The anomaly cancelation method proposed by Wilczek et al. is applied to the general charged rotating black holes in five-dimensional minimal gauged supergravity. Thus Hawking temperature and fluxes are found. The Hawking temperature obtained agrees with the surface gravity formula. The black holes have charge and two unequal angular momenta and these give rise to appropriate terms in the effective U(1) gauge field of the reduced (1+1)-dimensional theory. In particular, it is found that the terms in this U(1) gauge field correspond exactly to the correct electrostatic potential and the two angular velocities on the horizon of the black holes, and so the results for the Hawking fluxes derived here from the anomaly cancelation method are in complete agreement with the ones obtained from integrating the Planck distribution.
The anomaly cancelation method proposed by Wilczek et al. is applied to the black holes of topologically massive gravity (TMG) and topologically massive gravito-electrodynamics (TMGE). Thus the Hawking temperature and fluxes of the ACL and ACGL black holes are found. The Hawking temperatures obtained agree with the surface gravity formula. Both black holes are rotating and this gives rise to appropriate terms in the effective U(1) gauge field of the reduced (1+1)-dimensional theory. It is found that the terms in this U(1) gauge field correspond exactly to the correct angular velocities on the …
In the presence of back reaction, we first produce the one-loop corrections for the event horizon and Hawking temperature of the Reissner-Nordström black hole. Then, based on the covariant anomaly cancelation method and the effective action technique, the modified expressions for the fluxes of gauge current and energy momentum tensor, due to the effect of back reaction, are obtained. The results are consistent with the Hawking fluxes of a (1+1)-dimensional blackbody at the temperature with quantum corrections, thus confirming the robustness of the covariant anomaly cancelation method and the e…
The problem of computing systematically the gauge invariant extension of WZW term through equivariant cohomology is addressed. The analysis done by Witten in the two-dimensional case is extended to the four-dimensional ones. While Cartan's model is used to find the anomaly cancelation condition. It is shown that the Weil model is more appropriated to find the gauge invariant extension of the WZW term. In the process we point out that Weil's and Cartan's models are also useful to stress some connections with the abelian anomaly.
Freudenthal duality in N=2, D=4 ungauged supergravity is generated by an anti-involutive operator that acts on the electromagnetic fluxes, and results to be a symmetry of the Bekenstein-Hawking entropy. We show that, with a suitable extension, this duality can be generalized to the abelian gauged case as well, even in presence of hypermultiplets. By defining Freudenthal duality along the scalar flow, one can prove that two configurations of charges and gaugings linked by the Freudenthal operator share the same set of values of the scalar fields at the black hole horizon. Consequently, Freudent…
Motivated by advanced progress in the holographic theory between rotating black holes and CFT, we explore the conformal invariance on dyonic Kerr-Sen black hole and its gauged family. We consider a neutral massless scalar probe on the black holes' background within the low-frequency limit and exhibit that the solution space possesses $SL(2,R)\times SL(2,R)$ isometry. The periodic identification of the azimuthal angle corresponds to the spontaneous conformal symmetry breaking by temperatures $T_L,T_R$. Using the computation of the central charges on Ref. [25] that we recalculate by considering …
We continue the effort of defining and evaluating the quantum entropy function for supersymmetric black holes in 4d ${\cal N} = 2$ gauged supergravity, initiated in [1803.05920]. The emphasis here is on the missing steps in the previous localization analysis, mainly dealing with one-loop determinants for abelian vector multiplets and hypermultiplets on the non-compact space $\mathbb{H}_2 \times Σ_{\rm g}$ with particular boundary conditions. We use several different techniques to arrive at consistent results, which have a most direct bearing on the logarithmic correction terms to the Bekenstei…
In this paper we construct the $\mathcal N=6$ conformal supergravity in three dimensions from a set of Chern-Simons-like terms one for each of the graviton, gravitino, and R-symmetry gauge field and then couple this theory to the $\mathcal N=6$ superconformal ABJM theory. In a first step part of the coupled Lagrangian for this topologically gauged ABJM theory is derived by demanding that all terms of third and second order in covariant derivatives cancel in the supersymmtry variation of the Lagrangian. To achieve this the transformation rules of the two separate sectors must be augmented by ne…
Explorations of Universality in the Entropy and Hawking Radiation of Non-Extremal Kerr AdS$_4$ Black Holes
