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      "body": "<div class=\"text-justify\">Last week, I found out the sad news that the former Chilean president Sebastián Piñera had died, as did many, through the media. He was 74 years old. Throughout his life, Piñera, a <a href=\"https://www.youtube.com/watch?v=aTWj2-d4dPQ\">descendant</a> of Inca Huayna Cápac, cherished a special bond with Peru. Together with Alan García (Peru), Juan Manuel Santos (Colombia), and Felipe Calderón (Mexico), he was instrumental in forming the Pacific Alliance by signing the Lima Declaration in 2011. Moreover, during his initial term as president, the Free Trade Agreement between Peru and Chile was implemented in its maximum vigour. On November 25, 2010, he was decorated with a Medal of Honor by the Congress of the Republic of Peru. On the same day, at night, at the Peruvian government palace, he was honored with the Grand Collar of the Order of the Sun, a recognition of his significant role in fostering the open and ongoing dialogue that underpins the bilateral relationship between the two nations.</div>\n\n<center>![](https://images.hive.blog/DQmWDSvkjVG3eHMBGvZRn9L6ck1ZcEdBr6XBFQEjAkrwfha/image)\n<sub> <a href=\"https://diariocorreo.pe/mundo/sebastian-pinera-es-condecorado-con-el-gran-collar-de-la-orden-el-sol-del-peru-455667/\">source</a></sub></center>\n<div class=\"text-justify\">It's worth noting, I think, that Piñera was an alumnus at <a href=\"https://www.uc.cl/noticias/la-uc-lamenta-el-fallecimiento-del-expresidente-sebastian-pinera-reconociendo-su-aporte-al-pais/\">Pontifical Catholic University of Chile</a> where he pursued <a href=\"https://economiayadministracion.uc.cl/noticia/a-los-74-anos-fallecio-el-destacado-ingeniero-comercial-uc-sebastian-pinera-echenique/\">Commercial Engineering</a> and was acknowledged as the top graduate of his class with the Raúl Yver Award. In Chile, he is most remembered for the challenging circumstances he had to deal with as president. I am referring to the post-disaster reconstruction following the 2010 earthquake and tsunami, and the rescue of 33 miners who were trapped for more than 60 days in Atacama, during his initial term. And in his second term, to the COVID-19 pandemic and the violent protests and looting during 2019. With continuous ups and downs in his popularity, I think it must have been very satisfying for him to develop (at the very end) a close and friendly bond with President Boric, who had even accused him of human rights violation.</div>\n<br>\t\n<div class=\"text-justify\">Piñera was concerned about the tragedy faced by Valparaiso due to the fires and was keen on making all possible human capital available to the government to aid in the rebuilding efforts. As such, he reached out by phone to President Boric on Monday night to offer his full support in confronting the catastrophe of the fires. He shared this with his team early the next morning and they agreed to coordinate to crystallize their collaboration. A few hours later the tragedy would occur, when the former president boarded his helicopter to return home to have lunch with his wife and it came down in Ranco Lake. As is known, Piñera was an eager pilot for many years.</div>\n\n<center>![](https://images.hive.blog/DQmcnYakyM2MzWbnGcW3nXZr6v6q2CzNBC1KeN3CJhhW2is/image)\n<sub> Sebastián Piñera, an excellent pilot, prepares to take off a helicopter, in 2010.  <a href=\"https://youtu.be/e_v4BmLMTIA\">source</a></sub></center>\n<div class=\"text-justify\">On Wednesday, the body of Sebastián Piñera was brought to the former National Congress building for mourning. The state funeral took place on Friday, February 9, to pay respects to the ex-President. His body was then moved to the Metropolitan Cathedral of Santiago, where a funeral mass was held. After the funeral mass, the coffin was taken to La Moneda palace for the final tribute. Then, before going to the Memorial Park Cemetery for his burial, the coffin passed through the flower pergola for a traditional tribute. Goodbye to a true statesman.</div>\n\n<center>![](https://images.hive.blog/DQmYK78B4z5kxsgqNjcyrZzzwjPPS2y7qnU8tazc1eCzMVN/image)<sub> <a href=\"https://www.tvn.cl/noticias/actualidad/el-homenaje-popular-multitudinaria-despedida-de-las-floristas-en-la-pergola\">source</a></sub></center>\n\n\n\n***\n<center><sup>Originally posted on [Celestial Brane Amplitudes](http://brane.dblog.org/sebastian-pinera-1949-2024). Hive blog powered by [ENGRAVE](https://dblog.org).</sup></center>",
