The Condensate from Torus Knots

Abstract

We discuss recently formulated instanton-torus knot duality in $\Omega$-deformed 5D SQED on ${\mathbb{R}}^4\times S^1$ focusing at the microscopic aspects of the condensate formation in the instanton ensemble. Using the chain of dualities and geometric transitions we embed the SQED with a surface defect into the $SU(2)$ SQCD with $N_f=4$ and identify the numbers $(n,m)$ of the torus $T_{n,m}$ knot as instanton charge and electric charge. The HOMFLY torus knot invariants in the fundamental representation provide entropic factor in the condensate of the massless flavor counting the degeneracy of the instanton--W-boson web with instanton and electric numbers $(n,m)$ but different spin and flavor content. Using the inverse geometrical transition we explain how our approach is related to the evaluation of the HOMFLY invariants in terms of Wilson loop in 3d CS theory. The reduction to 4D theory is briefly considered and some analogy with baryon vertex is conjectured.

46 pages, 16 figures

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Cited by in corpus (7)

• A slow review of the AGT correspondence
• Surface defects and instanton-vortex interaction
• Bands and gaps in Nekrasov partition function
• On Elliptic Algebras and Large-n Supersymmetric Gauge Theories
• Quantum spectral curve for (q,t)-matrix model
• The colored Jones polynomials as vortex partition functions
• Instanton-torus knot duality in 5d SQED and $SU(2)$ SQCD