Generalized Gibbs Ensemble of 2D CFTs with U(1) charge from the AGT correspondence

2021/03/31 by Fábio Novaes · 2 citations
Physics and Astronomy · #Canonical ensemble #Central charge #Charge (physics) #Conformal field theory #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Partition function (quantum field theory) #Physics of Superconductivity and Magnetism #Quantum field theory #Quantum many-body systems #Quantum, superfluid, helium dynamics #Semiclassical physics #cond-mat.stat-mech #cond-mat.str-el #hep-th

paper · pdf · doi:10.1007/jhep05(2021)276

published in Journal of High Energy Physics 2021(5) (Springer Nature) · 33+19 pages. v2: added comments and refs on ETH for general operators, minor text corrections

openalex created_date 2021/03/29 · openalex publication_date 2021/05/01 · arxiv created 2021/06/01 · arxiv updated 2021/06/02 · openalex updated_date 2026/08/05

Abstract

A bstract The Generalized Gibbs Ensemble (GGE) is relevant to understand the thermalization of quantum systems with an infinite set of conserved charges. In this work, we analyze the GGE partition function of 2D Conformal Field Theories (CFTs) with a U(1) charge and quantum Benjamin-Ono 2 (qBO 2 ) hierarchy charges. We use the Alday-Gaiotto-Tachikawa (AGT) correspondence to express the thermal trace in terms of the Alba-Fateev-Litvinov-Tarnopolskiy (AFLT) basis of descendants, which diagonalizes all charges. We analyze the GGE partition function in the thermodynamic semiclassical limit, including the first order quantum correction. We find that the equality between GGE averages and primary eigenvalues of the qBO 2 charges is attainable in the strict large c limit and potentially violated at the subleading 1 /c order. We also obtain the finite c partition function when only the first non-trivial charge is turned on, expressed in terms of partial theta functions. Our results should be relevant to the eigenstate thermalization hypothesis for charged CFTs, Warped CFTs and effective field theory descriptions of condensed matter systems.

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