Effective Conformal Descriptions of Black Hole Entropy

illustrate the case of J(τ ) = j(τ ) − 744, whose coefficients turn out to be sums of the dimensions of the 194 irreducible representations of M. Such formulas are dictated by the structure of the graded monstrous moonshine modules. Recent works in moonshine suggest deep relations between number theory and physics. Number theoretic Kloosterman sums have reappeared in quantum gravity, and mock modular forms have emerged as candidates for the computation of black hole degeneracies. This paper is a survey of past and present research on moonshine. We also compute the quantum dimensions of the monster orbifold and obtain exact formulas for the multiplicities of the irreducible components of the moonshine modules. These formulas imply that such multiplicities are asymptotically proportional to dimensions.

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“…We refer to [32,33] for reviews that focus on the particular role of conformal field theory in understanding quantum gravity.…”

Section: Question 1 Assuming That the Moonshine Module V Serves As Tmentioning

confidence: 99%

Moonshine

Duncan

Griffin

Ono

2015

Mathematical Sciences

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“…Assuming the appropriate boundary conditions can be found, the full surface symmetry algebra is a central extension of either Diff(∂Σ) ⋉ (SL(2, R) ⋉ R 2 ) ∂Σ , or a larger, simple Lie algebra. The appearance of central charges in these algebras is familiar from similar constructions involving edge modes at asymptotic infinity or black hole horizons [42,44,45]. The construction of the extended phase space for arbitrary diffeomorphism-invariant theories is useful for a number of reasons.…”

Section: Introductionmentioning

confidence: 99%

Local phase space and edge modes for diffeomorphism-invariant theories

Speranza

2018

J. High Energ. Phys.

121

215

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We discuss an approach to characterizing local degrees of freedom of a subregion in diffeomorphism-invariant theories using the extended phase space of Donnelly and Freidel, [JHEP 2016[JHEP (2016. Such a characterization is important for defining local observables and entanglement entropy in gravitational theories. Traditional phase space constructions for subregions are not invariant with respect to diffeomorphisms that act at the boundary. The extended phase space remedies this problem by introducing edge mode fields at the boundary whose transformations under diffeomorphisms render the extended symplectic structure fully gauge invariant. In this work, we present a general construction for the edge mode symplectic structure. We show that the new fields satisfy a surface symmetry algebra generated by the Noether charges associated with the edge mode fields. For surface-preserving symmetries, the algebra is universal for all diffeomorphism-invariant theories, comprised of diffeomorphisms of the boundary, SL(2, R) transformations of the normal plane, and, in some cases, normal shearing transformations. We also show that if boundary conditions are chosen such that surface translations are symmetries, the algebra acquires a central extension.

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“…One speculative idea [4] is that such processes could be described as flows between conformal field theories. The direction of the flow during black hole evaporation is consistent with Zamolodchikov's c theorem [42], but for now I can say little more than that.…”

Section: What Are the States?mentioning

confidence: 99%