# ICHEP 2014

2-9 July 2014
Valencia, Spain

## N=2 SUGRA BPS Multi-center solutions, quadratic prepotentials and Freudenthal transformations

5 Jul 2014, 13:00
30m
Sala 8+9 ()

### Sala 8+9

Oral presentation Formal Theory Developments

### Speaker

Dr. torrente-lujan emilio (universidad de murcia)

### Description

We present a detailed description of $N=2$ stationary BPS multicenter black hole solutions for quadratic prepotentials with an arbitrary number of centers and scalar fields making a systematic use of the algebraic properties of the matrix of second derivatives of the prepotential, $\mathcal{S}$, which in this case is a scalar-independent matrix. In particular we obtain bounds on the physical parameters of the multicenter solution such as horizon areas and ADM mass. We discuss the possibility and convenience of setting up a basis of the symplectic vector space built from charge eigenvectors of the $\ssigma$, the set of vectors $(\Ppm q_a)$ with $\Ppm$ $\ssigma$-eigenspace projectors. The anti-involution matrix $\mathcal{S}$ can be understood as a Freudenthal duality $\tilde{x}=\ssigma x$. We show that this duality can be generalized to Freudenthal transformations'' $$x\to \lambda\exp(\theta \ssigma) x= a x+b\tilde{x}$$ under which the horizon area, ADM mass and intercenter distances scale up leaving constant the scalars at the fixed points. In the special case $\lambda=1$, $\ssigma$-rotations'', the transformations leave invariant the solution. The standard Freudenthal duality can be written as $\tilde x= \exp\left(\frac{\pi}{2} \ssigma\right) x .$ We argue that these generalized transformations leave invariant not only the quadratic prepotential theories but also the general stringy extremal quartic form $\Delta_4$, $\Delta_4(x)= \Delta_4(\cos\theta x+\sin\theta\tilde{x})$ and therefore its entropy at lowest order.

### Primary author

Dr. torrente-lujan emilio (universidad de murcia)

### Co-author

Dr. jose juan fernandez-melgarejo (harvard university)

 Slides

### Paper

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