[Paper Review] Background Dependent Lorentz Violation from String Theory

Tianjun Li, Dimitri V. Nanopoulos|arXiv (Cornell University)|Oct 3, 2011

Noncommutative and Quantum Gravity Theories14 citations

TL;DR

This paper proposes a background-dependent Lorentz violation in Type IIB string theory via D3-branes and D7-branes, where particle velocity deviations δv are proportional to energy and D3-brane density, and inversely proportional to the string scale. It explains superluminal neutrino results from OPERA and MINOS with a string scale near 10⁵ GeV, while simultaneously accounting for photon energy-dependent time delays in MAGIC, HESS, and FERMI via low interstellar D3-brane density, all while satisfying stringent astrophysical constraints.

ABSTRACT

We revisit Lorentz violation in the Type IIB string theory with D3-branes and D7-branes. We study the relativistic particle velocities in details, and show that there exist both subluminal and superluminal particle propagations. In particular, the additional contributions to the particle velosity δv\equiv (v-c)/c from string theory is proportional to both the particle energy and the D3-brane number density, and is inversely proportional to the string scale. Thus, we can realize the background dependent Lorentz violation naturally by varying the D3-brane number density in space time. To explain the superluminal neutrino propagations in the OPERA and MINOS experiments, the string scale should be around 10^5 GeV. With very tiny D3-brane number density on the interstellar scale, we can also explain the time delays for the high energy photons compared to the low energy photons in the MAGIC, HESS, and FERMI experiments simultaneously. Interestingly, we can automatically satisfy all the stringent constraints from the synchrotron radiation of the Crab Nebula, the SN1987a observations on neutrinos, and the cosmic ray experiments on charged leptons. We also address the possible phenomenological challenges to our models from the relevant experiments done on the Earth.

Motivation & Objective

• To explain the anomalous superluminal neutrino propagation observed in the OPERA and MINOS experiments.
• To account for energy-dependent time delays in high-energy photons from MAGIC, HESS, and FERMI experiments.
• To reconcile these phenomena with stringent astrophysical constraints from SN1987a, Crab Nebula synchrotron radiation, and cosmic ray experiments.
• To propose a natural mechanism for background-dependent Lorentz violation within Type IIB string theory using D3-brane number density as a tunable parameter.

Proposed method

• Derives particle velocity corrections δv ≡ (v−c)/c in Type IIB string theory with D3-branes and D7-branes, showing dependence on particle energy and D3-brane number density.
• Models the effective quantum gravity scale M_QG via parameters V_A3, η, and ξ, which are calibrated to match observed time delays in astrophysical experiments.
• Uses the D-particle model of spacetime foam to describe vacuum refractive index effects, linking them to stringy interactions with internal degrees of freedom.
• Adjusts D3-brane number density in different regions (Earth vs. interstellar space) to achieve distinct Lorentz violation effects in different environments.
• Applies constraints from SN1987a, Crab Nebula, and cosmic ray data to bound δv for electrons and muons, ensuring consistency with observations.
• Addresses terrestrial experimental challenges (e.g., LEP, KamLAND) by assuming vacuum properties differ between Earth-based and interstellar environments.

Experimental results

Research questions

• RQ1 Can a string-theoretic model with D3-branes and D7-branes naturally explain the superluminal neutrino results from the OPERA and MINOS experiments?
• RQ2 Can the same model simultaneously account for the energy-dependent time delays in high-energy photons observed by MAGIC, HESS, and FERMI?
• RQ3 How can the model satisfy the stringent constraints from SN1987a neutrino observations, Crab Nebula synchrotron radiation, and cosmic ray experiments on charged leptons?
• RQ4 What is the required string scale and D3-brane number density to reproduce the observed time delays while remaining consistent with terrestrial experiments?

Key findings

• The string scale required to explain the OPERA and MINOS neutrino anomalies is approximately 10⁵ GeV.
• With a very low D3-brane number density on the interstellar scale, the model reproduces the observed time delays in high-energy photons from MAGIC, HESS, and FERMI experiments.
• The effective quantum gravity scale M_QG ≈ 0.98×10¹⁸ GeV is achieved with interstellar parameters (V_A3)^1/3 ≈ 1.9×10⁸ GeV⁻¹, η^IS ≈ 1.6×10⁻⁴⁰, and ξ^IS ≈ 2.4×10¹³.
• The model automatically satisfies constraints from SN1987a, which limits |δv_ν| ≤ 2×10⁻⁹ at 15 MeV, and from cosmic ray observations, which constrain δv_e < 10⁻¹³ and δv_e < 10⁻¹⁵ for electrons.
• The model explains the FERMI GRB 090510 constraint by adjusting V_A3^IS to smaller values in the relevant direction, allowing M_QG > 1.22×10¹⁹ GeV.
• Terrestrial experimental challenges (e.g., LEP, KamLAND) are addressed by assuming the vacuum in the LEP tunnel differs from the interstellar vacuum, allowing δv_e to be consistent with observations.