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

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Fábio Novaes
Keyword(s):  
Partition Function ◽  
Semiclassical Limit ◽  
Theta Functions ◽  
Effective Field ◽  
Gibbs Ensemble ◽  
Conformal Field ◽  
Agt Correspondence ◽  
Partial Theta Functions ◽  
Infinite Set ◽  
Generalized Gibbs Ensemble

Abstract 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-Ono2 (qBO2) 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 qBO2 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.

scholarly journals Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Kouhei Fukai ◽  
Yuji Nozawa ◽  
Koji Kawahara ◽  
Tatsuhiko N. Ikeda
Keyword(s):  
Quantum Systems ◽  
Gibbs Ensemble ◽  
Integrable Quantum ◽  
Generalized Gibbs Ensemble

scholarly journals Searching for elusive dark sectors with terrestrial and celestial observations

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Roberto Contino ◽  
Kevin Max ◽  
Rashmish K. Mishra
Keyword(s):  
Field Theory ◽  
Broad Class ◽  
High Energy ◽  
Effective Field ◽  
Dark Sector ◽  
Minimum Requirement ◽  
Conformal Field ◽  
Starting Point ◽  
The Standard Model ◽  
Visible Sector

Abstract We consider the possible existence of a SM-neutral and light dark sector coupled to the visible sector through irrelevant portal interactions. Scenarios of this kind are motivated by dark matter and arise in various extensions of the Standard Model. We characterize the dark dynamics in terms of one ultraviolet scale Λuv, at which the exchange of heavy mediator fields generates the portal operators, and by one infrared scale ΛIR, setting the mass gap. At energies ΛIR « E « Λuv the dark sector behaves like a conformal field theory and its phenomenology can be studied model independently. We derive the constraints set on this scenario by high- and low-energy laboratory experiments and by astrophysical observations. Our results are conservative and serve as a minimum requirement that must be fulfilled by the broad class of models satisfying our assumptions, of which we give several examples. The experimental constraints are derived in a manner consistent with the validity of the effective field theory used to define the portal interactions. We find that high-energy colliders give the strongest bounds and exclude UV scales up to a few TeV, but only in specific ranges of the IR scale. The picture emerging from current searches can be taken as a starting point to design a future experimental strategy with broader sensitivity.

scholarly journals Toward AGT for Parabolic Sheaves

2020 ◽  
Author(s):  
Andrei Neguţ
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Conformal Field Theory ◽  
Moduli Spaces ◽  
Type A ◽  
Conformal Field ◽  
Toroidal Algebra ◽  
Agt Correspondence ◽  
K Theory ◽  
The Ideal

Abstract We construct explicit elements $W_{ij}^k$ in (a completion of) the shifted quantum toroidal algebra of type $A$ and show that these elements act by 0 on the $K$-theory of moduli spaces of parabolic sheaves. We expect that the quotient of the shifted quantum toroidal algebra by the ideal generated by the elements $W_{ij}^k$ will be related to $q$-deformed $W$-algebras of type $A$ for arbitrary nilpotent, which would imply a $q$-deformed version of the Alday-Gaiotto-Tachikawa (AGT) correspondence between gauge theory with surface operators and conformal field theory.

scholarly journals Signature of Generalized Gibbs Ensemble Deviation from Equilibrium: Negative Absorption Induced by a Local Quench

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 220
Author(s):  
Lorenzo Rossi ◽  
Fabrizio Dolcini ◽  
Fabio Cavaliere ◽  
Niccolò Traverso Ziani ◽  
Maura Sassetti ◽  
...  
Keyword(s):  
Optical Gain ◽  
Electron System ◽  
Bound State ◽  
Stimulated Emission ◽  
Optical Measurements ◽  
Gibbs Ensemble ◽  
Attractive Potential ◽  
Dimensional Electron System ◽  
Constants Of Motion ◽  
Generalized Gibbs Ensemble

When a parameter quench is performed in an isolated quantum system with a complete set of constants of motion, its out of equilibrium dynamics is considered to be well captured by the Generalized Gibbs Ensemble (GGE), characterized by a set {λα} of coefficients related to the constants of motion. We determine the most elementary GGE deviation from the equilibrium distribution that leads to detectable effects. By quenching a suitable local attractive potential in a one-dimensional electron system, the resulting GGE differs from equilibrium by only one single λα, corresponding to the emergence of an only partially occupied bound state lying below a fully occupied continuum of states. The effect is shown to induce optical gain, i.e., a negative peak in the absorption spectrum, indicating the stimulated emission of radiation, enabling one to identify GGE signatures in fermionic systems through optical measurements. We discuss the implementation in realistic setups.

scholarly journals Partial theta functions and mock modular forms as q-hypergeometric series

2012 ◽  
Vol 29 (1-3) ◽  
pp. 295-310 ◽  
Author(s):  
Kathrin Bringmann ◽  
Amanda Folsom ◽  
Robert C. Rhoades
Keyword(s):  
Modular Forms ◽  
Hypergeometric Series ◽  
Theta Functions ◽  
Mock Modular Forms ◽  
Partial Theta Functions

Partial Theta Functions

2009 ◽  
pp. 1-35
Author(s):  
Bruce C. Berndt ◽  
George E. Andrews
Keyword(s):  
Theta Functions ◽  
Partial Theta Functions

Some further Hecke-type identities

2020 ◽  
Vol 16 (09) ◽  
pp. 1945-1967
Author(s):  
Zhizheng Zhang ◽  
Hanfei Song
Keyword(s):  
Series Expansion ◽  
Theta Functions ◽  
Bailey Pairs ◽  
Expansion Formulae ◽  
Partial Theta Functions

In this paper, we obtain some Hecke-type identities by using two [Formula: see text]-series expansion formulae. And, the identities can also be proved directly in terms of Bailey pairs. In particular, we show that certain partial theta functions and the theta functions can be expressed in terms of Hecke-type identities.

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