Kinematic space and the orbit method

Penna, Robert F.; Zukowski, Claire

doi:10.1007/jhep07(2019)045

Cited by 15 publications

(13 citation statements)

References 57 publications

(87 reference statements)

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“…We wonder if it might be possible to obtain a nonlinear action in higher (even) dimensions by performing a coadjoint orbit quantization of kinematic space (2.1). It was already shown in [63] that higher-dimensional kinematic space is indeed a coadjoint orbit of the conformal group. It would be interesting to explore this further in light of the new perspective provided by the present paper.…”

Section: Discussionmentioning

confidence: 93%

Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs

Haehl

Reeves

Rozali

2019

J. High Energ. Phys.

152

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We study two novel approaches to efficiently encoding universal constraints imposed by conformal symmetry, and describe applications to quantum chaos in higher dimensional CFTs. The first approach consists of a reformulation of the shadow operator formalism and kinematic space techniques. We observe that the shadow operator associated with the stress tensor (or other conserved currents) can be written as the descendant of a field E with negative dimension. Computations of stress tensor contributions to conformal blocks can be systematically organized in terms of the "soft mode" E, turning them into a simple diagrammatic perturbation theory at large central charge.Our second (equivalent) approach concerns a theory of reparametrization modes, generalizing previous studies in the context of the Schwarzian theory and two-dimensional CFTs. Due to the conformal anomaly in even dimensions, gauge modes of the conformal group acquire an action and are shown to exhibit the same dynamics as the soft mode E that encodes the physics of the stress tensor shadow. We discuss the calculation of the conformal partial waves or the conformal blocks using our effective field theory. The separation of conformal blocks from shadow blocks is related to gauging of certain symmetries in our effective field theory of the soft mode.These connections explain and generalize various relations between conformal blocks, shadow operators, kinematic space, and reparametrization modes. As an application we study thermal physics in higher dimensions and argue that the theory of reparametrization modes captures the physics of quantum chaos in Rindler space. This is also supported by the observation of the pole skipping phenomenon in the conformal energy-energy two-point function on Rindler space. arXiv:1909.05847v2 [hep-th]

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Section: Discussionmentioning

confidence: 93%

Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs

Haehl

Reeves

Rozali

2019

J. High Energ. Phys.

152

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“…It will be interesting to see if we can define some version of a Poincare OPE block in a way analogous to the (conformal) OPE block defined in [15]. We expect also that the Kirillov-Kostant form on the co-adjoint orbit of the Poincare group should be related to the Crofton form on our kinematic space, in analogy with the AdS results of [30].…”

Section: Scrambled Subregions and What Makes Flat Space Differentmentioning

confidence: 99%

Bulk locality and asymptotic causal diamonds

Krishnan

2019

SciPost Phys.

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In AdS/CFT, the non-uniqueness of the reconstructed bulk from boundary subregions has motivated the notion of code subspaces. We present some closely related structures that arise in flat space. A useful organizing idea is that of an asymptotic causal diamond (ACD): a causal diamond attached to the conformal boundary of Minkowski space. The space of ACDs is defined by pairs of points, one each on the future and past null boundaries, I ± . We observe that for flat space with an IR cut-off, this space (a) encodes a preferred class of boundary subregions, (b) is a plausible way to capture holographic data for local bulk reconstruction, (c) has a natural interpretation as the kinematic space for holography, (d) leads to a holographic entanglement entropy in flat space that matches previous definitions and satisfies strong sub-additivity, and, (e) has a bulk union/intersection structure isomorphic to the one that motivated the introduction of quantum error correction in AdS/CFT. By sliding the cut-off, we also note one substantive way in which flat space holography differs from that in AdS. Even though our discussion is centered around flat space (and AdS), we note that there are notions of ACDs in other spacetimes as well. They could provide a covariant way to abstractly characterize tensor sub-factors of Hilbert spaces of holographic theories.

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“…The coadjoint orbit method [14][15][16][17] which we will benefit from in this work gives a geometric interpretation of the coadjoint representation of Lie groups and provides a systematic to construct field theory actions on a given Lie group orbit. For reviews and other applications and employment of the orbit method see [18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Warped Schwarzian theory

Afshar

2020

J. High Energ. Phys.

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We consider the (twisted) warped Virasoro group Diff(S 1 )⋉ C ∞ (S 1 ) in the presence of its three cocycles. We compute the Kirillov-Kostant-Souriau symplectic 2-form on coadjoint orbits. We then construct the Euclidean action of the 'warped Schwarzian theory' associated to the orbit with SL(2,R)×U(1) stabilizer as the effective theory of the reparametrization over the base circle and evaluate the corresponding one-loop-exact path integral.

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Kinematic space and the orbit method

Cited by 15 publications

References 57 publications

Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs

Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs

Bulk locality and asymptotic causal diamonds

Warped Schwarzian theory

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