Chern-Simons invariants from ensemble averages

Ashwinkumar, Meer; Dodelson, Matthew; Kidambi, Abhiram; Leedom, Jacob M.; Yamazaki, Masahito

doi:10.1007/jhep08(2021)044

Cited by 24 publications

(20 citation statements)

References 67 publications

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“…Furthermore, it is shown [12,35] that JT gravity is dual to a matrix ensemble. Later on more explicit 2d [12,[36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] and 3d [53][54][55][56][57][58][59][60][61][62][63][64] examples of ensemble duality are proposed. See further explorations of wormhole, baby universe and ensemble average in [9,.…”

Section: Introductionmentioning

confidence: 99%

Baby universes, ensemble averages and factorizations with matters

Peng

Tian

2021

Preprint

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We investigate 2D topological gravity theories with matter fields turned on. We compute correlators of boundary creation operators with extra matter insertions. We provide a systematic procedure to determine a set of α-states on which the correlation functions of the different boundary operators factorize. Our results suggest that the boundary dual is an ensemble average of theories with different numbers of replicas of a seed matter contribution that is represented by excitations on top of the gravity sector. The construction of the α-states and the subsequent computations in the Hilbert space point of view are most conveniently done when the bulk couplings of the matter fields are expanded in a basis of vortices, which can be thought of as a 1-dimensional analogue of the SD-branes. We further demonstrate the existence of null states and the conditions imposed by reflection positivity. Moreover, in the CGS model with only disk and cylinder topologies we map the baby universe creation and annihilation operators to the coupling constants in the one time SYK model, which allows us to match the wormhole and half-wormhole contributions in the CGS model explicitly to those identified in the SYK model. This explicitly realizes Coleman's initial idea. Some details of the computations in a variety of concrete models are presented.

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Section: Introductionmentioning

confidence: 99%

Baby universes, ensemble averages and factorizations with matters

Peng

Tian

2021

Preprint

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“…13 The gravitational description of the Narain ensemble was further studied in [61][62][63], and the discrete average of holomorphic free boson CFTs was discussed in [64]. Aspects of ensemble averages over other classes of rational two-dimensional conformal field theories have also been discussed [65][66][67][68][69]. 14 In fact, the subleading behaviour in (1.6) -and in particular the subleading term which scales like O(∆ 0 ) -requires the inclusion of the full "SL(2, Z)" family of Euclidean black holes.…”

Section: Jhep03(2022)004mentioning

confidence: 99%

Wormholes and spectral statistics in the Narain ensemble

Collier

Maloney

2022

J. High Energ. Phys.

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We study the spectral statistics of primary operators in the recently formulated ensemble average of Narain’s family of free boson conformal field theories, which provides an explicit (though exotic) example of an averaged holographic duality. In particular we study moments of the partition function by explicit computation of higher-degree Eisenstein series. This describes the analog of wormhole contributions coming from a sum of over geometries in the dual theory of “U(1) gravity” in AdS3. We give an exact formula for the two-point correlation function of the density of primary states. We compute the spectral form factor and show that the wormhole sum reproduces precisely the late time plateau behaviour related to the discreteness of the spectrum. The spectral form factor does not exhibit a linear ramp.

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“…See also [17] for the implication of harmonic analysis of SL(2, Z) in context of 2D CFT. In recent years, the ensemble average over some appropiate moduli space of 2D CFT has been considered in many papers, which includes [18][19][20][21][22][23][24][25][26][27][28], see also [29][30][31]. It deserves mention that the ensemble average over overall scaling induces a deformation is briefly discussed in the concluding section of [1].…”

Section: Deformation = Renormalizationmentioning

confidence: 99%

(Half) Wormholes under Irrelevant Deformation

Das,

Pal,

Sarkar

2022

Preprint

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Recently it has been shown by Almheiri and Lin [1] that the reconstruction of black-hole interior is sensitive to knowing the exact coupling of the boundary theory even if the coupling is irrelevant. This motivates us to enlarge the set of the one-time and two-time toy models inspired from the SYK by deforming the same with irrelevant coupling. We find that both half-wormholes as well as the wormholes persist in presence of the deformation, leading to a similar mechanism for curing the factorization problem. While for the one time case, the deformed partition function and its moments change by an overall factor, which can completely be absorbed into a renormalization of coupling, for the two time (or coupled one time) SYK we find non-trivial dynamics of the saddles as the couplings are varied. Curiously, the irrelevant deformations that we consider can also be thought of as an ensemble average over an overall scaling of the original undeformed Hamiltonian with an appropriate probability distribution, this allows for the possibility that half-wormholes may also be present in suitably defined ensemble of theories.

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Chern-Simons invariants from ensemble averages

Cited by 24 publications

References 67 publications

Baby universes, ensemble averages and factorizations with matters

Baby universes, ensemble averages and factorizations with matters

Wormholes and spectral statistics in the Narain ensemble

(Half) Wormholes under Irrelevant Deformation

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