N=4 BPS black holes and octonionic twistors

BPS Monopoles

We review classical BPS monopoles, their moduli spaces, twistor descriptions and dynamics. Particular emphasis is placed upon symmetric monopoles, where recent progress has been made. Some remarks on the role of monopoles in S-duality and Seiberg-Witten theory are also made.

Twistors and Black Holes

Motivated by black hole physics in N=2, D=4 supergravity, we study the geometry of quaternionic-Kahler manifolds M obtained by the c-map construction from projective special Kahler manifolds M_s. Improving on earlier treatments, we compute the Kahler potentials on the twistor space Z and Swann space S in the complex coordinates adapted to the Heisenberg symmetries. The results bear a simple relation to the Hesse potential Σof the special Kahler manifold M_s, and hence to the Bekenstein-Hawking entropy for BPS black holes. We explicitly construct the ``covariant c-map'' and the ``twistor map'',…

八元数魔法超引力、Niemeier格与例外及希尔伯特模形式

Octonionic Magical Supergravity, Niemeier Lattices, and Exceptional and Hilbert Modular Forms

本研究通过例外若尔当代数与模形式，给出了五维八元数魔法超引力中BPS黑洞的量子简并度，并关联了Niemeier格与希尔伯特模形式。

D-instantons and twistors

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is an outstanding open problem. We address this issue by relating the quaternionic-Kahler metric on the hypermultiplet moduli space to the complex contact geometry on its twistor space. In this framework, Euclidean D-brane instantons are captured by contact transformations between different patches. We derive those by recasting the previously known A-type D2-instanton corrections in the language of contact geometry, covariantizing the result under electro-…

自对偶 N=4 SYM 中的行列式与扭量空间

Determinants in self-dual N=4 SYM and twistor space

本文研究自对偶 N=4 SYM 中超对称行列式算符关联函数，提出扭量空间表示并借助矩阵对偶化为矩阵积分，验证十维对称性猜想并给出次数四的新公式。

Heavenly度量、BPS指标与twistors

Heavenly metrics, BPS indices and twistors

本文将Bridgeland定义的复超凯勒度量相关的Riemann-Hilbert问题转化为TBA型方程组，获得了度量和势函数的积分表达式，并求解了变形方程及推导了BPS结构下的τ函数。

On the constraints defining BPS monopoles

We discuss the explicit formulation of the transcendental constraints defining spectral curves of SU(2) BPS monopoles in the twistor approach of Hitchin, following Ercolani and Sinha. We obtain an improved version of the Ercolani-Sinha constraints, and show that the Corrigan-Goddard conditions for constructing monopoles of arbitrary charge can be regarded as a special case of these. As an application, we study the spectral curve of the tetrahedrally symmetric 3-monopole, an example where the Corrigan-Goddard conditions need to be modified. A particular 1-cycle on the spectral curve plays an im…

Remarks on the Atiyah-Hitchin metric

We outline the construction of the Atiyah-Hitchin metric on the moduli space of SU(2) BPS monopoles with charge 2, first as an algebraic curve in C^3 following Donaldson and then as a solution of the Toda field equations in the continual large N limit. We adopt twistor methods to solve the underlying uniformization problem, which by the generalized Legendre transformation yield the Kahler coordinates and the Kahler potential of the metric. We also comment on the connection between twistors and the Seiberg-Witten construction of quantum moduli spaces, as they arise in three dimensional supersym…

弦论紧致化中的黑洞与对偶性

Black holes and dualities in string theory compactifications

研究II型弦论在Calabi-Yau流形紧致化中的超多重态模空间、瞬子修正与BPS指标模性质，利用扭子空间、镜像对称和S对偶计算修正，并构造模完备化方程的解。

Stringy Black Holes and the Geometry of Entanglement

Recently striking multiple relations have been found between pure state 2 and 3-qubit entanglement and extremal black holes in string theory. Here we add further mathematical similarities which can be both useful in string and quantum information theory. In particular we show that finding the frozen values of the moduli in the calculation of the macroscopic entropy in the STU model, is related to finding the canonical form for a pure three-qubit entangled state defined by the dyonic charges. In this picture the extremization of the BPS mass with respect to moduli is connected to the problem of…

Quantum Attractor Flows

Motivated by the interpretation of the Ooguri-Strominger-Vafa conjecture as a holographic correspondence in the mini-superspace approximation, we study the radial quantization of stationary, spherically symmetric black holes in four dimensions. A key ingredient is the classical equivalence between the radial evolution equation and geodesic motion of a fiducial particle on the moduli space M^*_3 of the three-dimensional theory after reduction along the time direction. In the case of N=2 supergravity, M^*_3 is a para-quaternionic-Kahler manifold; in this case, we show that BPS black holes corres…

Strings, Black Holes, and Quantum Information

We find multiple relations between extremal black holes in string theory and 2- and 3-qubit systems in quantum information theory. We show that the entropy of the axion-dilaton extremal black hole is related to the concurrence of a 2-qubit state, whereas the entropy of the STU black holes, BPS as well as non-BPS, is related to the 3-tangle of a 3-qubit state. We relate the 3-qubit states with the string theory states with some number of D-branes. We identify a set of "large" black holes with the maximally entangled GHZ-class of states and "small" black holes with separable, bipartite and W sta…