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 deformed by anomaly mediated supersymmetry breaking (AMSB). We reproduce results found in previous work that used the full $\mathcal{N}=2$ machinery but via a much simpler $\mathcal{N}=1$ method. Our method easily extends to infinitely many more theories for which the full $\mathcal{N}=2$ approach becomes intractable. We identify values of $\theta$ for which the theory undergoes a phase transition, and find that they can occur at both fractional and irrational values of $\theta/\pi$.
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 e...
Arnav Advant, H. Anand, Nathan Benjamin et al.· 0 citations
We study correlation functions of topologically twisted $\mathcal N=2$ supersymmetric QCD with gauge group $\mathrm{SU}(N)$ on a compact four-manifold $X$. We derive the Coulomb branch integral for all $N$, including new couplings to background fluxes for the flavor symmetry. For $X$ of simple type with $b_2^+>1$, the...
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
At high temperature instantons form a dilute gas, so in QCD-like theories the breaking of the anomalous $U(1)_A$ symmetry is given by integral powers of the anomalous determinant, $\sim (\det \Phi)^{Q}$, where $\Phi\sim \overline{q}_L q_R$ is bilinear in the quark fields, and with untwisted boundary conditions, the top...
In the late 1990s, Suzuki and Yasuta proposed a compact formula that extracts the decay rate per unit volume of a false vacuum in the $D$-dimensional $O(N)$ $\lambda(\phi^2)^2$ theory with an unbounded potential from conventional perturbative coefficients of the vacuum energy density, i.e., vacuum bubble diagrams. The...
We study the superconformal index of four-dimensional $\mathcal{N}=2$ $\mathrm{SU}(N)$ elliptic models through the Bethe Ansatz approach, where the index is evaluated as a sum of vacua arising from a set of transcendental equations. Starting from the known discrete solutions of these equations, that we refer to as prog...
A. Amariti, Pietro Glorioso, Chiara Mascherpa et al.· 0 citations
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