Holographic confining QFTs on negative-curvature manifolds show no phase transitions with a dominant saddle, while positive-curvature cases exhibit first- and second-order transitions depending on the theory class, plus a Vafa-Witten theorem at theta zero.
Holographic RG flows on curved manifolds and quantum phase transitions
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In the quark-meson model on thermal AdS, chiral symmetry is always broken near the boundary with unique regular inhomogeneous condensate solutions; temperature restores symmetry while negative curvature favors breaking, and the phase diagram is modified by the Hawking-Page transition.
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The phase diagram of confining holographic theories on constant curvature manifolds in the presence of a $\theta$-angle
Holographic confining QFTs on negative-curvature manifolds show no phase transitions with a dominant saddle, while positive-curvature cases exhibit first- and second-order transitions depending on the theory class, plus a Vafa-Witten theorem at theta zero.
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Chiral symmetry breaking and inhomogeneous phases in thermal anti-de Sitter spacetime
In the quark-meson model on thermal AdS, chiral symmetry is always broken near the boundary with unique regular inhomogeneous condensate solutions; temperature restores symmetry while negative curvature favors breaking, and the phase diagram is modified by the Hawking-Page transition.