Conformally soft fermions

Celestial diamonds encode the global conformal multiplets of the conformally soft sector, elucidating the role of soft theorems, symmetry generators and Goldstone modes. Upon adding supersymmetry they stack into a pyramid. Here we treat the soft charges associated to the fermionic layers that tie this structure together. This extends the analysis of conformally soft currents for photons and gravitons which have been shown to generate asymptotic symmetries in gauge theory and gravity to infinite-dimensional fermionic symmetries. We construct fermionic charge operators in 2D celestial CFT from a suitable inner product between 4D bulk field operators and spin s = $$ \frac{1}{2} $$ 1 2 and $$ \frac{3}{2} $$ 3 2 conformal primary wavefunctions with definite SL(2, ℂ) conformal dimension ∆ and spin J where |J| ≤ s. The generator for large supersymmetry transformations is identified as the conformally soft gravitino primary operator with ∆ = $$ \frac{1}{2} $$ 1 2 and its shadow with ∆ = $$ \frac{3}{2} $$ 3 2 which form the left and right corners of the celestial gravitino diamond. We continue this analysis to the subleading soft gravitino and soft photino which are captured by degenerate celestial diamonds. Despite the absence of a gauge symmetry in these cases, they give rise to conformally soft factorization theorems in celestial amplitudes and complete the celestial pyramid.

Heavy + light pseudoscalar meson semileptonic transitions

A symmetry-preserving regularisation of a vector $$\times $$ × vector contact interaction (SCI) is used to deliver a unified treatment of semileptonic transitions involving $$\pi $$ π , K, $$D_{(s)}$$ D ( s ) , $$B_{(s,c)}$$ B ( s , c ) initial states. The framework is characterised by algebraic simplicity, few parameters, and the ability to simultaneously treat systems from Nambu–Goldstone modes to heavy+heavy mesons. Although the SCI form factors are typically somewhat stiff, the results are comparable with experiment and rigorous theory results. Hence, predictions for the five unmeasured $$B_{s,c}$$ B s , c branching fractions should be a reasonable guide. The analysis provides insights into the effects of Higgs boson couplings via current-quark masses on the transition form factors; and results on $$B_{(s)}\rightarrow D_{(s)}$$ B ( s ) → D ( s ) transitions yield a prediction for the Isgur–Wise function in fair agreement with contemporary data.

Emergent Replica Conformal Symmetry in Non-Hermitian SYK2 Chains

Recently, the steady states of non-unitary free fermion dynamics are found to exhibit novel critical phases with power-law squared correlations and a logarithmic subsystem entanglement. In this work, we theoretically understand the underlying physics by constructing solvable static/Brownian quadratic Sachdev-Ye-Kitaev chains with non-Hermitian dynamics. We find the action of the replicated system generally shows (one or infinite copies of) O(2)×O(2) symmetries, which is broken to O(2) by the saddle-point solution. This leads to an emergent conformal field theory of the Goldstone modes. We derive the effective action and obtain the universal critical behaviors of squared correlators. Furthermore, the entanglement entropy of a subsystem A with length LA corresponds to the energy of the half-vortex pair S∼ρslog⁡LA, where ρs is the total stiffness of the Goldstone modes. We also discuss special limits with more than one branch of Goldstone modes and comment on interaction effects.

Late time physics of holographic quantum chaos

Quantum chaotic systems are often defined via the assertion that their spectral statistics coincides with, or is well approximated by, random matrix theory. In this paper we explain how the universal content of random matrix theory emerges as the consequence of a simple symmetry-breaking principle and its associated Goldstone modes. This allows us to write down an effective-field theory (EFT) description of quantum chaotic systems, which is able to control the level statistics up to an accuracy {O} \left(e^{-S} \right)O(e−S) with SS the entropy. We explain how the EFT description emerges from explicit ensembles, using the example of a matrix model with arbitrary invariant potential, but also when and how it applies to individual quantum systems, without reference to an ensemble. Within AdS/CFT this gives a general framework to express correlations between ``different universes’’ and we explicitly demonstrate the bulk realization of the EFT in minimal string theory where the Goldstone modes are bound states of strings stretching between bulk spectral branes. We discuss the construction of the EFT of quantum chaos also in higher dimensional field theories, as applicable for example for higher-dimensional AdS/CFT dual pairs.

Control of traveling localized spots

Traveling localized spots represent an important class of self-organized two- dimensional patterns in reaction-diffusion systems. We study open-loop control intended to guide a stable spot along a desired trajectory with desired velocity. Simultaneously, the spot's concentration profile does not change under control. For a given protocol of motion, we first express the control signal analytically in terms of the Goldstone modes and the propagation velocity of the uncontrolled spot. Thus, detailed information about the underlying nonlinear reaction kinetics is unnecessary. Then, we confirm the optimality of this solution by demonstrating numerically its equivalence to the solution of a regularized, optimal control problem. To solve the latter, the analytical expressions for the control are excellent initial guesses speeding-up substantially the otherwise time-consuming calculations.

The non-linear σ-model near two dimensions: Phase structure

This chapter is devoted to the study of the non-linear σ-model, a quantum field theory (QFT) where the (scalar) field is an N-component vector of fixed length, mostly in dimensions close to 2. The model possesses a global, non-linearly realized symmetry, O(N) symmetry: under a group transformation, the transformed field is a non-linear function of the field itself. The non-linear σ-model belongs to a class of models constructed on special homogeneous spaces, symmetric spaces that, as Riemannian manifolds, admit a unique metric. Unlike what happens in a (ϕ2)2 -like field theory with the same symmetry, in the non-linear σ-model, in the tree approximation, the O(N) symmetry is always spontaneously broken: the action describes the interactions of (N−1) massless fields, the Goldstone modes. Since the fields are massless, in two dimensions infrared divergences appear in the perturbative expansion and an infrared regulator is required. To understand the phase structure beyond leading order, a renormalization group (RG) analysis is necessary. This requires understanding how the model renormalizes. Power counting shows that the model is renormalizable in two dimensions. Since the field then is dimensionless, although the degree of divergence of Feynman diagrams is bounded, an infinite number of counterterms is generated, because all correlation functions are divergent. A quadratic master equation satisfied by the generating functional of vertex functions is derived, which makes it possible to prove that the coefficients of all counterterms are related, and that the renormalized theory depends only on two parameters.