Macroscopic observables from the comparison of local reference systems

Meneses, Claudio; Zapata, José A.

doi:10.1088/1361-6382/ab49a7

Cited by 4 publications

(2 citation statements)

References 23 publications

(93 reference statements)

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“…31 We have absorbed a potential vacuum energy back into the definition of L0. 32 The Euclidean BTZ black hole solution is characterised by an imaginary spin J, and a positive mass…”

Section: Jhep03(2020)175 5 Entropy and Partition Functionmentioning

confidence: 99%

“…Section 4 deals with the quasilocal Hamiltonian analysis. We will introduce an extended gravitational phase space, and identify the gauge transformations (small diffeomorphisms and SU(2) frame rotations) of the extend bulk plus boundary system [16,[30][31][32][33][34]. The commutation relations between the Laurent modes of the boundary spinor ξ A are defined via the Dirac bracket, which yields a deformation of the infinite-dimensional Heisenberg algebra.…”

Section: Introductionmentioning

confidence: 99%

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Deformed Heisenberg charges in three-dimensional gravity

Namburi

Wieland

2020

J. High Energ. Phys.

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We consider the bulk plus boundary phase space for three-dimensional gravity with negative cosmological constant for a particular choice of conformal boundary conditions: the conformal class of the induced metric at the boundary is kept fixed and the mean extrinsic curvature is constrained to be one. Such specific conformal boundary conditions define so-called Bryant surfaces, which can be classified completely in terms of holomorphic maps from Riemann surfaces into the spinor bundle. To study the observables and gauge symmetries of the resulting bulk plus boundary system, we will introduce an extended phase space, where these holomorphic maps are now part of the gravitational bulk plus boundary phase space. The physical phase space is obtained by introducing two sets of Kac-Moody currents, which are constrained to vanish. The constraints are secondclass and the corresponding Dirac bracket yields an infinite-dimensional deformation of the Heisenberg algebra for the spinor-valued surface charges. Finally, we compute the Poisson algebra among the generators of conformal diffeomorphisms and demonstrate that there is no central charge. Although the central charge vanishes and the boundary CFT is likely non-unitary, we will argue that a version of the Cardy formula still applies in this context, such that the entropy of the BTZ black hole can be derived from the degeneracy of the eigenstates of quasi-local energy.

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“…31 We have absorbed a potential vacuum energy back into the definition of L0. 32 The Euclidean BTZ black hole solution is characterised by an imaginary spin J, and a positive mass…”

Section: Jhep03(2020)175 5 Entropy and Partition Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deformed Heisenberg charges in three-dimensional gravity

Namburi

Wieland

2020

J. High Energ. Phys.

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A discretization of Holst’s action for general relativity

Beltrán

Zapata

2023

Gen Relativ Gravit

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We present a simplicial model for gravity written in terms of a discretized Lorentz connection and a discretized tetrad field. The continuum limit of its action is Holst’s action for general relativity. With the intention of using it to construct spin foam modes for quantum gravity, we write two other equivalent models written in terms of a discretized and constrained B field. The differences between our model and existing models are most likely inessential in the sense that a quantization would lead to equivalent quantum theories in the Wilsonian continuum limit. Nevertheless, we mention two features leading to possible advantages: Curvature degrees of freedom are described at the level of each 4-simplex. Our model offers a picture of bulk geometry leading to actions for matter couplings that split as a sum over 4-simplices.

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Thin homotopy and the holonomy approach to gauge theories

Meneses¹

2021

Mexican Mathematicians in the World

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We survey several mathematical developments in the holonomy approach to gauge theory. A cornerstone of this approach is the introduction of group structures on spaces of based loops on a smooth manifold, relying on certain homotopy equivalence relations — such as the so-called thin homotopy — and the resulting interpretation of gauge fields as group homomorphisms to a Lie group G G satisfying a suitable smoothness condition, encoding the holonomy of a gauge orbit of smooth connections on a principal G G -bundle. We also prove several structural results on thin homotopy, and in particular we clarify the difference between thin equivalence and retrace equivalence for piecewise-smooth based loops on a smooth manifold, which are often used interchangeably in the physics literature. We conclude by listing a set of questions on topological and functional analytic aspects of groups of based loops, which we consider to be fundamental to establish a rigorous differential geometric foundation of the holonomy formulation of gauge theory.

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Macroscopic observables from the comparison of local reference systems

Cited by 4 publications

References 23 publications

Deformed Heisenberg charges in three-dimensional gravity

Deformed Heisenberg charges in three-dimensional gravity

A discretization of Holst’s action for general relativity

Thin homotopy and the holonomy approach to gauge theories

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