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A bstract We construct the Supersymmetric Effective Field Theory of Inflation, that is the most general theory of inflationary fluctuations when time-translations and supersymmetry are spontaneously broken. The non-linear realization of these invariances allows us to define a complete SUGRA multiplet containing the graviton, the gravitino, the Goldstone of time translations and the Goldstino, with no auxiliary fields. Going to a unitary gauge where only the graviton and the gravitino are present, we write the most general Lagrangian built out of the fluctuations of these fields, invariant under time-dependent spatial diffeomorphisms, but softly-breaking time diffeomorphisms and gauged SUSY. With a suitable Stückelberg transformation, we introduce the Goldstone boson of time translation and the Goldstino of SUSY. No additional dynamical light field is needed. In the high energy limit, larger than the inflationary Hubble scale for the Goldstino, these fields decouple from the graviton and the gravitino, greatly simplifying the analysis in this regime. We study the phenomenology of this Lagrangian. The Goldstino can have a non-relativistic dispersion relation. Gravitino and Goldstino affect the primordial curvature perturbations at loop level. The UV modes running in the loops generate three-point functions which are degenerate with the ones coming from operators already present in the absence of supersymmetry. Their size is potentially as large as corresponding to f NL equil., orthog.  ∼ 1 or, for particular operators, even ≫ 1. The non-degenerate contribution from modes of order H is estimated to be very small.

A bstract We study aspects of chaos and thermodynamics at strong coupling in a scalar model using LCT numerical methods. We find that our eigenstate spectrum satisfies Wigner-Dyson statistics and that the coefficients describing eigenstates in our basis satisfy Random Matrix Theory (RMT) statistics. At weak coupling, though the bulk of states satisfy RMT statistics, we find several scar states as well. We then use these chaotic states to compute the equation of state of the model, obtaining results consistent with Conformal Field Theory (CFT) expectations at temperatures above the scale of relevant interactions. We also test the Eigenstate Thermalization Hypothesis by computing the expectation value of local operators in eigenstates, and check that their behavior is consistent with thermal CFT values at high temperatures. Finally, we compute the Spectral Form Factor (SFF), which has the expected behavior associated with the equation of state at short times and chaos at long times. We also propose a new technique for extracting the connected part of the SFF without the need of disorder averaging by using different symmetry sectors.

A bstract We investigate symmetry and causality constraints on interacting Fermi liquids. Whereas Galilean or Lorentz boost symmetry leads to a well-known constraint on the first Landau parameter F 1 , we show that scale invariance similarly constrains F 0 . In the case of conformal Fermi liquids, we show that causality constraints on the particle-hole continuum and on zero sound strongly restrict the available parameter space for interacting Fermi liquids. We also consider nonlinear response, which we show is sensitive to additional “generalized Landau parameters” even at lowest orders in the long wavelength limit. We impose Galilean, Lorentz and scale symmetry on these generalized Landau parameters, obtaining further nonlinear constraints. We test our constraints in several microscopic models that enter a Fermi liquid phase.

A bstract Certain CFTs with a global U(1) symmetry become superfluids when coupled to a chemical potential. When this happens, a Goldstone effective field theory controls the spectrum and correlators of the lightest large charge operators. We show that in 3d, this EFT contains a single parity-violating 1-derivative term with quantized coefficient. This term forces the superfluid ground state to have vortices on the sphere, leading to a spectrum of large charge operators that is remarkably richer than in parity-invariant CFTs. We test our predictions in a weakly coupled Chern-Simons matter theory.

A bstract We explore the implications of the averaged null energy condition for thermal states of relativistic quantum field theories. A key property of such thermal states is the thermalization length. This lengthscale generalizes the notion of a mean free path beyond weak coupling, and allows finite size regions to independently thermalize. Using the eigenstate thermalization hypothesis, we show that thermal fluctuations in finite size ‘fireballs’ can produce states that violate the averaged null energy condition if the thermalization length is too short or if the shear viscosity is too large. These bounds become very weak with a large number N of degrees of freedom but can constrain real-world systems, such as the quark-gluon plasma.

