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.
The Self-Tuning of the Cosmological Constant and the Holographic Relaxion
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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.