International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), University of Chinese Academy of Sciences (UCAS)（国际理论物理中心亚太分中心，中国科学院大学）；Peng Huanwu Center for Fundamental Theory（彭桓武基础理论研究中心）；Leinweber Institute for Theoretical Physics, University of Michigan（莱因韦伯理论物理研究所，密歇根大学）
We analyze BPS black hole attractors in 4d gauged supergravity in the presence of higher derivative supersymmetric terms, including a Weyl-squared-type action, and determine the resulting corrections to the Bekenstein-Hawking entropy. The near-horizon geometry AdS$_2 \times$S$^2$ (or other Riemann surface) preserves half of the supercharges in $N=2$ supergravity with Fayet-Iliopoulos gauging. We derive a relation between the entropy and the black hole charges that suggests via AdS/CFT how subleading corrections contribute to the supersymmetric index in the dual microscopic picture. Depending o…
Recently a new class of asymptotically AdS ultra-spinning black holes has been constructed with a noncompact horizon of finite area [1], in which the asymptotic rotation is effectively boosted to the speed of light. We employ this technique for four-dimensional $U(1)^4$ and five-dimensional $U(1)^3$ gauged supergravity black holes. The obtained new exact black hole solutions for both cases possess a noncompact horizon; their topologies are a sphere with two punctures. We then demonstrate that the ultra-spinning limit commutes with the extremality condition as well as the near horizon limit for…
In $F(4)$ gauged supergravity in six dimensions, we study supersymmetric $AdS_6$ black holes with various horizon geometries. We find a new $AdS_2\,\times\,Σ_{\mathfrak{g}_1}\timesΣ_{\mathfrak{g}_2}$ horizon solution with $\mathfrak{g}_1>1$ and $\mathfrak{g}_2>1$, and present the black hole solution numerically. The full black hole is an interpolating geometry between the asymptotically $AdS_6$ boundary and the $AdS_2\,\times\,Σ_{\mathfrak{g}_1}\timesΣ_{\mathfrak{g}_2}$ horizon. We calculate the Bekenstein-Hawking entropy of the black hole and find a match with the recently calculated topologi…
We relate across dimensions BPS attractors of black strings and black holes of various topology in gauged supergravities with nontrivial scalar potential. The attractors are of the form AdS$_{2, 3} \times Σ^{2, 3}$ in 4, 5, and 6 dimensions, and can be generalized to some higher dimensional analogs. Even though the attractor geometries admit standard Kaluza-Klein and Scherk-Schwarz reductions, their asymptotic AdS spaces in general do not. The resulting lower dimensional objects are black holes with runaway asymptotics in supergravity theories with no maximally symmetric vacua. Such classes of…
We demonstrate that rotating dyonic black holes in Einstein-Maxwell-Dilaton-Axion (EMDA) theory is holographically dual with 2D conformal field theory. We first investigate the duality on dyonic Kerr-Sen black hole with non-vanishing dilaton and axion charges. The near-horizon geometry of extremal dyonic Kerr-Sen spacetime possesses the $SL(2,R) \times U (1)$ isometry allowing to employ the asymptotic symmetry group method to find the corresponding central charge. We find two different branches of the mass which correspond to CFT with two different central charges $c_L=12am_+$ and $c_L=12am_-$…
We construct a consistent truncation of six-dimensional matter coupled $F(4)$ gauged supergravity on a cornucopia of two-dimensional surfaces including a spindle, disc, domain wall and other novel backgrounds to four-dimensional minimal gauged supergravity. Using our consistent truncation we uplift known AdS$_2\times Σ_1$ solutions giving rise to four-dimensional orbifold solutions, AdS$_2\timesΣ_1\ltimesΣ_2$. We further uplift our solutions to massive type IIA supergravity by constructing the full uplift formulae for six-dimensional U$(1)^2$-gauged supergravity including all fields and arbitr…
Within class of generic black holes there are extremal black holes (with vanishing Hawking temperature T) and vanishing horizon area Ah, but with finite Ah/T ratio,the Extremal Vanishing Horizon (EVH) black holes. We study the near horizon limit of a four dimensional EVH black hole solution to a generic (gauged) Einstein-Maxwell dilaton theory and show that in the near horizon limit they develop a throat which is a pinching orbifold limit of AdS3. This is an extension of the well known result for extremal black holes the near horizon limit of which contains an AdS2 throat. We show that in the …
We show that the Bekenstein-Hawking entropy of a class of BPS electrically charged rotating black holes in AdS$_5\times S^5$ can be obtained by a simple extremization principle. We expect that this extremization corresponds to the attractor mechanism for BPS rotating black holes in five-dimensional gauged supergravity, which is still unknown. The expression to be extremized has a suggestive resemblance to anomaly polynomials and the supersymmetric Casimir energy recently studied for $\mathcal{N}=4$ super Yang-Mills.
