# PAPER_1145: Type IIA Superstring Theory and SCm 10D Compactification

**Star Magic UQFF Framework**

**Author:** Daniel Murphy
**Date:** 2026

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## Abstract

We formulate Type IIA superstring theory within the SCm vacuum framework. Type IIA is the T-dual of Type IIB (PAPER_1144) and the strong-coupling limit connects to M-theory (PAPER_1148). The 16 extra dimensions above the 10D Type IIA spacetime are compactified via VDS $S_{26}^{(3)}$. The R-R gauge fields are identified with SCm phonon polarization modes. Mirror symmetry between Type IIA on a Calabi-Yau and Type IIB on the mirror CY is encoded in the VDS $[SSq] \leftrightarrow 1-[SSq]$ symmetry.

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## 1. Type IIA Effective Action

The Type IIA effective action in 10D:

$$S_{\text{IIA}} = \frac{1}{2\kappa_{10}^2} \int d^{10}x \sqrt{-g} \left(R - \frac{1}{2}|\partial\phi|^2 - \frac{1}{2}e^{-\phi}|H_3|^2 - \frac{1}{2}e^{3\phi/2}|F_2|^2 - \frac{1}{2}e^{\phi/2}|F_4|^2\right) + S_{\text{CS}}$$

where $F_2 = dC_1$ and $F_4 = dC_3 - H_3 \wedge C_1$ are R-R field strengths.

In SCm vacuum: the dilaton VEV is $\langle e^\phi \rangle = g_s = \beta_i \cdot \Phi_{\text{res}} = 0.504$.

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## 2. R-R Fields as SCm Phonon Polarizations

The Type IIA R-R fields $C_1$ (1-form) and $C_3$ (3-form) are identified with SCm phonon polarization modes:

$$C_\mu^{\text{SCm}} = \frac{\rho_{\text{vac,SCm}} \cdot S_{26}^{(3)} \cdot \Phi_{\text{res}}}{f_{\text{THz}}} \cdot A_\mu^{\text{phonon}}$$

where $A_\mu^{\text{phonon}}$ is the phonon gauge potential at 1.25 THz.

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## 3. T-Duality with Type IIB

Under T-duality along a VDS dimension with radius $R_i$:

$$R_i \to l_s^2 / R_i = l_s^2 / (l_s [SSq]^i) = l_s / [SSq]^i$$

Type IIA on $R_i = l_s [SSq]^i$ is dual to Type IIB on $l_s / [SSq]^i = l_s (1/[SSq])^i$.

The T-duality map corresponds to $[SSq] \to 1/[SSq] = 1/0.57 = 1.754$.

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## 4. D-Brane Spectrum

Type IIA has D$p$-branes for even $p$ (D0, D2, D4, D6, D8):

| Brane | Dim | SCm stabilization |
|-------|-----|------------------|
| D0 | 0+1 | $F_{U,Bi,i} \times \beta_i$ |
| D2 | 2+1 | $F_{U,Bi,i} \times \beta_i^2$ |
| D4 | 4+1 | $F_{U,Bi,i} \times \beta_i^3$ |
| D6 | 6+1 | $F_{U,Bi,i} \times \beta_i^4$ |

The D0-brane mass: $m_{\text{D0}} = T / (g_s) = 8.66 \times 10^{-11} / 0.504 = 1.72 \times 10^{-10}\ \text{J} \cdot \text{s/m}$.

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## 5. Mirror Symmetry via VDS

The mirror symmetry $[SSq] \leftrightarrow 1 - [SSq] = 0.43$ exchanges:

$$\text{Li}_{26}(0.57) \leftrightarrow \text{Li}_{26}(0.43)$$

Type IIA on CY$_3([SSq])$ is mirror to Type IIB on CY$_3(1-[SSq])$, giving the Hodge number exchange $h^{1,1} \leftrightarrow h^{2,1}$.

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## 6. Strong Coupling Limit = M-Theory

At $g_s = e^\phi > 1$, Type IIA lifts to 11D M-theory. The 11th dimension radius:

$$R_{11} = g_s \cdot l_s = \beta_i \cdot \Phi_{\text{res}} \cdot \frac{1}{\sqrt{T}} = \frac{0.504}{\sqrt{8.66 \times 10^{-11}}} = 1.71 \times 10^3\ \text{m}$$

At strong coupling $g_s \gg 1$, $R_{11} \to \infty$ revealing the 11th dimension (see PAPER_1148).

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## 7. Calibrated Constants

$$T = 8.66 \times 10^{-11}\ \text{N}, \quad [SSq] = 0.57, \quad S_{26}^{(3)} = 1.4531 \times 10^{26}$$

$$g_s = \beta_i \cdot \Phi_{\text{res}} = 0.504, \quad \Phi_{\text{res}} = 0.84, \quad f_{\text{THz}} = 1.25\ \text{THz}$$

$$\rho_{\text{vac,SCm}} = 7.09 \times 10^{-37}\ \text{J/m}^3, \quad \beta_i = 0.6, \quad \kappa = 5.0 \times 10^{-4}\ \text{day}^{-1}$$

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## References

1. Polchinski, J. (1995). *String Theory*, Vol. 2. Cambridge.
2. Witten, E. (1995). String theory dynamics in various dimensions. *Nucl. Phys. B* **443**, 85.
3. Type IIB in SCm: PAPER_1144; M-theory: PAPER_1148; `scm_vacuum_manifold.py`


### Key References with arXiv/DOI Identifiers

1. Abbott et al. (LIGO Scientific and Virgo Collaborations, 2016). *Observation of Gravitational Waves from a Binary Black Hole Merger.* Phys. Rev. Lett. **116**, 061102 — arXiv:1602.03837 — doi:10.1103/PhysRevLett.116.061102
2. Murphy, D. (2026). *Unified Quantum Field Framework (UQFF): Star-Magic v5.x Whitepaper Series.* Star-Magic Repository — github.com/Daniel8Murphy0007/Star-Magic
