Anisotropic Type I String Compactification, Winding Modes and Large Extra Dimensions

TL;DR

<$Problem$> address the reconciliation of gravity with gauge interactions in Type I string theory using anisotropic compactifications to realize large extra dimensions. <$Approach$> develop Type I D$p$-brane frameworks, derive $G_N$ and gauge couplings in terms of $M_s$, $ abla$, and $M_i$, and propose a Planck-duality connecting $M_{Planck}$ to the lightest mass scale; explore TeV-, intermediate-, and GUT-scale string regimes and their winding-mode phenomenology. <$Findings$> winding modes can appear below the string scale and dominate signatures in some parameter ranges; in the n=2 large extra dimensions case current data bound the 6D Planck mass and compactification radius (e.g., $M_{(6)} \\\ge 1.8$ TeV, $R_1 \\\le 0.15$ mm), with stronger future constraints expected from collider searches. <$Significance$> provides a testable framework linking Planck-scale physics to anisotropic geometry and winding-mode dynamics, offering collider- and gravity-based probes and guiding stabilization considerations for extra dimensions.

Abstract

We discuss the structure of general Anisotropic Compactification in Type I D=4, N=1 string theory. It is emphasized that, in this context, a possible interpretation of M_{Planck} as ``dual'' to (at least) one of the Kaluza-Klein or Windings Modes could provide interesting interpretations of the ``physical scales'' and the GUT coupling. Some of the scenarios presented here are strictly connected with the phenomenological proposal of TeV-scale gravity (i.e. millimiter compactification). We show that in this scenario new and probably dominant effects should arise from the presence of ``low-energy'' Winding Modes of usual SM particles. Stringent bounds on the Planck mass in 4+n dimensions are derived from the existing experimental limits on massive replicas of SM gauge bosons. Non-observation of Winding Modes at the planned accelerators could provide stronger bounds on the 4+n dimensional Planck mass than those from graviton emission into the bulk. Some comments on other possible phenomenological interesting scenarios are addressed.

Figures (4)

• Figure 1: General pattern of mass scales in scenario (1), where the lowest scale is the compactification mass $M_1$ and $M_{\omega_1} = M_{Planck}$.
• Figure 2: General pattern of mass scales in scenario (1), where the lowest scale is the winding mass $M_{\omega_1}$ and $M_1 = M_{Planck}$.
• Figure 3: Bounds on $M_{(6)}$ as a function of $M_{\omega_c}$ for different values of $\alpha_3 = \alpha_{em}, \alpha_{GUT}, \alpha_s, 1$. The dashed lines are the excluded region if no deviation from Newton law is found at $R_1 = 1 \ {\rm mm} , 10 \ {\mu \rm m}$. The lower shaded area is the excluded region from present gravitational experiments testing the Newton law down to $R \sim 1 \ {\rm cm}$. The vertical left shaded area represent the excluded region from non observation of massive replicas of SM bosons.
• Figure 4: Bounds on $R_1$ as a function of $M_{\omega_c}$ for different values of $\alpha_3 = \alpha_{em}, \alpha_{GUT}, \alpha_s, 1$. The upper shaded area is the excluded region from present gravitational experiments testing the Newton law down to $R \sim 1 \ {\rm cm}$. The vertical left shaded area represent the excluded region from non observation of massive replicas of SM bosons.