First law of black hole mechanics with fermions

We consider the compactification on a circle of the Heterotic Superstring effective action to first order in the Regge slope parameter α′ and re-derive the α′-corrected Buscher rules first found in ref. [42], proving the T duality invariance of the dimensionally-reduced action to that order in α′. We use Iyer and Wald’s prescription to derive an entropy formula that can be applied to black-hole solutions which can be obtained by a single non-trivial compactification on a circle and discuss its invariance under the α′-corrected T duality transformations. This formula has been successfully applied to α′-corrected 4-dimensional non-extremal Reissner-Nordström black holes in ref. [21] and we apply it here to a heterotic version of the Strominger-Vafa 5-dimensional extremal black hole.

Section: Jhep10(2020)097mentioning

confidence: 99%

T duality and Wald entropy formula in the Heterotic Superstring effective action at first-order in α′

Elgood

Ortı́n

2020

“…There, we first focus on BF theory, and then introduce Einstein-Cartan (-Holst) gravity (ECH) as a constrained BF theory. As it turns out, the superficial analysis of the corner symmetries of tetrad gravity, which we recall in section 3.2, reveals the algebra diff(S) sl(2, C) S , where the sl(2, C) is due to internal Lorentz symmetries, and the boost component sl(2, R) ⊥ is absent (this last observation was first noted in [61] and further analyzed in [55,[62][63][64]). Compared with the metric case, much more work is required in order to decompose the potential of Einstein-Cartan-Holst gravity in terms of the fundamental bulk piece θ GR and a corner potential.…”

Section: Canonical General Relativity (Gr)mentioning

confidence: 82%

Edge modes of gravity. Part I. Corner potentials and charges

Freidel

Geiller

Pranzetti

2020

155

288

This is the first paper in a series devoted to understanding the classical and quantum nature of edge modes and symmetries in gravitational systems. The goal of this analysis is to: i) achieve a clear understanding of how different formulations of gravity provide non-trivial representations of different sectors of the corner symmetry algebra, and ii) set the foundations of a new proposal for states of quantum geometry as representation states of this corner symmetry algebra. In this first paper we explain how different formulations of gravity, in both metric and tetrad variables, share the same bulk symplectic structure but differ at the corner, and in turn lead to inequivalent representations of the corner symmetry algebra. This provides an organizing criterion for formulations of gravity depending on how big the physical symmetry group that is non-trivially represented at the corner is. This principle can be used as a “treasure map” revealing new clues and routes in the quest for quantum gravity. Building up on these results, we perform a detailed analysis of the corner pre-symplectic potential and symmetries of Einstein-Cartan-Holst gravity in [1], use this to provide a new look at the simplicity constraints in [2], and tackle the quantization in [3].

“…The combined transformation is sometimes referred to as Kosmann derivative in the literature; see e.g. [14][15][16][17], where it was shown that this prescription correctly reproduces the metric Noether charges for any diffeomorphism, and the metric Hamiltonian charges for isometries (see also [10,18]). For asymptotic symmetries at spatial infinity, the metric Hamiltonian charges (namely the Poincaré charges) are reproduced using either the Kosmann or the standard Lie derivative variations: their difference vanishes in the limit [9,19,20].…”

Section: Jhep12(2020)079mentioning

confidence: 99%

“…But the difference of the symplectic potentials by an exact 3-form remains, therefore this dual contribution is inequivalent to the one computed using tetrad variables. For the related topic of the contribution of torsion to the first law of black hole mechanics, see [18,26].…”

Section: Jhep12(2020)079mentioning

confidence: 99%

A note on dual gravitational charges

Oliveri

Speziale

2020

Dual gravitational charges have been recently computed from the Holst term in tetrad variables using covariant phase space methods. We highlight that they originate from an exact 3-form in the tetrad symplectic potential that has no analogue in metric variables. Hence there exists a choice of the tetrad symplectic potential that sets the dual charges to zero. This observation relies on the ambiguity of the covariant phase space methods. To shed more light on the dual contributions, we use the Kosmann variation to compute (quasi-local) Hamiltonian charges for arbitrary diffeomorphisms. We obtain a formula that illustrates comprehensively why the dual contribution to the Hamiltonian charges: (i) vanishes for exact isometries and asymptotic symmetries at spatial infinity; (ii) persists for asymptotic symmetries at future null infinity, in addition to the usual BMS contribution. Finally, we point out that dual gravitational charges can be equally derived using the Barnich-Brandt prescription based on cohomological methods, and that the same considerations on asymptotic symmetries apply.