31 research outputs found
Elliptic genera from multi-centers
I show how elliptic genera for various Calabi-Yau threefolds may be
understood from supergravity localization using the quantization of the phase
space of certain multi-center configurations. I present a simple procedure that
allows for the enumeration of all multi-center configurations contributing to
the polar sector of the elliptic genera\textemdash explicitly verifying this in
the cases of the quintic in , the sextic in
, the octic in and the
dectic in . With an input of the corresponding
`single-center' indices (Donaldson-Thomas invariants), the polar terms have
been known to determine the elliptic genera completely. I argue that this
multi-center approach to the low-lying spectrum of the elliptic genera is a
stepping stone towards an understanding of the exact microscopic states that
contribute to supersymmetric single center black hole entropy in
supergravity.Comment: 30+1 pages, Published Versio
Soft graviton exchange and the information paradox
We show that there is a remarkable phase in quantum gravity where
gravitational scattering amplitudes mediated by virtual gravitons can be
calculated explicitly in effective field theory, when the impact parameter
satisfies , with being the Schwarzschild
radius. This phase captures collisions with energies satisfying (with ) near the horizon. We call
this the black hole eikonal phase, in contrast to its flat space analogue where
collisions are trans-Planckian. Hawking's geometric optics approximation
neglects gravitational interactions near the horizon, and results in thermal
occupation numbers in the Bogoliubov coefficients. We show that these
interactions are mediated by graviton exchange in scattering
near the horizon, and explicitly calculate the S-matrix non-perturbatively in
. This involves a re-summation of infinitely many ladder
diagrams near the horizon, all mediated by virtual soft gravitons. The S-matrix
turns out to be a pure phase upon this re-summation and is agnostic of
Planckian physics. Our calculation suggests that non-renormalisability of
gravity is irrelevant for a resolution of the information problem, and is
agnostic of any specific ultraviolet completion. In contrast to the flat space
eikonal limit, the black hole eikonal phase captures collisions of extremely
low energy near the horizon.Comment: 54 pages + Appendices; v3: typos corrected, references added; v4:
corrected eqns 4.81 and 4.8
Baby Universes born from the Void
We propose a novel construction of a third quantised baby universe Hilbert
space for the quantum gravity path integral. In contrast to
the original description of -parameters, both the bulk and boundary
microscopic parameters are fixed in our proposal. Wormholes and baby universes
appear due to refined observables, of the boundary dual quantum field theories,
that crucially involve the space of representations of the gauge group.
Irreducible representations, on which the path integral factorises, give rise
to field theoretic superselection sectors and replace the states.Comment: 10 pages; Extended version of an essay written for the Gravity
Research Foundation 2022 Awards for Essays on Gravitatio
Charged particle scattering near the horizon
We study Maxwell theory, in the presence of charged scalar sources, near the
black hole horizon in a partial wave basis. We derive the gauge field
configuration that solves Maxwell equations in the near-horizon region of a
Schwarzschild black hole when sourced by a charge density of a localised
charged particle. This is the electromagnetic analog of the gravitational
Dray-'t Hooft shockwave near the horizon. We explicitly calculate the S-matrix
associated with this shockwave in the first quantised
formalism. We develop a theory for scalar QED near the horizon using which we
compute the electromagnetic eikonal S-matrix from elastic
scattering of charged particles exchanging soft photons in the black hole
eikonal limit. The resulting ladder resummation agrees perfectly with the
result from the first quantised formalism, whereas the field-theoretic
formulation allows for a computation of a wider range of amplitudes. As a
demonstration, we explicitly compute sub-leading corrections that arise from
four-vertices.Comment: 23 pages + appendices. v2: typos corrected, some clarifications
added. v3: fixed an incorrect Feynman diagra
Modular bootstrap for D4-D2-D0 indices on compact Calabi-Yau threefolds
We investigate the modularity constraints on the generating series
of BPS indices counting D4-D2-D0 bound states with fixed D4-brane
charge in type IIA string theory compactified on complete Intersection
Calabi-Yau threefolds with . For unit D4-brane, transforms as a
(vector-valued) modular form under the action of and thus is
completely determined by its polar terms. We propose an Ansatz for these terms
in terms of rank 1 Donaldson-Thomas invariants, which incorporates
contributions from a single D6-anti-D6 pair. Using an explicit overcomplete
basis of the relevant space of weakly holomorphic modular forms (valid for any
), we find that for 10 of the 13 allowed threefolds, the Ansatz leads to a
solution for with integer Fourier coefficients, thereby predicting an
infinite series of DT invariants.For , is mock modular and
determined by its polar part together with its shadow. Restricting to ,
we use the generating series of Hurwitz class numbers to construct a series
with exactly the same modular anomaly as , so that the
difference is an ordinary modular form fixed by its polar
terms. For lack of a satisfactory Ansatz, we leave the determination of these
polar terms as an open problem.Comment: 44 pages; a Mathematica notebook is provided as an ancillary fil
Soft graviton exchange and the information paradox
We show that there is a remarkable soft limit in quantum gravity where the information paradox is readily resolved due to virtual soft graviton exchange on the black hole horizon. This regime is where collision energies satisfy (with ) near the horizon. We call this the black hole eikonal phase, in contrast to its flat space analogue where collisions are trans-Planckian. Hawking's geometric optics approximation neglects gravitational interactions near the horizon, and results in thermal occupation numbers in the Bogoliubov coefficients. We show that these interactions are mediated by graviton exchange in scattering near the horizon, and explicitly calculate the S-matrix non-perturbatively in and . This involves a re-summation of infinitely many ladder diagrams near the horizon, all mediated by virtual soft gravitons. The S-matrix turns out to be a pure phase \textit{only} upon this re-summation. The impact parameter satisfies , where is the Schwarzschild radius; therefore, our results are agnostic of Planckian physics. Our calculation shows that non-renormalisability of gravity is irrelevant for a resolution of the information problem, and is agnostic of any specific ultraviolet completion. In contrast to the flat space eikonal limit, the black hole eikonal phase involves collisions of extremely low energy near the horizon, thereby avoiding firewalls for black holes much larger than Planck size
Quantum gravity on the black hole horizon
We study scattering on the black hole horizon in a partial wave basis, with an impact parameter of the order of the Schwarzschild radius or less. This resembles the strong gravity regime where quantum gravitational effects appear. The scattering is governed by an infinite number of virtual gravitons exchanged on the horizon. Remarkably, they can all be summed non-perturbatively in and . These results generalise those obtained from studying gravitational backreaction. Unlike in the eikonal calculations in flat space, the relevant centre of mass energy of the collisions is not necessarily Planckian; instead it is easily satisfied, , for semi-classical black holes. Therefore, infalling observers experience no firewalls. The calculation lends further support to the scattering matrix approach to quantum black holes, and is a second-quantised generalisation of the same