Talks

The search for algebraic foundations of colour-kinematics duality and the double-copy construction has brought into focus a generalization of Batalin--Vilkovisky algebras, referred to here as coexact BV-algebras and as $\textrm{BV}^\square$-algebras in other sources. While these structures capture the cubic sector, they fail to encode higher-valence phenomena, for which a homotopy-theoretic extension becomes necessary. This work introduces a conceptual notion of homotopy coexact BV-algebra, defined through the homotopical interplay of commutative and BV structures, and provides a concrete model in terms of generators and relations, obtained through an extension the theory of Koszul duality for operads.

Irrational CFTs in 1+1d with a discrete spectrum and no conserved currents other than the stress-tensor are expected to be generic, unsolvable by standard methods, and hard to construct explicitly. In this talk, I will discuss a lattice model that realizes a candidate for such a CFT as a conformal phase of matter without fine-tuning. The model is constructed by coupling N ≥ 3 golden anyon chains together, preserving N copies of the Fibonacci non-invertible symmetry. I will briefly describe the N=2 case, where a weakly first-order phase transition (previously misidentified as an irrational CFT) occurs and some non-trivial (but rational) CFTs appear as unstable fixed points. For N = 3 we will show that a short RG flow occurs towards a stable CFT in the infrared with c~2.09. We indirectly argue that the CFT is irrational by comparing with a list of known rational CFTs with similar central charge. We will end with a discussion of other approaches that could be used to confirm/disprove our claim.

We showcase cosmology's ability to constrain long-range forces between dark matter particles. Specifically, we consider a fermionic dark matter interacting via a Yukawa-coupled light scalar, focusing on regimes where the dark forces are stronger than gravitational and yet unconstrained. We show that the dark sector dynamics, both at the background and perturbation levels, is far richer than what can be captured with just the static interparticle Yukawa potential. The background dynamics includes an attractor that funnels a wide range of initial conditions onto an evolution unique to each parameter space. In a large swath of parameter space beyond existing limits, the dark sector deviates drastically from cold dark matter in observable epochs. We rule out this parameter space using existing constraints on dark-sector equation of state and small-scale cosmic perturbations, thus setting the strongest constraints yet on dark matter self-interactions at length scales shorter than 100 kpc. In addition, we briefly discuss repulsive dark forces and place cosmological limits that are stricter than in the attractive case.