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UV/IR relations from the worldsheet

Christian Aoufia, Ivano Basile, Giorgio Leone, Matteo Lotito

Abstract

We derive universal scaling relations for the low-energy effective action of string theory, connecting the vacuum energy and gauge couplings to higher-derivative Wilson coefficients. At one-loop in string perturbation theory, these generic parametric relations follow from modular and conformal invariance of the worldsheet, independently of the specific low-energy phase of the theory, and they become non-trivial in species limits. As a result, we substantially strengthen our previous case for the emergent string conjecture and connect UV/IR mixing to swampland principles. We argue that our results persist to higher loops, hinting at a pathway to study strong couplings using dualities. Further accounting for open-string contributions, if any, our results lead to parametric inequalities which reproduce holographic bounds and support the magnetic weak-gravity conjecture and the dark dimension scenario.

UV/IR relations from the worldsheet

Abstract

We derive universal scaling relations for the low-energy effective action of string theory, connecting the vacuum energy and gauge couplings to higher-derivative Wilson coefficients. At one-loop in string perturbation theory, these generic parametric relations follow from modular and conformal invariance of the worldsheet, independently of the specific low-energy phase of the theory, and they become non-trivial in species limits. As a result, we substantially strengthen our previous case for the emergent string conjecture and connect UV/IR mixing to swampland principles. We argue that our results persist to higher loops, hinting at a pathway to study strong couplings using dualities. Further accounting for open-string contributions, if any, our results lead to parametric inequalities which reproduce holographic bounds and support the magnetic weak-gravity conjecture and the dark dimension scenario.
Paper Structure (57 sections, 211 equations, 4 figures)

This paper contains 57 sections, 211 equations, 4 figures.

Table of Contents

  1. Introduction
  2. New physics at the EFT cutoff.
  3. Quantum gravity and the species scale.
  4. UV/IR mixing and low-energy data.
  5. Toward generic features of low-energy string theory
  6. Our setup.
  7. The worldsheet framework.
  8. Summary of contents.
  9. Gauge couplings and higher-derivative corrections
  10. Background-field method
  11. The flavor and helicity partition functions
  12. Comparison with other methods
  13. Gauge couplings in the background-field method.
  14. Example: heterotic gauge thresholds
  15. Expressing the partition function in terms of characters.
  16. ...and 42 more sections

Figures (4)

  • Figure 1: Field-theoretic diagrams contributing to the string-theoretic correlator in \ref{['eq:f2correlator']}. Dashed lines represent states in the gravitational sector, such as the dilaton. Panel (1) corresponds to the contribution from charged states. Panel (2) instead shows the universal contribution coming from the photon coupling to the gravitational sector, which itself couples to any other state.
  • Figure 2: A depiction of the standard ${\text{SL}}(2,\mathbb{Z})$ fundamental domain $\mathcal{F}$, which parametrizes by a complex coordinate $\tau = \tau_1 + i \tau_2$ the moduli space of conformal (equivalently complex) structures of tori.
  • Figure 3: A complete factorization channel for one-loop closed-string amplitudes, which can be built via the sewing construction of Sonoda:1988mfSonoda:1988fq. These configurations in worldsheet moduli space dominate the low-energy limit of the amplitude in the presence of kinematic poles. These are produced by massless states propagating in each thin long tube of the worldsheet. In particular, the depicted half-ladder arrangement leaves the maximum possible number of legs on the torus at fixed pole order.
  • Figure 4: The boundary of the (cut-off) ${\text{SL}}(2,\mathbb{Z})$ fundamental domain $\mathcal{F}$ depicted in \ref{['fig:fundamental_domain']}. The contributions from vertical lines in the integral of the subleading parts of the reduced partition function cancel by T-modular invariance (i.e. periodicity in $\tau_1$, whereas the contribution from the arc is a priori non-vanishing, since the split in \ref{['eq:sum_states_split']} is not modular invariant.