Partition functions and elliptic genera from supergravity

Kraus, Per; Larsen, Finn

doi:10.1088/1126-6708/2007/01/002

Cited by 121 publications

(180 citation statements)

References 30 publications

(66 reference statements)

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“…This will be seen to fit exactly within the considerations of [12], [13]. In this background geometry, the 5D supergravity action contains a Chern-Simons term…”

Section: Geometric Interpretation Using Split-spectral Flowssupporting

confidence: 65%

More rings to rule them all: fragmentation, 4D↔ 5Dand split-spectral flows

Arsiwalla

2008

J. High Energy Phys.

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In this note we set-up an explicit 5D construction of AdS-fragmentation, whereby a single black ring splits-up into a multi-black ring configuration. Furthermore it is seen that these fragmented rings are equivalent to a direct 5D lift of 4D multicenter black holes. Along the way we also determine the 4D/5D transformations relevant for multi-center charges. It is seen that the physical charges involved in black ring fragmentation are Page charges arising due to 5D Chern-Simons terms.As an application of these methods, we reproduce the total angular momentum of concentric black rings, originally due to Gauntlett and Gutowski. Finally we provide a geometric interpretation of fragmented black rings using the idea of split-spectral flows, which seeks to study charge shifts of a given black ring due to fluxes generated in a multi-ring background.

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“…This will be seen to fit exactly within the considerations of [12], [13]. In this background geometry, the 5D supergravity action contains a Chern-Simons term…”

Section: Geometric Interpretation Using Split-spectral Flowssupporting

confidence: 65%

More rings to rule them all: fragmentation, 4D↔ 5Dand split-spectral flows

Arsiwalla

2008

J. High Energy Phys.

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“…It is well known that Chern-Simons theory captures many aspects of (0, 4) SCFT's not only at the on-shell level [48][49][50] but also at the quantum level [4,6,14]. On the other hand, the anomaly can be computed at long wavelengths depending only, as we show, on global properties of the space given by a certain cohomology structure of the gauge transformations.…”

Section: Jhep07(2017)022mentioning

confidence: 76%

Exact Holography and Black Hole Entropy in N = 8 $$ \mathcal{N}=8 $$ and N = 4 $$ \mathcal{N}=4 $$ String Theory

Gomes

2017

J. High Energ. Phys.

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Abstract:We compute the exact entropy of one-eighth and one-quarter BPS black holes in N = 8 and N = 4 string theory respectively. This includes all the N = 4 CHL models in both K3 and T 4 compactifications. The main result is a measure for the finite dimensional integral that one obtains after localization of supergravity on AdS 2 × S 2 . This measure is determined entirely by an anomaly in supersymmetric Chern-Simons theory on local AdS 3 and takes into account the contribution from all the supergravity multiplets. In Chern-Simons theory on compact manifolds, this is the anomaly that computes a certain one-loop dependence on the volume of the manifold. For one-eighth BPS black holes, our results are a first principles derivation of a measure proposed in arXiv:1111.1161, while in the case of one-quarter BPS black holes our result computes exactly all the perturbative or area corrections. Moreover, we argue that instantonic contributions can be incorporated and give evidence by computing the measure, which matches precisely the microscopics. Along with this, we find a unitary condition that truncates the answer to a finite sum of instantons in perfect agreement with a microscopic formula. Our results therefore solve a number of puzzles related to localization in supergravity and constitute a larger number of examples where holography can be shown to hold exactly.

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“…The Hamiltonian expression for the elliptic genus is simply obtained by omitting this prefactor (see e.g. [27]); we finally find…”

Section: Jhep08(2014)087mentioning

confidence: 96%

Higher poles and crossing phenomena from twisted genera

Ashok

Dell’Aquila

Troost

2014

J. High Energ. Phys.

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We demonstrate that Appell-Lerch sums with higher order poles as well as their modular covariant completions arise as partition functions in the cigar conformal field theory with worldsheet supersymmetry. The modular covariant derivatives of the elliptic genus of the cigar give rise to operator insertions corresponding to (powers of) right-moving momentum, left-moving fermion number, as well as a term corresponding to an ordinary zero mode partition sum. To show this, we demonstrate how the right-moving supersymmetric quantum mechanics (and in particular the Hamiltonian and spectral density) depend on the imaginary part of the chemical potential for angular momentum. A consequence of our analysis is that varying the imaginary part of the chemical potential for angular momentum on the cigar gives rise to a wall-crossing phenomenon in the bound state contribution to the elliptic genus, while the full elliptic genus is a continuous function of the chemical potential.

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Partition functions and elliptic genera from supergravity

Cited by 121 publications

References 30 publications

More rings to rule them all: fragmentation, 4D↔ 5Dand split-spectral flows

More rings to rule them all: fragmentation, 4D↔ 5Dand split-spectral flows

Exact Holography and Black Hole Entropy in N = 8 $$ \mathcal{N}=8 $$ and N = 4 $$ \mathcal{N}=4 $$ String Theory

Higher poles and crossing phenomena from twisted genera

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