Field theory expansions of string theory amplitudes (2401.05733v5)

Abstract: Motivated by quantum field theory (QFT) considerations, we present new representations of the Euler-Beta function and tree-level string theory amplitudes using a new two-channel, local, crossing symmetric dispersion relation. Unlike standard series representations, the new ones are analytic everywhere except at the poles, sum over poles in all channels and include contact interactions, in the spirit of QFT. This enables us to consider mass-level truncation, which preserves all the features of the original amplitudes. By starting with such expansions for generalized Euler-Beta functions and demanding QFT like features, we single out the open superstring amplitude. We demonstrate the difficulty in deforming away from the string amplitude and show that a class of such deformations can be potentially interesting when there is level truncation. Our considerations also lead to new QFT-inspired, parametric representations of the Zeta function and $\pi$, which show fast convergence.

• The paper introduces a novel dispersion relation framework to expand string amplitudes using QFT techniques.
• It achieves over 99% accuracy in approximating open superstring amplitudes through mass-level truncation while preserving key scattering characteristics.
• The approach bridges theoretical divides by enhancing convergence properties and suggesting new methods for high-energy particle simulations.

Field Theory Expansions of String Theory Amplitudes

The paper "Field Theory Expansions of String Theory Amplitudes" by Arnab Priya Saha and Aninda Sinha presents a compelling investigation into the analytical convergence between string theory amplitudes and quantum field theory (QFT) forms. By illuminating a path to expand string amplitudes using QFT-inspired methodologies, the authors bridge a prominent theoretical divide, addressing points of symbiosis and variants in the structural interpretation of amplitude formulation.

Key Contributions and Findings

The authors introduce a novel representation of the Euler-Beta function and tree-level string theory amplitudes via a two-channel, local, crossing symmetric dispersion relation. This approach diverges from classical series representations by ensuring analyticity everywhere except the poles and permits a summation over poles across all channels. This perspective aligns more closely with the conceptual framework of QFT, particularly facilitating mass-level truncation while preserving the integral features of the full string amplitudes.

A central theme of the paper is the demonstration of how string amplitudes, specifically the open superstring amplitude, can be represented through a mass-truncation approach while retaining key characteristics such as Regge behavior and soft high-energy scattering profiles. This effectively counters the traditional understanding that string theory amplitudes cannot be reconciled within a field theory framework due to their exponential softness and the implicit complexity of interactions.

Further, the authors explore a parametric representation strategy, adding a layer of deformability which is absent in traditional representations. They provide evidence that the contact terms derived from truncated series representations can remain consistent across different parameterizations, importantly capturing qualitative and quantitative aspects of string amplitudes.

Numerical Results and Analytical Insights

The paper provides robust numerical evidence supporting the validity of their analytic approaches. For instance, they demonstrate the capacity of truncated series to approximate the full string amplitude with high fidelity, even within limited truncation levels. Through calculations that show more than 99% accuracy within minimal truncations, the authors articulate an efficient method to engage with high-energy scattering phenomena without loss of essential characteristics inherent to string theory.

Additionally, the route taken offers refreshing insights into the convergence properties of mathematical constructs often associated with string amplitudes, such as the Zeta function and $\pi$, signifying rapid convergence through their new representations. This enhancement in convergence properties might suggest pivotal advancements in computational string theory applications and beyond.

Theoretical and Practical Implications

Theoretically, this paper challenges prevailing assumptions about the relationship between string theory and QFT, fortifying the case for a field theory analog that can encapsulate higher mass poles typically descriptive of string theory amplitudes. This can motivate new theoretical frameworks that bridge these domains, enriching our fundamental understanding of particle interaction paradigms.

Practically, the insights from this paper could fuel advancements in simulation techniques, particularly in areas where string and QFT overlap, such as quantum gravity contexts or in the precise modeling of particle collisions at extremely high energy scales.

Future Directions

The paper speculates on numerous future directions, including refining the approach to accommodate other configurations of string interactions and expanding upon the analytic expressibility of functions foundational to string theory. It invites further exploration into deformative approaches to standard string amplitudes and their functional adaptability within constrained approximation schemas.

Overall, the work by Saha and Sinha provides a concrete yet innovative contribution to bridging string theory's mathematical formulations with the pragmatic utilities of QFT approaches, potentially redrawing foundational landscapes in theoretical physics.