论文标题
BPS黑洞的熵和非常特殊的几何形状的吸引子。立方形式，梯度图及其反转
BPS Black Hole Entropy and Attractors in Very Special Geometry. Cubic Forms, Gradient Maps and their Inversion
论文作者
论文摘要
我们认为Bekenstein-Hawking的熵和极值BPS黑洞的吸引子，$ \ Mathcal {n} = 2 $，$ d = 4 $ ungauged超级Gravity，以减少最小的物质耦合$ d = 5 $ supergravity。它们通常以对耦合二次方程的不均匀系统（称为BPS系统）的解决方案表示，具体取决于极端黑洞背景中的立方前稳态以及电磁通量。重点关注均质的非对称标量歧管（其分类以$ L（Q，Q，p，\ dot {p}）$模型而言），在某些假设上，在与Clifford矩阵有关的一定假设下四），因此，要明确确定BPS系统的解决方案，进而为BPS黑洞熵提供了新颖的，明确的表达式，将相关的吸引子作为BPS吸引子方程的解决方案。 After a general treatment, we present a number of explicit examples with $\dot{P}=0$, such as $L(q,P)$, $1\leqslant q\leqslant 3$ and $P\geqslant 1$,or $L(q,1)$, $4\leqslant q\leqslant 9$, and one model with $ \ dot {p} = 1 $，即$ l（4,1,1）$。我们还简要评论了克莱恩的签名和分裂代数。特别是，我们首次提供了BPS黑洞熵的明确形式和无限级别的$ L（1，p）$ $ $ P \ geqslant 2 $非对称型号的$ \ Mathcal {n} = 2 $，$ d $ d = 4 = 4 $ supergravity的无限类吸引子。
We consider Bekenstein-Hawking entropy and attractors in extremal BPS black holes of $\mathcal{N}=2$, $D=4$ ungauged supergravity obtained as reduction of minimal, matter-coupled $D=5$ supergravity. They are generally expressed in terms of solutions to an inhomogeneous system of coupled quadratic equations, named BPS system, depending on the cubic prepotential as well as on the electric-magnetic fluxes in the extremal black hole background. Focussing on homogeneous non-symmetric scalar manifolds (whose classification is known in terms of $L(q,P,\dot{P})$ models), under certain assumptions on the Clifford matrices pertaining to the related cubic prepotential, we formulate and prove an invertibility condition for the gradient map of the corresponding cubic form (to have a birational inverse map which is an homogeneous polynomial of degree four), and therefore for the solutions to the BPS system to be explicitly determined, in turn providing novel, explicit expressions for the BPS black hole entropy and the related attractors as solution of the BPS attractor equations. After a general treatment, we present a number of explicit examples with $\dot{P}=0$, such as $L(q,P)$, $1\leqslant q\leqslant 3$ and $P\geqslant 1$,or $L(q,1)$, $4\leqslant q\leqslant 9$, and one model with $\dot{P}=1$, namely $L(4,1,1)$. We also briefly comment on Kleinian signatures and split algebras. In particular, we provide, for the first time, the explicit form of the BPS black hole entropy and of the related BPS attractors for the infinite class of $L(1,P)$ $P\geqslant 2$ non-symmetric models of $\mathcal{N}=2$, $D=4$ supergravity.
