Lagrangians of N = 2 supergravity-matter systems

We construct interpolating solutions describing single-center static extremal non-supersymmetric black holes in four-dimensional N = 2 supergravity theories with cubic prepotentials. To this end, we derive and solve first-order flow equations for rotating electrically charged extremal black holes in a Taub-NUT geometry in five dimensions. We then use the connection between five-and four-dimensional extremal black holes to obtain four-dimensional flow equations and we give the corresponding solutions.

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“…The four-dimensional N = 2 supergravity action corresponding to (A.1) is based on the prepotential [40,41] …”

Section: A Review Of Very Special Geometrymentioning

confidence: 99%

First-order flow equations for extremal black holes in very special geometry

Cardoso

Ceresole

Dall’Agata

et al. 2007

J. High Energy Phys.

117

194

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“…When N = 2 hypermultiplets are added to the theory, the β function still vanishes above 1-loop, since the kinetic terms for the hypermultiplets are not renormalized [23], so there is no need to rescale them to go back to canonical normalization.…”

Section: N = 2 Theoriesmentioning

confidence: 99%

Holomorphy, rescaling anomalies and exact β functions in supersymmetric gauge theories

Arkani-Hamed

Murayama

2000

J. High Energy Phys.

205

278

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There have long been known "exact" β functions for the gauge coupling in N = 1 supersymmetric gauge theories, the so-called Novikov-Shifman-Vainshtein-Zakharov (NSVZ) β functions. Shifman and Vainshtein further related these β functions to the exact 1-loop running of the gauge coupling in a "Wilsonian" action. All these results, however, remain somewhat mysterious. We attempt to clarify these issues by presenting new perspectives on the NSVZ β function. Our interpretation of the results is somewhat different than the one given by Shifman and Vainshtein, having nothing to do with the distinction between "Wilsonian" and "1PI" effective actions. Throughout we work in the context of the Wilsonian Renormalization Group; namely, as the cutoff of the theory is changed from M to M ′ , we seek to determine the appropriate changes in the bare couplings needed in order to keep the low energy physics fixed. The entire analysis is therefore free of infrared subtleties. When the bare Lagrangian given at the cutoff is manifestly holomorphic in the gauge coupling, we show that the required change in the holomorphic gauge coupling is exhausted at 1-loop to all orders of perturbation theory, and even non-perturbatively in some cases. On the other hand, when the bare Lagrangian at the cutoff has canonically normalized kinetic terms, we find that the required change in the gauge coupling is given by the NSVZ β function. The higher order contributions in the NSVZ β function are due to anomalous Jacobians under the rescaling of the fields done in passing from holomorphic to canonical normalization. We also give prescriptions for regularizing certain N = 1 theories with an ultraviolet cutoff M preserving manifest holomorphy, starting from finite N = 4 and N = 2 theories. It is then at least in principle possible to check the validity of the exact β function by higher order calculations in these theories. * This work was supported in part by the

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“…These details have been studied extensively in previous works [31,32,42,[44][45][46]. We will first discuss the construction of the relevant supersymmetry multiplets and then go into detail discussing the bosonic part of the N = 2 conformal supergravity action that couples these multiplets together, complete with higherderivative interactions.…”

Section: Jhep08(2017)048mentioning

confidence: 99%

Non-renormalization for non-supersymmetric black holes

Charles

Larsen

Mayerson

2017

J. High Energ. Phys.

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Abstract:We analyze large logarithmic corrections to 4D black hole entropy and relate them to the Weyl anomaly. We use duality to show that counter-terms in EinsteinMaxwell theory can be expressed in terms of geometry alone, with no dependence on matter terms. We analyze the two known N = 2 supersymmetric invariants for various non-supersymmetric black holes and find that both reduce to the Euler invariant. The c-anomaly therefore vanishes in these theories and the coefficient of the large logarithms becomes topological. It is therefore independent of continuous black hole parameters, such as the mass, even far from extremality.

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Lagrangians of N = 2 supergravity-matter systems

Cited by 586 publications

References 37 publications

First-order flow equations for extremal black holes in very special geometry

First-order flow equations for extremal black holes in very special geometry

Holomorphy, rescaling anomalies and exact β functions in supersymmetric gauge theories

Non-renormalization for non-supersymmetric black holes

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