BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Geometric Singularities\, Moduli Stabilization\, and Gravitational
  Wave Signatures in String Compactifications
DTSTART;VALUE=DATE-TIME:20260922T131500Z
DTEND;VALUE=DATE-TIME:20260922T132000Z
DTSTAMP;VALUE=DATE-TIME:20260914T044727Z
UID:indico-contribution-501@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Tetiana Obikhod (Institute for Nuclear Research NAS 
 of Ukraine)\nWe present a unified framework connecting Calabi--Yau geometr
 y\, singularity theory\, and early-universe cosmology within heterotic and
  Type IIB string compactifications. Starting from the Tian--Yau threefold 
 defined by its complete-intersection configuration matrix $P^3$ [3  0  1] 
  ${P}^3$ [0  3  1]\, we demonstrate how a free $\\mathbb{Z}_3$ quotient re
 duces the Euler characteristic to $\\chi=-6$\, yielding precisely three ch
 iral generations. By embedding a stable $SU(4)$ vector bundle with $c_1(V)
 =0$ and $c_2(V)=12 \\leq c_2(TX)=50$\, we satisfy the Green--Schwarz anoma
 ly cancellation condition while preserving $N=1$ supersymmetry and enablin
 g Wilson-line breaking of $E_6$ to the Standard Model gauge group.\n\nA ce
 ntral result is the identification of universal singularity structures gov
 erning vacuum transitions. Generic multi-field scalar potentials correspon
 d to non-simple singularities with Milnor number $\\mu=9$\, but near criti
 cal degeneracy loci the Hessian vanishes and the system universally reduce
 s to an $A_2$ cusp with $\\mu=2$ [1]. This reduction controls the dynamics
  of first-order phase transitions in the early universe. We derive the sto
 chastic gravitational-wave spectrum generated near these critical points\,
  showing that potential flattening enhances the signal amplitude as $\\Ome
 ga_{\\text{GW}} \\propto \\delta^{-3}$\, where $\\delta=1-\\hat{\\xi}/\\ha
 t{\\xi}_c$ measures the distance to criticality. The predicted peak freque
 ncies naturally lie in the milli-Hertz band\, and benchmark points satisfy
 ing strong first-order transition criteria yield $\\Omega_{\\text{GW}}h^2 
 \\sim 10^{-12}\\text{--}10^{-11}$\, placing them directly within the sensi
 tivity window of the LISA mission.\n\nWe systematically analyse the KKLT m
 oduli stabilisation mechanism [2] incorporating leading $\\alpha'^3$ corre
 ctions to the Kähler potential. The correction breaks the classical no-sc
 ale structure and generates three distinct vacuum regimes separated by a c
 ritical threshold $\\hat{\\xi}_c$. For $\\hat{\\xi}  \\hat{\\xi}_c$\, the 
 potential exhibits runaway behaviour characteristic of the Large Volume Sc
 enario or decompactification. The conifold transition mechanism [3]\, wher
 e massless black holes resolve geometric singularities via flop transition
 s\, provides a dynamical pathway connecting parent manifolds to the three-
 generation Tian--Yau/$\\mathbb{Z}_3$ vacuum. We quantify the tension betwe
 en shallow dS vacua near $\\hat{\\xi}_c$ and the de~Sitter swampland conje
 cture\, mapping the parameter space where controlled string constructions 
 remain consistent with quantum gravity constraints. Detailed derivations\,
  explicit benchmark tables\, and the full Hessian analysis are provided in
  [1]. Our results establish a direct observational bridge between compacti
 fication topology\, singularity-driven cosmology\, and gravitational-wave 
 detectors.\nKeywords: String compactification\, Tian--Yau threefold\, coni
 fold transitions\, singularity theory\, Milnor number\, KKLT mechanism\, $
 \\alpha'^3$ corrections\, gravitational waves\, LISA\, de~Sitter swampland
  conjecture.\n\n1.T. Obikhod\, "Supersymmetry\, Supergravity and Non--Pert
 urbative Dynamics of Gauge Theories\," arXiv:2604.19817v1 [hep-th] (2026).
 \n2.S. Kachru\, R. Kallosh\, A. Linde\, S.P. Trivedi\, "De Sitter vacua in
  string theory\," Phys. Rev. D68 (2003) 046005.\n3.A. Strominger\, "Massle
 ss black holes and conifolds in string theory\," Nucl. Phys. B451 (1995) 9
 6--108.\n\nhttps://indico.bitp.kiev.ua/event/18/contributions/501/
LOCATION:Bogolyubov Institute for Theoretical Physics Conference Hall
URL:https://indico.bitp.kiev.ua/event/18/contributions/501/
END:VEVENT
END:VCALENDAR