On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

Superstring theoryをめぐって(放談室)

We derive an exact formula for the cusp anomalous dimension at small angles. This is done by relating the latter to the computation of certain 1/8 BPS Wilson loops which was performed by supersymmetric localization. This function of the coupling also determines the power emitted by a moving quark in $\mathcal{N} = 4$
 super Yang Mills, as well as the coefficient of the two point function of the displacement operator on the Wilson loop. By a similar method we compute the near BPS expansion of the generalized cusp anomalous dimension.

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An exact formula for the radiation of a moving quark in {N} = 4 super Yang Mills

We derive a set of integral equations of the TBA type for the generalized cusp anomalous dimension, or the quark antiquark potential on the three sphere, as a function of the angles. We do this by considering a family of local operators on a Wilson loop with charge L. In the large L limit the problem can be solved in terms of a certain boundary reflection matrix. We determine this reflection matrix by using the symmetries and the boundary crossing equation. The cusp is introduced through a relative rotation between the two boundaries. Then the TBA trick of exchanging space and time leads to an exact equation for all values of L. The L = 0 case corresponds to the cusped Wilson loop with no operators inserted. We then derive a slightly simplified integral equation which describes the small angle limit. We solve this equation up to three loops in perturbation theory and match the results that were obtained with more direct approaches.

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The quark anti-quark potential and the cusp anomalous dimension from a TBA equation

We consider a spherical region with a heavy quark in the middle We compute the extra entanglement entropy due to the presence of a heavy quark both in $ \mathcal{N} $
 = 4 Super Yang Mills and in the $ \mathcal{N} $
 = 6 Chern-Simons matter theory (ABJM) This is done by relating the computation to the expectation value of a circular Wilson loop and a stress tensor insertion We also give an exact expression for the Bremsstrahlung function that determines the energy radiated by a quark in the ABJM theory

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Exact results for the entanglement entropy and the energy radiated by a quark

In this work (which supersedes our previous preprint [1]) we determine the expectation value of the $ \mathcal{N} = 4 $
 SU(N) SYM Lagrangian density operator in the presence of an infinitely heavy static particle in the symmetric representation of SU(N), by means of a D3-brane probe computation. The result that we obtain coincides with two previous computations of different observables, up to kinematical factors. We argue that these agreements go beyond the D-brane probe approximation, which leads us to propose an exact formula for the expectation value of various operators. In particular, we provide an expression for the total energy loss by radiation of a heavy particle in the fundamental representation.

Exact results for static and radiative fields of a quark in $ \mathcal{N} = 4 $ super Yang-Mills

We propose an exact formula for the energy radiated by an accelerating quark in N=2 superconformal theories in four dimensions. This formula reproduces the known bremsstrahlung function for N=4 theories and provides a prediction for all the perturbative and instanton corrections in N=2 theories. We perform a perturbative check of our proposal up to three loops.

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Exact Bremsstrahlung Function in N=2 Superconformal Field Theories.

We use the AdS/CFT correspondence to compute the energy radiated by an infinitely massive half-Bogomol'nyi-Prasad-Sommerfeld particle charged under N=4 super Yang-Mills theory, transforming in the symmetric or antisymmetric representation of the gauge group, and moving in the vacuum, to all orders in 1/N and for large 't Hooft coupling. For the antisymmetric case we consider D5-branes reaching the boundary of five-dimensional anti-de Sitter space (AdS(5)) at arbitrary timelike trajectories, while for the symmetric case, we consider a D3-brane in AdS(5) that reaches the boundary at a hyperbola. We compare our results to the one obtained for the fundamental representation, deduced by considering a string in AdS(5).

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Energy loss of an infinitely massive half-Bogomol'nyi-Prasad-Sommerfeld particle by radiation to all orders in 1/N.

In this work we consider a heavy quark moving with constant proper acceleration in the vacuum of any four dimensional conformal field theory. We argue that the two-point function of its momentum fluctuations is exactly captured by the Bremsstrahlung function that gives the total radiated power. For the particular case of $ \mathcal{N} $
 = 4 SU(N) SYM this function is exactly known, so in this case we obtain an explicit expression for the momentum diffusion coefficient, and check that various limits of this result are reproduced by probe computations in AdS5. Finally, we evaluate this transport coefficient for a heavy quark accelerated in the vacuum of $ \mathcal{N} $
 = 4 SU(3) SYM, and comment on possible lessons of our results for the study of heavy quarks traversing the super Yang-Mills plasma.

Exact momentum fluctuations of an accelerated quark in $ \mathcal{N} $ = 4 super Yang-Mills

We obtain the perturbative expansion of the free energy on S4 for four dimensional Lagrangian 

$$ \mathcal{N} $$
 = 2 superconformal field theories, to all orders in the ’t Hooft coupling, in the planar limit. We do so by using supersymmetric localization, after rewriting the 1-loop factor as an effective action involving an infinite number of single and double trace terms. The answer we obtain is purely combinatorial, and involves a sum over tree graphs. We also apply these methods to the perturbative expansion of the free energy at finite N , and to the computation of the vacuum expectation value of the 1/2 BPS circular Wilson loop, which in the planar limit involves a sum over rooted tree graphs.

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Bartomeu Fiol

Papers

Exact results for static and radiative fields of a quark in $ \mathcal{N} = 4 $ super Yang-Mills

Exact Bremsstrahlung Function in N=2 Superconformal Field Theories.

Energy loss of an infinitely massive half-Bogomol'nyi-Prasad-Sommerfeld particle by radiation to all orders in 1/N.

Exact momentum fluctuations of an accelerated quark in $ \mathcal{N} $ = 4 super Yang-Mills

The planar limit of $\mathcal{N}=2$ superconformal field theories