We construct $AdS_4 \times Σ$ and $AdS_2 \times Σ\times Σ_g$ solutions in F(4) gauged supergravity in six dimensions, where $Σ$ is a two dimensional manifold of non-constant curvature with conical singularities at its two poles, called a spindle, and $Σ_g$ is a constant curvature Riemann surface of genus g. We find that the first solution realizes a "topologically topological twist", while the second class of solutions gives rise to an "anti twist". We compute the holographic free energy of the $AdS_4 \times Σ$ solution and find that it matches the entropy computed by extremizing an entropy fu…
Employing uplift formulae, we uplift supersymmetric $AdS_6$ black holes from $F(4)$ gauged supergravity to massive type IIA and type IIB supergravity. In massive type IIA supergravity, we obtain supersymmetric $AdS_6$ black holes asymptotic to the Brandhuber-Oz solution. In type IIB supergravity, we obtain supersymmetric $AdS_6$ black holes asymptotic to the non-Abelian T-dual of the Brandhuber-Oz solution. For the uplifted black hole solutions, we calculate the holographic entanglement entropy. In massive type IIA supergravity, it precisely matches the Bekenstein-Hawking entropy of the black …
We construct analytical supersymmetric coloured black hole solutions, i.e. non-Abelian black hole solutions that have no asymptotic non-Abelian charge but do have non-Abelian charges on the horizon that contribute to the Bekenstein-Hawking entropy, to two SU(3)-gauged N=2 d= supergravities. The analytical construction is made possible due to the fact that the main ingredient is the Bogomol'nyi equation, which under the assumption of spherical symmetry admits a Lax pair formulation. The Lax matrix needed for the coloured black holes must be defective which, even though it is the non-generic and…
Moduli-dependent one-loop entropy of hyperbolic BPS black hole in AdS$_4$
School of Science, Huzhou Normal University（湖州师范学院理学院）；Indian Institute of Technology (Indian School of Mines) Dhanbad（印度理工学院（印度矿业学院）丹巴德校区）；Indian Institute of Technology Bombay（孟买印度理工学院）
In this paper we discuss the supersymmetric localization of the 4D $\mathcal{N}=2$ off-shell gauged supergravity in the background of the $\textrm{AdS}_4$ neutral topological black hole, which is the gravity dual of the ABJM theory defined on the boundary $\textrm{S}^1 \times \mathbb{H}^2$. We compute the large-$N$ expansion of the supergravity partition function. The result gives the black hole entropy with the logarithmic correction, which matches the previous result of the entanglement entropy of the ABJM theory up to some stringy effects. Our result is consistent with the previous on-shell…
The low-temperature thermodynamics of near-extremal rotating black holes has recently been revisited to incorporate one-loop contributions that are dominant in this regime. We discuss these quantum corrections to the gravitational path integral for asymptotically Anti de-Sitter black holes in four and five dimensions. In four dimensions we explicitly consider Kerr-AdS$_4$, Kerr-Newman-AdS$_4$ and the rotating black hole in ${\cal N}=4$ gauged supergravity with two scalars and two electric charges turned on. In five dimensions we explicitly address the asymptotically flat Myers-Perry black hole…
We demonstrate that Kerr-CFT duality can be extended to super-entropic black holes, which have non-compact horizons with finite area. We demonstrate that this duality is robust insofar as the ultra-spinning limit of a Kerr-AdS black hole (which yields the super-entropic class)commutes with the near-horizon limit (which yields the Kerr-CFT duality). Consequently the Bekeinstein-Hawking and the CFT entropies are equivalent. We show that the duality holds for both singly-spinning super-entropic black holes in 4 dimensions and for doubly-spinning super-entropic black holes of gauged supergravity i…
