We analyze fractional phase-transition energies with periodic heterogeneities at the critical H1/2 scaling. We prove that the Γ-limit is a sharp-interface functional whose surface energy density combines homogenization and averaging effects. The resulting coefficient is a weighted combination of the minimum and the mean of the oscillatory parameter, reflecting the coexistence of multiple interaction scales. This behavior is specific to the critical regime and differs from the case s > 1/2.
The origin of obscuration in active galactic nuclei (AGN) is still a matter of contention. It is unclear whether obscured AGN are primarily due to line-of-sight effects (Orientation model), a transitory, dust-enshrouded phase in galaxy evolution (Evolution models), or a combination of both. The role of an inner torus around the central supermassive black hole also remains unclear in pure Evolution models. We use cosmological semi-analytic models and semi-empirical prescriptions to explore obscuration effects in AGN at cosmic noon, in the range 1 < z < 3. We consider a realistic object-by-object modelling of AGN evolution including different AGN light curves (LCs) composed of phases of varying levels of obscuration, usually (but not uniquely) with a larger degree of obscuration before the peak of AGN activity, mimicking the possible clearing effects of strong AGN feedback. Evolution models characterized by AGN LCs with relatively short pre-peak obscured phases followed by more extended optical/ultraviolet (UV) visible post-peak phases, struggle to reproduce the high fraction of obscured AGN at z similar to 2-3 inferred from X-ray surveys. Evolution models characterized by AGN LCs with sharp post-peak declines or persistent or multiple obscuration phases are more successful, although they still face challenges in reproducing the steady drop in the fractions of obscured AGN with increasing luminosity measured by some groups. Invoking a fine-tuning in the input LCs, with more luminous AGN defined by longer optical/UV visible windows, can improve the match to the decreasing fractions of obscured AGN with luminosity. Alternatively, a long-lived central torus-like component, with thickness decreasing with increasing AGN power, naturally boosts the luminosity-dependent fractions of obscured AGN, suggesting that small-scale orientation effects may still represent a key component even in Evolution models. We also find that in our models major mergers and starbursts, when considered in isolation, fall short in accounting for the large fractions of highly obscured faint AGN detected at cosmic noon.
We study QCD on AdS space with scalars or fermions in the fundamental representation, extending earlier results on pure Yang-Mills theory. In the latter, the Dirichlet boundary condition is conjectured to disappear via merger and annihilation, as signaled by the lightest scalar singlet operator approaching marginality as the coupling increases. With matter, there are two candidate operators for this mechanism. We compute their one-loop anomalous dimensions via broken conformal Ward identities and Witten diagrams. In the confining phase, with Dirichlet (Neumann) boundary condition, their anomalous dimensions are negative (positive), consistent with the disappearance (persistence) of the associated boundary CFT in the flat-space limit. In the conformal window, one of these operators becomes the displacement operator of the IR CFT, as signaled by the vanishing of its one-loop anomalous dimension in the perturbative Banks-Zaks regime. Possible scenarios for the lower edge of the conformal window are discussed. Finally, we consider general boundary conditions on fermions and discuss their relation to chiral symmetry breaking in flat space.
We study the N = 3 case of the CPN-1 model, which is a field theory of N complex scalars in 3d coupled to an Abelian gauge field with SU(N) & times; U(1) global symmetry. Recent evidence suggests the N = 2 theory is not critical, which makes the N = 3 theory the simplest possibility of deconfined quantum criticality. We apply the conformal bootstrap to correlators of charge q = 0, 1, 2 scalar operators under the U(1) symmetry, which gives us access also to q = 3, 4 operators. After imposing that only the lowest q = 0, 1, 2 scalar operators are relevant, we find that the bootstrap bounds are saturated by the large N prediction for q = 1, 2, 3, 4 scalar monopole operator scaling dimensions, which were shown earlier to be accurate even for small N, as well as a lattice prediction for the q = 0 non-monopole scalar operator. We also predict the scaling dimensions of the lowest spinning monopole operators, which we match to the large charge prediction for spinning operators. This suggests that the critical CP2 model is described by this bootstrap bound.
The upcoming Laser Interferometer Space Antenna will detect up to thousands of extreme-massratio inspirals (EMRIs). These sources will spend 105 cycles in band and are therefore sensitive to tiny changes in the general-relativistic dynamics, potentially induced by astrophysical environments or modifications of general relativity (GR). Previous studies have shown that these effects can be highly degenerate for a single source. However, it may be possible to distinguish between them at the population level, because environmental effects should impact only a fraction of the sources, while modifications of GR would affect all. We therefore introduce a population-based hierarchical framework to disentangle the two hypotheses. Using simulated EMRI populations, we perform tests of the null vacuum-GR hypothesis and two alternative beyond-vacuum-GR hypotheses, namely, migration torques (environmental effects) and time-varying G (modified gravity). We find that with as few as X20 detected sources our framework can statistically distinguish between these three hypotheses and even indicate if both environmental and modified gravity effects are simultaneously present in the population. Our framework can be applied to other models of beyond-vacuum-GR effects available in the literature.
