How General Is Holography? Flat Space and Higher-Spin Holography in 2+1 Dimensions
Sep 9, 2016261 pages
Supervisors:
Thesis: PhD - Daniel Grumiller,
- Radoslav Rashkov
- Vienna, Tech. U.
e-Print:
- 1609.02733 [hep-th]
URN/HDL:
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Abstract: (Vienna, Tech. U.)
"How general is the holographic principle?- This is the question I will explore in this thesis. As this question is very fundamental, one is well advised to try and tackle the problem in an environment which is as simple as possible but still interesting and complex enough to allow for a general interpretation of the results. Since gravity in 2+1 dimensions satisfies those requirements I will focus on holography involving 2+1 dimensional spacetimes and 1+1 dimensional quantum field theories. The two most important reasons for this are: (i) gravity in 2+1 dimensions can be described very efficiently on a technical level. (ii) The dual quantum field theories have infinitely many symmetries and thus allow for a very high degree of control. This allows one to explicitly and exactly check new holographic correspondences. Of very special interest regarding the generality of the holographic principle are so-called higher-spin gravity theories which extend the usual local invariance under coordinate changes by a more general set of symmetries. In this thesis I will first focus on higher-spin holography which is based on spacetimes that do not asymptote to Anti-de Sitter spacetimes. Starting from a given higher-spin theory I will determine the corresponding asymptotic symmetries of the corresponding dual quantum field theories and their unitary representations. Furthermore, using "non-Anti-de Sitter holography" I will describe a dual quantum field theory, which allows for an arbitrary (albeit not infinitely) large number of quantum microstates. The second part of this thesis is concerned with holography for asymptotic flat spacetimes. First I will show how to obtain various results, like an analogue of a (higher-spin) Cardy formula which counts the number of microstates of a conformal field theory at a given temperature, or the asymptotic symmetries of asymptotically flat spacetimes, as a limit of vanishing cosmological constant from the known Anti-de Sitter results. Furthermore, I will explore unitary representations of the asymptotic symmetry algebras of asymptotically flat spacetimes, which under certain assumptions, will result in a NO-GO theorem that forbids having flat space, higher-spins and unitarity at the same time. In addition I will elaborate on a specific example that allows to circumvent this NO-GO theorem. I will also show how to consistently describe asymptotically flat spacetimes with additional (higher-spin) chemical potentials in a holographic setup and how to determine the corre- sponding thermal entropy of certain cosmological asymptotically flat spacetimes. The finale of this thesis will be an explicit check of the holographic principle for asymp- totically flat spacetimes. I will present a method, using a special version of a Wilson-line, which allows one to determine the entanglement entropy of field theories which are assumed to be dual to asymptotically flat spacetimes in a holographic manner. I will also extend this method in order to be able to also successfully include higher-spin symmetries and determine the thermal entropy of the corresponding dual field theories.Note:
- PhD Thesis; Defended on Sept. 7th, 2016; This thesis won the Victor-Franz Hess Prize awarded by the Austrian Physical Society
- holographic principle
- lowerdimensional models of gravity
- higher spin gravity
- holographic entanglement entropy
- representation: unitarity
- entropy: entanglement
- potential: chemical
- symmetry: algebra
- holography
- space-time
References(178)
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