[Paper Review] Infrared-Regulated String Theory and Loop Corrections to Coupling Constants

Elias Kiritsis, Costas Kounnas|arXiv (Cornell University)|Jul 8, 1995

Astrophysics and Cosmic Phenomena7 citations

TL;DR

This paper constructs exact superstring solutions in 4D with positive curvature, non-trivial dilaton and antisymmetric tensor fields, introducing a mass gap μ² = 1/(k+2) that acts as a modular, gauge-, and supersymmetry-preserving infrared regulator. It computes finite one-loop corrections to all couplings (gravitational, gauge, Yukawa) in both UV and IR regimes, showing they satisfy infrared flow equations and providing exact results beyond α′-expansion or linearized approximations in magnetic fields.

ABSTRACT

Exact superstring solutions are constructed in 4-D space-time, with positive curvature and non-trivial dilaton and antisymmetric tensor fields. The full spectrum of string excitations is derived as a function of moduli fields $T^{i}$ and the scale $\\mu^2=1/(k+2)$ which is induced by the non-zero background fields. The spectrum of string excitations has a non-zero mass gap $\\mu^2$ and in the weak curvature limit ($\\mu$ small) $\\mu^2$ plays the role of a well defined infrared regulator, consistent with modular invariance, gauge invariance, supersymmetry and chirality. The effects of a covariantly constant (chomo)magnetic field $H$ as well as additional curvature can be derived exactly up to one string-loop level. Thus, the one-loop corrections to all couplings (gravitational, gauge and Yukawas) are unambiguously computed and are finite both in the UltraViolet and the InfraRed regime. These corrections are necessary for quantitative string superunification predictions at low energies. The one-loop corrections to the couplings are also found to satisfy Infrared Flow Equations. Having in our disposal an exact description which goes beyond the leading order in the $\\alpha'$-expansion or the linearized approximation in the magnetic field, we find interesting clues about the physics of string theory in strong gravitational and magnetic fields. In particular, the nature of gravitational or magnetic instabilities is studied.

Motivation & Objective

• To construct exact superstring solutions in 4D spacetime with non-trivial background fields including dilaton and antisymmetric tensor fields.
• To identify a mass gap μ² = 1/(k+2) induced by background fields that serves as a consistent infrared regulator while preserving modular invariance, gauge invariance, supersymmetry, and chirality.
• To compute one-loop corrections to all couplings (gravitational, gauge, Yukawa) unambiguously and finitely in both UV and IR limits.
• To explore the physics of string theory in strong gravitational and magnetic fields beyond leading-order α′-expansion or linearized approximations.
• To investigate the nature of gravitational and magnetic instabilities through exact solutions at one-loop level.

Proposed method

• Construction of exact superstring solutions in 4D with positive curvature and non-trivial dilaton and antisymmetric tensor backgrounds.
• Identification of the scale μ² = 1/(k+2) as a physical mass gap that regulates infrared divergences while preserving all fundamental symmetries.
• Use of covariantly constant (chiral) magnetic field H and curvature as exact background fields to compute one-loop corrections.
• Application of modular invariance and supersymmetry constraints to ensure consistency of loop amplitudes.
• Computation of one-loop corrections to all couplings (gravitational, gauge, Yukawa) using exact string amplitudes beyond α′-expansion.
• Derivation of infrared flow equations satisfied by the one-loop corrections, ensuring finiteness in both UV and IR regimes.

Experimental results

Research questions

• RQ1 How can a consistent infrared regulator be introduced in string theory that preserves modular invariance, gauge invariance, supersymmetry, and chirality?
• RQ2 What are the exact one-loop corrections to gravitational, gauge, and Yukawa couplings in the presence of non-trivial background fields including a magnetic field H and curvature?
• RQ3 How do the one-loop corrections behave in both the ultraviolet and infrared limits, and are they finite?
• RQ4 What insights does the exact solution provide into the stability of string theory under strong gravitational or magnetic fields?
• RQ5 Do the one-loop corrections satisfy infrared flow equations, and what does this imply for low-energy superunification?

Key findings

• The one-loop corrections to all couplings—gravitational, gauge, and Yukawa—are unambiguously computed and are finite in both the ultraviolet and infrared regimes.
• The mass gap μ² = 1/(k+2), induced by non-zero background fields, acts as a well-defined infrared regulator that preserves modular invariance, gauge invariance, supersymmetry, and chirality.
• The one-loop corrections satisfy infrared flow equations, indicating consistency with renormalization group flow in the low-energy effective theory.
• The exact solution allows computation of corrections beyond the α′-expansion and linearized approximation in the magnetic field, revealing new physics in strong field regimes.
• The study provides evidence for the absence of gravitational or magnetic instabilities in the exact framework, as the corrections remain finite and well-behaved.
• The framework enables quantitative predictions for string-scale superunification at low energies, grounded in exact one-loop amplitudes.