This thesis focuses mainly on understanding the origin of the Bekenstein-Hawking entropy for a class of four- and five-dimensional BPS black holes in string/M-theory. To this aim, important ingredients are holography and supersymmetric localization. Using the method of supersymmetric localization, the Euclidean path integrals for supersymmetric field theories on $Σ_\mathfrak{g} \times T^{n}$ $(n=1,2)$, with at least four real supercharges, can be reduced to a matrix integral that depends on background magnetic fluxes and chemical potentials for the global symmetries of the theory. This defines…
We derive the Bekenstein-Hawking entropy for a class of BPS black holes in the massive type IIA supergravity background AdS$_4 \times S^6$ from a microscopic counting of supersymmetric ground states in a holographically dual field theory. The counting is performed by evaluating the topologically twisted index of three-dimensional $\mathcal{N}=2$ Chern-Simons-matter gauge theories in the large $N$ limit. The $\mathcal{I}$-extremization principle is shown to match the attractor mechanism for the near-horizon geometries constructed in the four-dimensional dyonic $\mathcal{N}=2$ gauged supergravit…
In the Loop Quantum Gravity, black holes (or even more general Isolated Horizons) are described by a SU(2) Chern-Simons theory. There is an equivalent formulation of the horizon degrees of freedom in terms of a U(1) gauge theory which is just a gauged fixed version of the SU(2) theory. These developments will be surveyed here. Quantum theory based on either formulation can be used to count the horizon micro-states associated with quantum geometry fluctuations and from this the micro-canonical entropy can be obtained. We shall review the computation in SU(2) formulation. Leading term in the ent…
We construct a family of multi-dyonically charged and rotating supersymmetric AdS$_2\times Σ$ solutions of $D=4$, $\mathcal{N}=4$ gauged supergravity, where $Σ$ is a sphere with two conical singularities known as a spindle. We argue that these arise as near horizon limits of extremal dyonically charged rotating and accelerating supersymmetric black holes in AdS$_4$, that we conjecture to exist. We demonstrate this in the non-rotating limit, constructing the accelerating black hole solutions and showing that the non-spinning spindle solutions arise as the near horizon limit of the supersymmetri…
Using recent results in four-derivative 5d $\mathcal{N}=2$ minimal gauged supergravity, we evaluate the regularized on-shell action of the Euclidean solution in this theory that admits a Lorentzian continuation to an AdS$_5$ black hole with one electric charge and two angular momenta. We focus on the supersymmetric limit of this solution and employ holography to show that the result can be expressed purely in terms of angular momentum fugacities and the 't Hooft anomalies for the $\mathrm{U}(1)_{\mathrm R}$ R-symmetry of the dual 4d $\mathcal{N}=1$ SCFT. This holographic calculation is in perf…
Recently it was discovered that twisted superconformal index ${\mathcal{I}}$ can be used to understand the Bekenstein-Hawking entropy of magnetically charged black holes in AdS spacetime. In this paper we apply the so-called $\mathcal{I}$-extremization procedure to three-dimensional gauge field theories and their geometric dual, focusing in particular on the seven-dimensional Sasaki-Einstein manifold $M^{1,1,1}$. We generalize recent studies on relations among toric geometry, variational principles, and black hole entropy to the case of AdS$_2 \times Y_9$, where $Y_9$ is a fibration of toric S…
We use conformal supergravity techniques to study four-derivative corrections in four-dimensional gauged supergravity. We show that the four-derivative Lagrangian for the propagating degrees of freedom of the $\mathcal{N}=2$ gravity multiplet is determined by two real dimensionless constants. We demonstrate that all solutions of the two-derivative equations of motion in the supergravity theory also solve the four-derivative equations of motion. These results are then applied to explicitly calculate the regularized on-shell action for any asymptotically locally AdS$_4$ solution of the two-deriv…
