We discuss partition function of 2d CFTs decorated by higher qKdV charges in the thermodynamic limit when the size of the spatial circle goes to infinity. In this limit the saddle point approximation is exact and at infinite central charge generalized partition function can be calculated explicitly. We show that leading 1/c corrections to free energy can be reformulated as a sum over Young tableaux which we calculate for the first two qKdV charges. Next, we compare generalized ensemble with the "eigenstate ensemble" that consists of a single primary state. At infinite central charge the ensembles match at the level of expectation values of local operators for any values of qKdV fugacities. When the central charge is large but finite, for any values of the fugacities the aforementioned ensembles are distinguishable.

We continue a previous study about the infrared loop effects in the D-dimensional de Sitter space for a real scalar φ 4 theory from the complementary series whose bare mass belongs to the interval √ 3 4 (D − 1) < m ≤ D−1 2 , in units of the Hubble scale. The lower bound comes from the appearance of discrete states in the mass spectrum of the theory when that bound is violated, causing large IR loop effects in the vertices. We derive an equation which allows to perform a selfconsistent resummation of the leading IR contributions from all loops to the two-point correlation functions in an expanding Poincaré patch of the de Sitter manifold. The resummation can be done for density perturbations of the Bunch-Davies state which violate the de Sitter isometry. There exist solutions having a singular (exploding) behavior and therefore the backreaction can change the de Sitter geometry.

Infinite-dimensional conformal symmetry in two dimensions leads to integrability of 2d conformal field theories by giving rise to an infinite tower of local conserved qKdV charges in involution. We discuss how presence of conserved charges constraints equilibration in 2d CFTs. We propose that in the thermodynamic limit large central charge 2d CFTs satisfy generalized eigenstate thermalization, with the values of qKdV charges forming a complete set of thermodynamically relevant quantities, which unambiguously determine expectation values of all local observables from the vacuum family. Equivalence of ensembles further provides that local properties of an eigenstate can be described by the Generalized Gibbs Ensemble that only includes qKdV charges. In the case of a general initial state, upon equilibration, emerging Generalized Gibbs Ensemble will necessary include negative chemical potentials and holographically will be described by a quasi-classical black hole with quantum soft hair.The topic of thermalization, and more generally, equilibration of isolated many-body quantum systems has been an active area of research during the past decade. In case of non-integrable systems, i.e. those without an extensive number of local conserved quantities, emergence of the thermal equilibrium has been traced to eigenstate thermalization hypothesis (ETH) which postulates thermal properties of individual energy eigenstates [1-3]. In the simplest form it requires the expectation value of some appropriate (often taken to be local) observable O in a many-body eigenstate |E i to be a smooth function of energy,(1)Qualitatively, eq.(1) postulates that energy is the only thermodynamically relevant quantity, which completely specifies local properties of an eigenstate. The condition (1) may apply to all or most eigenstates, in which case it is referred as strong or weak ETH. The eigenstate thermalization ensures equivalence between the expectation value in the eigen-ensemble, f O (E i ), and thermal expectation value of O in the Gibbs ensemble, f O (E i ) = Tr(e −βH O)/Z, where the effective temperature β is fixed through the energy balance relation, E i = Tr(e −βH O)/Z [4].When the system is integrable, with an extensive number of conserved charges Q i , ETH does not apply. Accordingly emerging equilibrium can be different from the Gibbs state. In this case the equilibrium can be described by the Generalized Gibbs Ensemble (GGE), a generalization of grand canonical ensemble that includes an infinite tower of conserved charges [5]. Validity of the GGE has been related to the generalized eigenstate thermalization [6][7][8], which generalizes (1) to include an infinite number of conserved quantities,( 2) Here |E i is a mutual eigenstate of the Hamiltonian and charges Q k , Q k (E i ) are the eigenvalues of Q k associated with |E i , and function f O is assumed to be a smooth function of all of its arguments. Similarly to (1), at the qualitative level, (2) postulates that charges Q k form a complete set of thermodynamically relevant quant...