the gravity-mediated scattering of scalar fields based on a parameterization of the Lorentzian quantum effective action. We demonstrate that the interplay of infinite towers of spin zero and spin two poles at imaginary squared momentum leads to scattering amplitudes that are compatible with unitarity bounds, causal, and scale-free at trans-Planckian energy. Our construction avoids introducing nonlocalities or the massive higher-spin particles that are characteristic in string theory.

Unified Description of Polarized and Unpolarized Quark Distributions in the Proton

We propose a unified new approach to describe polarized and unpolarized quark distributions in the proton based on the gauge-gravity correspondence, light-front holography, and the generalized Veneziano model. We find that the spin-dependent quark distributions are uniquely determined in terms of the unpolarized distributions by chirality separation without the introduction of additional free parameters. The predictions are consistent with existing experimental data and agree with perturbative QCD constraints at large longitudinal momentum x. In particular, we predict the sign reversal of the polarized down-quark distribution in the proton at x=0.8±0.03, a key property of nucleon substructure which will be tested very soon in upcoming experiments.

Overview of High Energy String Scattering Amplitudes and Symmetries of String Theory

In this paper, we studied symmetries of string scattering amplitudes in the high energy limits of both the fixed angle or Gross regime (GR) and the fixed momentum transfer or Regge regime (RR). We calculated high energy string scattering amplitudes (SSA) at arbitrary mass levels for both regimes. We discovered the infinite linear relations among fixed angle string amplitudes and the ifinite recurrence relations among Regge string amplitudes. The linear relations we obtained in the GR corrected the saddle point calculations by Gross, Gross and Mende. In addition, for the high energy closed string scatterings, our results differ from theirs by an oscillating prefactor which was crucial to recover the KLT relation valid for all energies. We showed that all the high energy string amplitudes can be solved using the linear or recurrence relations, so that all the string amplitudes can be expressed in terms of a single string amplitude. We further found that, at each mass level, the ratios among the fixed angle amplitudes can be extracted from the Regge string scattering amplitudes. Finally, we reviewed the recent developments on the discovery of infinite number of recurrence relations valid for all energies among Lauricella SSA. The symmetries or relations among SSA at various limits obtained previously can be exactly reproduced. It leads us to argue that the known S L ( K + 3 , C ) dynamical symmetry of the Lauricella function may be crucial to probe spacetime symmetry of string theory.

Universality of Generalized Parton Distributions in Light-Front Holographic QCD

The structure of generalized parton distributions is determined from light-front holographic QCD up to a universal reparametrization function w(x) which incorporates Regge behavior at small x and inclusive counting rules at x→1. A simple ansatz for w(x) that fulfills these physics constraints with a single-parameter results in precise descriptions of both the nucleon and the pion quark distribution functions in comparison with global fits. The analytic structure of the amplitudes leads to a connection with the Veneziano model and hence to a nontrivial connection with Regge theory and the hadron spectrum.

Exploring New Physics Frontiers Through Numerical Relativity

The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology.

My 50 years of research in particle physics

Some of my work of the last 50 years in the field of theoretical particle physics is described with particular emphasis on the motivation, the process of investigation, relationship to the work of others, and its impact. My judgment is unavoidably subjective, although I do present the comments of other researchers as much as possible.

Dijet signals for low mass strings at the Large Hadron Collider

Assuming that the fundamental string mass scale is in the TeV range and the theory is weakly coupled, we discuss possible signals of string physics at the Large Hadron Collider (LHC). In D-brane constructions, the dominant contributions to full-fledged string amplitudes for all the common QCD parton subprocesses leading to dijets are completely independent of the details of compactification, and can be evaluated in a parameter-free manner. We make use of these amplitudes evaluated near the first resonant pole to determine the discovery potential of LHC for the first Regge excitations of the quark and gluon. Remarkably, the reach of LHC after a few years of running can be as high as 6.8 TeV. Even after the first 100 pb(-1) of integrated luminosity, string scales as high as 4.0 TeV can be discovered. Data on pp-->directgamma + jet can provide corroboration for string physics at scales as high as 5 TeV.

Evidence for quark-hadron duality in the proton spin asymmetry A1

Spin-dependent lepton-nucleon scattering data have been used to investigate the validity of the concept of quark-hadron duality for the spin asymmetry A1. Longitudinally polarized positrons were scattered off a longitudinally polarized hydrogen target for values of Q2 between 1.2 and 12 GeV2 and values of W2 between 1 and 4 GeV2. The average double-spin asymmetry in the nucleon resonance region is found to agree with that measured in deep-inelastic scattering at the same values of the Bjorken scaling variable x. This finding implies that the description of A1 in terms of quark degrees of freedom is valid also in the nucleon resonance region for values of Q2 above 1.6 GeV2.

Scaling Laws for Geometry and Macromolecules in Solution: An Interdisciplinary Approach to Statistical and Thermal Physics

An interdisciplinary program, dealing with statistics within basic geometry, is presented and discussed across some modern physics. Its fundamentals are of general interest in physical chemistry, but specially suit investigating conformational statistics and universal scaling of polymer chains in solution. We pointed out an equivalence principle for shape and statistics that can straightforwardly link probability distributions to geometrical quantities at smaller length scales. The average polymer size is thus expected following analytically from the energy surface of its dimeric unit. This would finally suggest extending molecular mechanics to a geometrical setting that reaches the limit of vanishing scales.