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A<sc>bstract</sc> We introduce a Hamiltonian lattice model for the (1 + 1)-dimensional SU(Nc) gauge theory coupled to one adjoint Majorana fermion of massm. The discretization of the continuum theory uses staggered Majorana fermions. We analyze the symmetries of the lattice model and find lattice analogs of the anomalies of the corresponding continuum theory. An important role is played by the lattice translation by one lattice site, which in the continuum limit involves a discrete axial transformation. On a lattice with periodic boundary conditions, the Hilbert space breaks up into sectors labeled by theNc-alityp= 0, …Nc− 1. Our symmetry analysis implies various exact degeneracies in the spectrum of the lattice model. In particular, it shows that, form= 0 and evenNc, the sectorspandp′ are degenerate if |p−p′| =Nc/2. In theNc= 2 case, we explicitly construct the action of the Hamiltonian on a basis of gauge-invariant states, and we perform both a strong coupling expansion and exact diagonalization for lattices of up to 12 lattice sites. Upon extrapolation of these results, we find good agreement with the spectrum computed previously using discretized light-cone quantization. One of our new results is the first numerical calculation of the fermion bilinear condensate.
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Spectrum of quantum KdV hierarchy in the semiclassical limit
A<sc>bstract</sc> We employ semiclassical quantization to calculate spectrum of quantum KdV charges in the limit of large central chargec. Classically, KdV chargesQ2n−1generate completely integrable dynamics on the co-adjoint orbit of the Virasoro algebra. They can be expressed in terms of action variablesIk, e.g. as a power series expansion. Quantum-mechanically this series becomes the expansion in 1/c, while action variables become integer-valued quantum numbersni. Crucially, classical expression, which is homogeneous inIk, acquires quantum corrections that include terms of subleading powers innk. At first two non-trivial orders in 1/cexpansion these “quantum” terms can be fixed from the analytic form ofQ2n−1acting on the primary states. In this way we find explicit expression for the spectrum ofQ2n−1up to first three orders in 1/cexpansion. We apply this result to study thermal expectation values ofQ2n−1and free energy of the KdV Generalized Gibbs Ensemble.
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- Award ID(s):
- 2013812
- PAR ID:
- 10483044
- Publisher / Repository:
- Springer (Journal of High Energy Physics)
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2022
- Issue:
- 9
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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The eigenstate thermalization hypothesis (ETH) in chaotic two-dimensional CFTs is subtle due to the presence of infinitely many conserved KdV charges. Previous works have shown that primary CFT eigenstates exhibit a flat entanglement spectrum, which is very different from that of the microcanonical ensemble. This appears to contradict conventional ETH, which does not account for KdV charges. In a companion paper \cite{1}, we resolve this discrepancy by analyzing the subsystem entropy of a chaotic CFT in KdV-generalized Gibbs and microcanonical ensembles. In this paper, we perform parallel computations within the framework of AdS/CFT. We focus on the high-density limit, which corresponds to the thermodynamic limit in conformal theories. In this regime, holographic Rényi entropy can be calculated using the so-called *gluing construction*. We specifically study the KdV-generalized microcanonical ensemble where the densities of the first two KdV charges are fixed: $$ \langle Q_1 \rangle = q_1, \quad \langle Q_3 \rangle = q_3 $$ with the condition $$q_3 - q_1^2 \ll q_1^2$$. In this regime, we find that the refined Rényi entropy $$\tilde{S}_n$$ becomes independent of $$n$$ for $$n > n_{\text{cut}}$$, where $$n_{\text{cut}}$$ depends on $$q_1$$ and $$q_3$$. By taking the primary state limit $$q_3 \to q_1^2$$, we recover the flat entanglement spectrum characteristic of fixed-area states, consistent with the behavior of primary states. This result supports the consistency of KdV-generalized ETH in 2d CFTs.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP09(2022)169
