Derives universal quadratic response of 3D CFT free energy to S^3 squashing proportional to c_T and constructs thermal effective action for high-T Seifert manifolds with explicit Wilson coefficients.
Conformal QED$_d$, $F$-Theorem and the $\epsilon$ Expansion
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abstract
We calculate the free energies $F$ for $U(1)$ gauge theories on the $d$ dimensional sphere of radius $R$. For the theory with free Maxwell action we find the exact result as a function of $d$; it contains the term $\frac{d-4}{2} \log R$ consistent with the lack of conformal invariance in dimensions other than 4. When the $U(1)$ gauge theory is coupled to a sufficient number $N_f$ of massless 4 component fermions, it acquires an interacting conformal phase, which in $d<4$ describes the long distance behavior of the model. The conformal phase can be studied using large $N_f$ methods. Generalizing the $d=3$ calculation in arXiv:1112.5342, we compute its sphere free energy as a function of $d$, ignoring the terms of order $1/N_f$ and higher. For finite $N_f$, following arXiv:1409.1937 and arXiv:1507.01960, we develop the $4-\epsilon$ expansion for the sphere free energy of conformal QED$_d$. Its extrapolation to $d=3$ shows very good agreement with the large $N_f$ approximation for $N_f>3$. For $N_f$ at or below some critical value $N_{\rm crit}$, the $SU(2N_f)$ symmetric conformal phase of QED$_3$ is expected to disappear or become unstable. By using the $F$-theorem and comparing the sphere free energies in the conformal and broken symmetry phases, we show that $N_{\rm crit}\leq 4$. As another application of our results, we calculate the one loop beta function in conformal QED$_6$, where the gauge field has a 4-derivative kinetic term. We show that this theory coupled to $N_f$ massless fermions is asymptotically free.
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Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
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de Sitter Vacua & pUniverses
The charge-p Schwinger model on de Sitter space has p distinct, locally indistinguishable, de Sitter-invariant Hadamard vacuum states produced by spontaneously broken discrete Z_p symmetries.