The free energy of any CFT, $ \ln Z(\beta; \omega_i)$, admits two expansions: high temperature ($\beta \rightarrow 0$) and fast rotation ($\omega_i \rightarrow 1$). We demonstrate that in $4d$, locality of the thermal effective action forces $\ln Z$ to take a simple analytic form at all orders in the high temperature expansion, and further imposes an infinite number of sharp relations on the coefficients in this expansion. All are homogeneous, except at order $\beta^1$ due to the Weyl anomaly. From this, the $a$-anomaly can be extracted from the partition function. The relations resum in the fast-spinning expansion into differential equations in $\beta$ obeyed by the semi-universal limit and its corrections. We verify the relations in a variety of CFTs. We generalize to any even $d$, but find no similar relations at odd $d$.
We discuss the tension one encounters in trying to solve, simultaneously, the $U(1)$ and strong-$CP$ problems in QCD with light quarks and a small $\bar{\theta}$ angle within QCD itself. We do so by considering the low-energy expansion of a $1$PI effective action $\Gamma$, a functional of a properly chosen set of gauge...
P. Di Vecchia, Francesco Sannino, G. M. Shore et al.· 2 citations
We study the thermal partition function of the critical large-$N$ $O(N)$ model on rotating $S^1\times S^2$. Rotation makes the saddle latitude dependent, with its leading profile governed by the local temperature. Using a Weyl-covariant hydrostatic expansion, we determine the partition function through four-derivative...
We calculate the three-loop $\mathcal{O}(\alpha\alpha_s^2)$ mixed QCD-EW corrections to the top quark mass and obtain the relationships between the pole ($M_t$) and $\overline{\rm{MS}}$ ($m_t(\mu)$) masses at this order. In performing our calculation, we express the three-loop self-energies as a function of three-loop...
We calculate the $\theta$ dependence of the vacuum energy in an infinite family of cousins of QCD, where the vacuum structure can be analyzed exactly. These theories are $\mathcal{N}=1$ EFTs that descend from $\mathcal{N}=2$ $SU(N_c)$ gauge theory with $N_f$ flavors of fundamental hypermultiplets, that are then deforme...
Dhruv Aldas, Hitoshi Murayama, B. Noether et al.· 0 citations
In this work we estimate the first unknown QCD correction to the decay of the Higgs boson into gluons, $H\to gg$, in the heavy-top limit using Pad\'e approximants built to the perturbative series and to its Borel transform. In the process, we also obtain estimates for the first unknown coefficients of the QCD $\beta$ f...
D. Boito, C. Y. London, Guilherme A. Nogueira· 0 citations
We develop an analytic theory of the recently proposed $U(1)$ symmetry breaking at interacting 1+1D Lifshitz quantum critical points. The low-energy theory contains two compact fields, $\theta$ and $\phi$, coupled by a Berry term that makes $\theta$ canonically conjugate to the conserved density $\partial_x\phi$. Withi...
E. S. Andriyakhina, A. S. Shankar, T. Senthil et al.· 1 citation
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