No Ensemble Averaging Below the Black Hole Threshold

in Journal of High Energy Physics (2022), 7

In the AdS/CFT correspondence, amplitudes associated to connected bulk manifolds with disconnected boundaries have presented a longstanding mystery. A possible interpretation is that they reflect the ... [more ▼]

In the AdS/CFT correspondence, amplitudes associated to connected bulk manifolds with disconnected boundaries have presented a longstanding mystery. A possible interpretation is that they reflect the effects of averaging over an ensemble of boundary theories. But in examples in dimension D≥3, an appropriate ensemble of boundary theories does not exist. Here we sharpen the puzzle by identifying a class of "sub-threshold" observables that we claim do not show effects of ensemble averaging. These are amplitudes that do not involve black hole states. To support our claim, we explore the example of D=3, and show that connected solutions of Einstein's equations with disconnected boundary never contribute to sub-threshold observables. To demonstrate this requires some novel results about the renormalized volume of a hyperbolic three-manifold, which we prove using modern methods in hyperbolic geometry. Why then do any observables show apparent ensemble averaging? We propose that this reflects the chaotic nature of black hole physics and the fact that the Hilbert space describing a black hole does not have a large N limit. [less ▲]

Unitary W-algebras and three-dimensional higher spin gravities with spin one symmetry

in Journal of High Energy Physics (2014)

2d gauge theories and generalized geometry

in Journal of High Energy Physics (2014)

We show that in the context of two-dimensional sigma models minimal coupling of an ordinary rigid symmetry Lie algebra g leads naturally to the appearance of the “generalized tangent bundle” TM ≡ T M ⊕ T ... [more ▼]

We show that in the context of two-dimensional sigma models minimal coupling of an ordinary rigid symmetry Lie algebra g leads naturally to the appearance of the “generalized tangent bundle” TM ≡ T M ⊕ T ∗ M by means of composite fields. Gauge transformations of the composite fields follow the Courant bracket, closing upon the choice of a Dirac structure D ⊂ TM (or, more generally, the choide of a “small Dirac-Rinehart sheaf” D), in which the fields as well as the symmetry parameters are to take values. In these new variables, the gauge theory takes the form of a (non-topological) Dirac sigma model, which is applicable in a more general context and proves to be universal in two space-time dimensions: a gauging of g of a standard sigma model with Wess-Zumino term exists, iff there is a prolongation of the rigid symmetry to a Lie algebroid morphism from the action Lie algebroid M × g → M into D → M (or the algebraic analogue of the morphism in the case of D). The gauged sigma model results from a pullback by this morphism from the Dirac sigma model, which proves to be universal in two-spacetime dimensions in this sense. [less ▲]

Dirac sigma models from gauging

in Journal of High Energy Physics (2013)

The G/G WZW model results from the WZW-model by a standard procedure of gauging. G/G WZW models are members of Dirac sigma models, which also contain twisted Poisson sigma models as other examples. We ... [more ▼]

The G/G WZW model results from the WZW-model by a standard procedure of gauging. G/G WZW models are members of Dirac sigma models, which also contain twisted Poisson sigma models as other examples. We show how the general class of Dirac sigma models can be obtained from a gauging procedure adapted to Lie algebroids in the form of an equivariantly closed extension. The rigid gauge groups are generically infinite dimensional and a standard gauging procedure would give a likewise infinite number of 1-form gauge fields; the proposed construction yields the requested finite number of them. Although physics terminology is used, the presentation is kept accessible also for a mathematical audience. [less ▲]

Three point functions in higher spin AdS3 supergravity

in Journal of High Energy Physics (2013), 2013(1),

In a previous work we have proposed that the Prokushkin-Vasiliev higher spin N = 2 supergravity on AdS3 is dual to a large N limit of the N = (2,2) ℂPN Kazama- Suzuki model. There is now strong evidence ... [more ▼]

In a previous work we have proposed that the Prokushkin-Vasiliev higher spin N = 2 supergravity on AdS3 is dual to a large N limit of the N = (2,2) ℂPN Kazama- Suzuki model. There is now strong evidence supporting this proposal based on symmetry and spectrum comparison. In this paper we will give further evidence for the duality by studying correlation functions. We compute boundary three point functions with two fermionic operators and one higher spin bosonic current in terms of the bulk supergravity theory. Then we compare with the results in the dual CFT, where the supersymmetry of the theory turns out to be very helpful. In particular we use it to confirm results conjectured in the bosonic case. Moreover, correlators with a fermionic current can be obtained via supersymmetry. © 2013 SISSA, Trieste, Italy. [less ▲]

A minimal BV action for Vasiliev's four-dimensional higher spin gravity

in Journal of High Energy Physics (2012)

The action principle for Vasiliev's four-dimensional higher-spin gravity proposed recently by two of the authors, is converted into a minimal BV master action using the AKSZ procedure, which amounts to ... [more ▼]

The action principle for Vasiliev's four-dimensional higher-spin gravity proposed recently by two of the authors, is converted into a minimal BV master action using the AKSZ procedure, which amounts to replacing the classical differential forms by vectorial superfields of fixed total degree given by the sum of form degree and ghost number. The nilpotency of the BRST operator is achieved by imposing boundary conditions and choosing appropriate gauge transitions between charts leading to a globally-defined formulation based on a principal bundle. [less ▲]