We set up and analyze the lightcone Hamiltonian for an abelian Chern-Simons field coupled to Nf fermions in the limit of large Nf using conformal truncation, i.e. with a truncated space of states corresponding to primary operators with dimension below a maximum cutoff Δmax. In both the Chern-Simons theory, and in the O(N) model at infinite N, we compute the current spectral functions analytically as a function of Δmax and reproduce previous results in the limit that the truncation Δmax is taken to ∞. Along the way, we determine how to preserve gauge invariance and how to choose an optimal discrete basis for the momenta of states in the truncation space.

A bstract We set up and analyze the lightcone Hamiltonian for an abelian Chern-Simons field coupled to N f fermions in the limit of large N f using conformal truncation, i.e. with a truncated space of states corresponding to primary operators with dimension below a maximum cutoff Δ max . In both the Chern-Simons theory, and in the O ( N ) model at infinite N , we compute the current spectral functions analytically as a function of Δ max and reproduce previous results in the limit that the truncation Δ max is taken to ∞. Along the way, we determine how to preserve gauge invariance and how to choose an optimal discrete basis for the momenta of states in the truncation space.

Transport and the approach to equilibrium in interacting classical and quantum systems is a challenging problem of both theoretical and experimental interest. One useful organizing principle characterizing equilibration is the dissipative universality class, the most prevalent one being diffusion. In this paper, we use the effective field theory (EFT) of diffusion to systematically obtain universal power-law corrections to diffusion. We then employ large-scale simulations of classical and quantum systems to explore their validity. In particular, we find universal scaling functions for the corrections to the dynamical structure factor \\(\\langle n(x,t)n\\rangle\\), in the presence of a single \\(U(1)\\) or \\(SU(2)\\) charge in systems with and without particle-hole symmetry, and present the framework to generalize the calculation to multiple charges. Classical simulations show remarkable agreement with EFT predictions for subleading corrections, pushing precision tests of effective theories for thermalizing systems to an unprecedented level. Moving to quantum systems, we perform large-scale tensor-network simulations in unitary and noisy 1d Floquet systems with conserved magnetization. We find a qualitative agreement with EFT which becomes quantitative in the case of noisy systems. Additionally, we show how the knowledge of EFT corrections allows for fitting methods, which can improve the estimation of transport parameters at the intermediate times accessible by simulations and experiments. Finally, we explore non-linear response in quantum systems and find that EFT provides an accurate prediction for its behavior. Our results provide a basis for a better understanding of the non-linear phenomena present in thermalizing systems.

Approximate symmetries abound in Nature. If these symmetries are also spontaneously broken, the would-be Goldstone modes acquire a small mass, or inverse correlation length, and are referred to as pseudo-Goldstones. At nonzero temperature, the effects of dissipation can be captured by hydrodynamics at sufficiently long scales compared to the local equilibrium. Here we show that in the limit of weak explicit breaking, locality of hydrodynamics implies that the damping of pseudo-Goldstones is completely determined by their mass and diffusive transport coefficients. We present many applications: superfluids, QCD in the chiral limit, Wigner crystal and density wave phases in the presence of an external magnetic field or not, nematic phases and (anti-)ferromagnets. For electronic density wave phases, pseudo-Goldstone damping generates a contribution to the resistivity independent of the strength of disorder, which can have a linear temperature dependence provided the associated diffusivity saturates a bound. This is reminiscent of the phenomenology of strange metal high \\(T_c\\) superconductors, where charge density waves are observed across the phase diagram.

We construct an effective field theory (EFT) that captures the universal behavior of out-of-time-order correlators (OTOCs) at late times in generic quantum many-body systems with conservation laws. The EFT hinges on a generalization of the strong-to-weak spontaneous symmetry breaking pattern adapted to out-of-time-order observables, and reduces to conventional fluctuating hydrodynamics when time-ordered observables are probed. We use the EFT to explain different power-law behavior observed in OTOCs at late times, and show that many OTOCs are entirely fixed by conventional transport data. Nevertheless, we show that a specific combination of OTOCs is sensitive to novel transport parameters, not visible in regular time-ordered correlators. We test our predictions in Hamiltonian and Floquet spin chains in one dimension.