String Theory Effects on Five-Dimensional Black Hole Physics

Abstract

We review recent developments in understanding quantum/string corrections to BPS black holes and strings in five-dimensional supergravity. These objects are solutions to the effective action obtained from M-theory compactified on a Calabi-Yau threefold, including the one-loop corrections determined by anomaly cancellation and supersymmetry. We introduce the off-shell formulation of this theory obtained through the conformal supergravity method and review the methods for investigating supersymmetric solutions. This leads to quantum/string corrected attractor geometries, as well as asymptotically flat black strings and spinning black holes. With these solutions in hand, we compare our results with analogous studies in four-dimensional string-corrected supergravity, emphasizing the distinctions between the four and five dimensional theories.

Heterotic black holes

“…When used in Cardy formula (3.13) this gives in the BPS case (nw > 0) 17) which exactly agrees with the expression obtained from direct microstate counting (3.11). The virtue of AdS/CFT method is that it can give us the result also in the non-BPS case in which n < 0…”

“…Solution (2.6) is extremal: it has vanishing Hawking temperature, and it can be obtained in a particular limit from multiparameter regular black hole solutions (with the same charge content) having regular horizons with non-vanishing temperature and entropy, and with mass satisfying 17) where unequality is saturated for solutions (2.6).…”

“…We are interested in extremal black hole solutions of the action obtained by combining (6.1) and (6.4): 17 A…”

“…Explicitly, 17 Our conventions in this section are different from the rest of the text. We take for Newton constant G 5 = π 2 /4 and for the string tension α = 1.…”

Duality covariant non-BPS first order systems

“…For supersymmetric black holes, it has been possible to find these solutions explicitly, making use of the constraint imposed by the residual supercharges, even including higher derivative corrections, see e.g. [1][2][3][4][5][6][7][8][9]. Such a task however has proven more difficult for more general black holes, since one is forced to consider the full second order equations of motion rather than the first order BPS conditions.…”