Statistical Mechanics of Vortices from D-branes and T-duality

Abstract

We propose a novel and simple method to compute the partition function of statistical mechanics of local and semi-local BPS vortices in the Abelian-Higgs model and its non-Abelian extension on a torus. We use a D-brane realization of the vortices and T-duality relation to domain walls. We there use a special limit where domain walls reduce to gas of hard (soft) one-dimensional rods for Abelian (non-Abelian) cases. In the simpler cases of the Abelian-Higgs model on a torus, our results agree with exact results which are geometrically derived by an explicit integration over the moduli space of vortices. The equation of state for U(N) gauge theory deviates from van der Waals one, and the second virial coefficient is proportional to 1/sqrt{N}, implying that non-Abelian vortices are "softer" than Abelian vortices. Vortices on a sphere are also briefly discussed.

20 pages, 18 figures

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Cited by in corpus (28)

• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Constructing Non-Abelian Vortices with Arbitrary Gauge Groups
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• Domain Walls with Non-Abelian Clouds
• On the L^2-metric of vortex moduli spaces
• Intersecting Solitons, Amoeba and Tropical Geometry
• Non-Abelian Vortices in SO(N) and USp(N) Gauge Theories
• Fractional Vortices and Lumps
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• Non-Abelian Sine-Gordon Solitons: Correspondence between $SU(N)$ Skyrmions and $\mathbb{C}{P}^{N-1}$ Lumps
• Interactions of Non-Abelian Global Strings
• Relations among topological solitons
• Non-Abelian Monopoles in the Higgs Phase
• Dynamics of Strings between Walls
• Non-Abelian Global Vortices
• Non-Abelian Global Strings at Chiral Phase Transition
• Static Interactions of non-Abelian Vortices
• The Moduli Space Metric for Well-Separated Non-Abelian Vortices
• Group Theory of Non-Abelian Vortices
• Neutral bions in the CP^{N-1} model for resurgence
• Chiral Magnets from String Theory
• Vortex counting from field theory
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• The Volume of the Quiver Vortex Moduli Space
• Vortex counting and the quantum Hall effect
• Quantum Statistical Mechanics of Vortices
• Counting BPS Solitons and Applications