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.
Sachdev,Polylogarithm identities in a conformal field theory in three-dimensions,Phys
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abstract
The $N=\infty$ vector $O(N)$ model is a solvable, interacting field theory in three dimensions ($D$). In a recent paper with A. Chubukov and J. Ye~\cite{self}, we have computed a universal number, $\tilde{c}$, characterizing the size dependence of the free energy at the conformally-invariant critical point of this theory. The result~\cite{self} for $\tilde{c}$ can be expressed in terms of polylogarithms. Here, we use non-trivial polylogarithm identities to show that $\tilde{c}/N = 4/5$, a rational number; this result is curiously parallel to recent work on dilogarithm identities in $D=2$ conformal theories. The amplitude of the stress-stress correlator of this theory, $c$ (which is the analog of the central charge), is determined to be $c/N=3/4$, also rational. Unitary conformal theories in $D=2$ always have $c = \tilde{c}$; thus such a result is clearly not valid in $D=3$.
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A thermal normal-ordering scheme yields systematic epsilon-expansions for thermal observables in PT-symmetric cubic and quintic O(N) models, agreeing with exact 2D results from minimal models M(2,5) and M(3,8)_D and providing higher-d extrapolations.
Lectures summarizing the construction of hydrodynamic EFTs through strong-to-weak symmetry breaking, with examples from spin chains to relativistic QFTs and UV/IR constraints on transport coefficients.
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CFTs on Squashed Spheres and the Thermal Effective Action
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.
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$\mathcal{PT}$-symmetric Field Theories at Finite Temperature
A thermal normal-ordering scheme yields systematic epsilon-expansions for thermal observables in PT-symmetric cubic and quintic O(N) models, agreeing with exact 2D results from minimal models M(2,5) and M(3,8)_D and providing higher-d extrapolations.
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Boulder Lectures on Thermal Dynamics and Hydrodynamic EFTs
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