Flux Compactification for the Critical Non-Abelian Vortex and Quark Masses

Abstract

It has been shown that non-Abelian solitonic vortex strings supported in four-dimensional (4D) $\mathcal{N}=2$ supersymmetric QCD (SQCD) with the U($N=2$) gauge group and $N_f=4$ quark flavors behave as critical superstrings. In addition to four translational moduli non-Abelian strings under consideration carry six orientational and size moduli. Together they form a ten-dimensional space required for a superstring to be critical. The target space of the string sigma model is a product of the flat four-dimensional space ${\mathbb{R}}^4$ and a Calabi-Yau non-compact threefold $Y_6$, namely, the conifold. The spectrum of low lying closed string states in the associated type IIA string theory was found and interpreted as a spectrum of hadrons in 4D $\mathcal{N}=2$ SQCD. In particular, the lowest string state appears to be a massless BPS baryon associated with the deformation of the complex structure modulus $b$ of the conifold. Here we address a problem of switching on quark masses in 4D SQCD, which classically breaks the world sheet conformal invariance in the string sigma model. To avoid this problem we follow a standard string theory approach and use a flux "compactification" to lift the complex structure modulus of the conifold. Namely, we find a solution of supergravity equations of motion with non-zero NS 3-form flux. It produces a potential for the baryon $b$, which leads to the run-away vacuum. Using field theory arguments we interpret 3-form flux in terms of a particular choice of quark masses in 4D SQCD. At the run-away vacuum the conifold degenerates to lower dimensions. We interpret this as a flow from a non-Abelian string to an Abelian one.

arXiv comment32 pages. arXiv admin note: text overlap with arXiv:2006.12054, arXiv:1704.00825

References in corpus (34)

• Phases of $N=2$ Theories In Two Dimensions
• Supergravity and a Confining Gauge Theory: Duality Cascades and $\chi$SB-Resolution of Naked Singularities
• Gravity Duals of Supersymmetric SU(N) x SU(N+M) Gauge Theories
• Vortices, Instantons and Branes
• Semilocal and Electroweak Strings
• On Classification of N=2 Supersymmetric Theories, (e-mail uncorrupted version)
• 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
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Gravity Duals of Fractional Branes and Logarithmic RG Flow
• Type II Theories Compactified on Calabi-Yau Threefolds in the Presence of Background Fluxes
• Branes and N=2 Theories in Two Dimensions
• Monopoles in the Higgs Phase
• TASI Lectures on Solitons
• Quantum Vortex Strings: A Review
• Non-Abelian Semilocal Strings in N=2 Supersymmetric QCD
• On the moduli space of semilocal strings and lumps
• The BPS Spectra of Gauge Theories in Two and Four Dimensions
• 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
• The BPS Spectra of Two-Dimensional Supersymmetric Gauge Theories with Twisted Mass Terms
• 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
• Quantum Dynamics of Low-Energy Theory on Semilocal Non-Abelian Strings
• 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
• Long Way to Ricci Flatness

Cited by in corpus (3)

• Critical Non-Abelian Vortex and Holography for Little String Theory
• NS Three-form Flux Deformation for the Critical Non-Abelian Vortex String
• Search for NS 3-form Flux Induced Vacua for the Critical Non-Abelian Vortex String