String Compactification, Effective Field Theory And Holography Swampland

This thesis primarily dives into investigating the details of four-dimensional vacua within String Theory using the AdS/CFT correspondence. In the first and second part of the thesis, we study the fibred Calabi-Yau and M-theory moduli stabilization scenario. We consider both flux-stabilized models and non-perturbative stabilization methods. We perform a holographic analysis to determine the spectrum of the assumed dual $CFT_3$ to understand its AdS/CFT implications. For the flux stabilization, which relies on a large complex Chern-Simons invariant, moduli have integer dimensions similar to the DGKT flux-stabilized model in type IIA. For the non-perturbative stabilization, the results are similar to race-track models in type IIB. In the last part of the thesis, we solve the Wheeler DeWitt equation for the planar Reissner-Nordstrom-AdS black hole in a minisuperspace approximation. We construct semiclassical Wheeler-DeWitt states from Gaussian wavepackets that are peaked on classical black hole interior solutions. By using the metric component $g_{xx}$ as a clock, these states are evolved through both the exterior and interior horizons. Close to the singularity, we show that quantum fluctuations in the wavepacket become important, and therefore the classicality of the minisuperspace approximation breaks down. Towards the AdS boundary, the Wheeler-DeWitt states are used to recover the Lorentzian partition function of the dual theory living on this boundary. This partition function is specified by an energy and a charge. Finally, we show that the Wheeler-DeWitt states know about the black hole thermodynamics, recovering the grand canonical thermodynamic potential after an appropriate averaging at the black hole horizon.

💡 Research Summary

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This thesis investigates four‑dimensional vacua in string theory from two complementary perspectives: holographic analysis of moduli‑stabilized compactifications and canonical quantum‑gravity description of charged AdS black holes.

In the first part (Chapters 2‑3) the author studies two classes of compactifications. Chapter 2 focuses on fibred Calabi‑Yau manifolds that realize a “fibred Large Volume Scenario” (LVS). The Kähler potential includes one or two fibre moduli together with the overall volume. Flux‑stabilized models rely on a large complex Chern‑Simons invariant; the resulting superpotential yields integer conformal dimensions for the volume and fibre axions, mirroring the DGKT type‑IIA constructions. Non‑perturbative stabilization is achieved by combining gaugino condensation and Euclidean D‑brane instantons, producing a racetrack‑type potential. In the two‑fibre case the mixed Kähler metric leads to a positive mixed anomalous dimension between different axions, contradicting the earlier “mixed anomalous dimension negativity” conjecture and suggesting a refinement of the swampland criteria.

Chapter 3 extends the analysis to M‑theory compactified on G₂ manifolds. Both flux‑induced superpotentials (from G₄ flux) and non‑perturbative effects (M2‑brane instantons and gaugino condensation) are incorporated. The mass spectrum shows that both the volume modulus and the axionic partners acquire integer scaling dimensions, satisfying the integer‑dimension swampland conjecture and providing a concrete example of a scale‑separated AdS₄ vacuum.

For each compactification the author assumes the existence of a three‑dimensional holographic dual CFT. By matching the moduli masses to operator dimensions, the work extracts qualitative features of the putative CFT₃: integer dimensions correspond to protected or BPS operators, while racetrack potentials imply non‑protected operators with non‑trivial mixing. This holographic interpretation serves as a test of swampland constraints in a setting where explicit CFT data are unavailable.

The second part (Chapter 4) switches to a canonical quantum‑gravity framework. The Wheeler‑DeWitt (WDW) equation for a planar Reissner‑Nordström‑AdS black hole is solved in a minisuperspace truncation where the only dynamical variable is the spatial metric component (g_{xx}) (used as an internal clock) together with the conserved charge (Q). Gaussian wave‑packets are constructed that are sharply peaked on classical interior solutions. Evolving these packets across the outer horizon, the Cauchy horizon, and toward the singularity shows that quantum fluctuations become dominant near the singularity, signaling the breakdown of the minisuperspace approximation.

By extending the WDW states to the AdS boundary, the author recovers a Lorentzian partition function (Z(E,Q)) specified by an energy (E) and charge (Q). This partition function matches the grand‑canonical thermodynamic potential of the black hole after an appropriate averaging over the horizon. The analysis demonstrates that the semiclassical WDW states encode the full thermodynamic data (temperature, chemical potential) of the charged AdS black hole, providing a concrete bridge between bulk quantum gravity wavefunctions and boundary statistical mechanics.

Overall, the thesis makes three principal contributions: (1) it identifies integer operator dimensions and positive mixed anomalous dimensions in concrete string/M‑theory compactifications, offering new data points for swampland conjectures; (2) it presents a detailed holographic interpretation of fibred LVS and M‑theory vacua, highlighting how moduli spectra map to CFT₃ operator content; (3) it shows that Wheeler‑DeWitt wavefunctions, constructed in a simple minisuperspace model, faithfully reproduce black‑hole thermodynamics and the associated boundary partition function, while also exposing the limits of minisuperspace near timelike singularities. Future directions suggested include deriving the WDW equation from string beta‑functions, refining mixed‑anomalous‑dimension criteria for multi‑axion systems, and extending the holographic analysis to more realistic, less symmetric compactifications.