Search for NS 3-form Flux Induced Vacua for the Critical Non-Abelian Vortex String

Abstract

It has been demonstrated that the non-Abelian solitonic vortex string in four-dimensional (4D) $\mathcal{N}=2$ supersymmetric QCD (SQCD) with gauge group U(2) and $N_f=4$ quark hypermultiplets behaves as a critical superstring. This string propagates in a ten-dimensional space comprising the flat 4D space and an internal Calabi-Yau noncompact threefold, specifically, the conifold. The lowest state of this string is a massless BPS baryon associated with the deformation of the conifold's complex structure modulus, $b$. Previous studies considered deformations of the 10-dimensional background by a nonzero Neveu-Schwarz (NS) 3-form flux, which was interpreted as selecting specific quark masses in 4D SQCD. These deformations and the corresponding back reaction on the metric were analyzed at the leading order at small 3-form flux. In this paper, we first derive the exact potential for the conifold complex structure modulus $b$ generated by the 3-form flux assuming a fixed conifold background. Then we include the back reaction effects and solve the corresponding gravity equations of motion. We show that the resulting potential gives a runaway vacuum. At this runaway vacuum the conifold undergoes degeneration.

arXiv comment41 pages, 3 figures; v2: typos corrected. arXiv admin note: text overlap with arXiv:2209.08118, arXiv:2105.02645

References in corpus (31)

• Hierarchies from Fluxes in String Compactifications
• Phases of $N=2$ Theories In Two Dimensions
• Supergravity and a Confining Gauge Theory: Duality Cascades and $\chi$SB-Resolution of Naked Singularities
• Massless Black Holes and Conifolds in String Theory
• Gravity Duals of Supersymmetric SU(N) x SU(N+M) Gauge Theories
• Vortices, Instantons and Branes
• Semilocal and Electroweak Strings
• Nonabelian Superconductors: Vortices and Confinement in $\mathcal{N}=2$ SQCD
• Solitons in the Higgs phase -- the moduli matrix approach --
• Vortex Strings and Four-Dimensional Gauge Dynamics
• Non-Abelian String Junctions as Confined Monopoles
• Gauge Theory and the Excision of Repulson Singularities
• Gravity Duals of Fractional Branes and Logarithmic RG Flow
• Type II Theories Compactified on Calabi-Yau Threefolds in the Presence of Background Fluxes
• Monopoles in the Higgs Phase
• Quantum Vortex Strings: A Review
• Non-Abelian Semilocal Strings in N=2 Supersymmetric QCD
• On the moduli space of semilocal strings and lumps
• Deformation of Conifold and Intersecting Branes
• Moduli Potentials in Type IIA Compactifications with RR and NS Flux
• 3-branes on spaces with R x S^2 x S^3 topology
• Effective World-Sheet Theory for Non-Abelian Semilocal Strings in N = 2 Supersymmetric QCD
• The long flow to freedom
• Critical String from Non-Abelian Vortex in Four Dimensions
• Non-Abelian Vortex in Four Dimensions as a Critical String on a Conifold
• Critical Non-Abelian Vortex in Four Dimensions and Little String Theory
• Hadrons of N=2 Supersymmetric QCD in Four Dimensions from Little String Theory
• Studying Critical String Emerging from Non-Abelian Vortex in Four Dimensions
• String "Baryon'' in Four-Dimensional $\mathcal{N}=2$ Supersymmetric QCD from 2D-4D Correspondence
• Flux Compactification for the Critical Non-Abelian Vortex and Quark Masses
• NS Three-form Flux Deformation for the Critical Non-Abelian Vortex String