A DK Phase Transition in q-Deformed Yang-Mills on S^2 and Topological Strings

Abstract

We demonstate the existence of a large $N$ phase transition with respect to the 't Hooft coupling in q-deformed Yang-Mills theory on $S^2$. The strong coupling phase is characterized by the formation of a clump of eigenvalues in the associated matrix model of Douglas-Kazakov (DK) type (hep-th/9305047). By understanding this in terms of instanton contributions to the q-deformed Yang-Mills theory, we gain some insight into the strong coupling phase as well as probe the phase diagram at nonzero values of the $\theta$ angle. The Ooguri-Strominger-Vafa relation (hep-th/0405146) of this theory to topological strings on the local Calabi-Yau $\mathcal{O}(-p)\oplus \mathcal{O}(p-2)\to {\mathbb{P}}^1$ via a chiral decompostion at large $N$ hep-th/0411280, motivates us to investigate the phase structure of the trivial chiral block, which corresponds to the topological string partition function, for $p>2$. We find a phase transition at a different value of the coupling than in the full theory, indicating the likely presence of a rich phase structure in the sum over chiral blocks.

arXiv comment24 pages + 2 Appendices, 5 figures, LaTeX; v2: typos and minor errors corrected, references added, parts of sections 2.3 and 3.3 rewritten for clarity, figure 4 corrected

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Cited by in corpus (19)

• Phases of large $N$ vector Chern-Simons theories on $S^2\times S^1$
• Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory
• Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory
• Phase transitions, double-scaling limit, and topological strings
• Duality and Higher Temperature Phases of Large $N$ Chern-Simons Matter Theories on $S^2\times S^1$
• Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory
• Phase transitions in q-deformed 2d Yang-Mills theory and topological strings
• Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory
• Interacting systems and wormholes
• Partial-Symmetry-Breaking Phase Transitions
• Black-holes, topological strings and large N phase transitions
• A Note on Knot Invariants and q-Deformed 2d Yang-Mills
• Localization for Wilson Loops in Chern-Simons Theory
• Black Holes in Type IIA String on Calabi-Yau Threefolds with Affine ADE Geometries and q-Deformed 2d Quiver Gauge Theories
• Thermodynamics of Noncritical M-Theory and the Topological A-Model
• Refined Chern-Simons theory and (q,t)-deformed Yang-Mills theory: Semi-classical expansion and planar limit
• New Phase Transitions in Chern-Simons Matter Theory
• Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles
• Topological Gauge Theories on Local Spaces and Black Hole Entropy Countings