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      "body": "<div class=\"text-justify\">Last week, I found out the sad news that the former Chilean president Sebastián Piñera had died, as did many, through the media. He was 74 years old. Throughout his life, Piñera, a <a href=\"https://www.youtube.com/watch?v=aTWj2-d4dPQ\">descendant</a> of Inca Huayna Cápac, cherished a special bond with Peru. Together with Alan García (Peru), Juan Manuel Santos (Colombia), and Felipe Calderón (Mexico), he was instrumental in forming the Pacific Alliance by signing the Lima Declaration in 2011. Moreover, during his initial term as president, the Free Trade Agreement between Peru and Chile was implemented in its maximum vigour. On November 25, 2010, he was decorated with a Medal of Honor by the Congress of the Republic of Peru. On the same day, at night, at the Peruvian government palace, he was honored with the Grand Collar of the Order of the Sun, a recognition of his significant role in fostering the open and ongoing dialogue that underpins the bilateral relationship between the two nations.</div>\n\n<center>![](https://images.hive.blog/DQmUyAqzB4oiScJNkspPhE3PxPaoDtyx3fgsmXQ8ZXzAXfP/image)\n<sub> <a href=\"https://diariocorreo.pe/mundo/sebastian-pinera-es-condecorado-con-el-gran-collar-de-la-orden-el-sol-del-peru-455667/\">source</a></sub></center>\n<div class=\"text-justify\">It's worth noting, I think, that Piñera was an alumnus at <a href=\"https://www.uc.cl/noticias/la-uc-lamenta-el-fallecimiento-del-expresidente-sebastian-pinera-reconociendo-su-aporte-al-pais/\">Pontifical Catholic University of Chile</a> where he pursued <a href=\"https://economiayadministracion.uc.cl/noticia/a-los-74-anos-fallecio-el-destacado-ingeniero-comercial-uc-sebastian-pinera-echenique/\">Commercial Engineering</a> and was acknowledged as the top graduate of his class with the Raúl Yver Award. In Chile, he is most remembered for the challenging circumstances he had to deal with as president. I am referring to the post-disaster reconstruction following the 2010 earthquake and tsunami, and the rescue of 33 miners who were trapped for more than 60 days in Atacama, during his initial term. And in his second term, to the COVID-19 pandemic and the violent protests and looting during 2019. With continuous ups and downs in his popularity, I think it must have been very satisfying for him to develop (at the very end) a close and friendly bond with President Boric, who had even accused him of human rights violation.</div>\n<br>\t\n<div class=\"text-justify\">Piñera was concerned about the tragedy faced by Valparaiso due to the fires and was keen on making all possible human capital available to the government to aid in the rebuilding efforts. As such, he reached out by phone to President Boric on Monday night to offer his full support in confronting the catastrophe of the fires. He shared this with his team early the next morning and they agreed to coordinate to crystallize their collaboration. A few hours later the tragedy would occur, when the former president boarded his helicopter to return home to have lunch with his wife and it came down in Ranco Lake. As is known, Piñera was an eager pilot for many years.</div>\n\n<center>![](https://images.hive.blog/DQmcnYakyM2MzWbnGcW3nXZr6v6q2CzNBC1KeN3CJhhW2is/image)\n<sub> Sebastián Piñera, an excellent pilot, prepares to take off a helicopter, in 2010.  <a href=\"https://youtu.be/e_v4BmLMTIA\">source</a></sub></center>\n<div class=\"text-justify\">On Wednesday, the body of Sebastián Piñera was brought to the former National Congress building for mourning. The state funeral took place on Friday, February 9, to pay respects to the ex-President. His body was then moved to the Metropolitan Cathedral of Santiago, where a funeral mass was held. After the funeral mass, the coffin was taken to La Moneda palace for the final tribute. Then, before going to the Memorial Park Cemetery for his burial, the coffin passed through the flower pergola for a traditional tribute. Goodbye to a true statesman.</div>\n\n<center>![](https://images.hive.blog/DQmYK78B4z5kxsgqNjcyrZzzwjPPS2y7qnU8tazc1eCzMVN/image)<sub> <a href=\"https://www.tvn.cl/noticias/actualidad/el-homenaje-popular-multitudinaria-despedida-de-las-floristas-en-la-pergola\">source</a></sub></center>\n\n\n\n***\n<center><sup>Originally posted on [Celestial Brane Amplitudes](http://brane.dblog.org/sebastian-pinera-1949-2024). Hive blog powered by [ENGRAVE](https://dblog.org).</sup></center>",
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      "body": "<div class=\"text-justify\">Since the proposal of Celestial Holography, an idea that promises to provide a new approach to quantum gravity in a four-dimensional asymptotically flat spacetime, remarkable progress has been made. However, the original proposed dictionary causes massless two-point correlators to take the following delta-distribution like behavior</div><img \n    src=\"https://images.hive.blog/DQmfGPE8bU6kkWefHPzBUQMNNE8JgHBrSBkVeHJPmpMEn5T/image\" \n    />\n<div class=\"text-justify\">rather than the expected power-law </div>\n<img \n    src=\"https://images.hive.blog/DQmfPAnaFD6ztFncgXa2ry6WH6zfc5aWu46wKXN3FDQ2YYg/image\"/>\t\n<div class=\"text-justify\">Furthermore, this behavior clashes with the operator product expansion (OPE). Recently, Hideo Furugori, Naoki Ogawa, Sotaro Sugishita and Takahiro Waki proposed a breathtaking solution in their relatively new paper:\n <h5><b><center> <a href=\"https://arxiv.org/abs/2312.07057\">Celestial two-point functions and rectified dictionary</a></center></b></h5></div>\n<br>\t \n<div class=\"text-justify\">Celestial holography propounds a duality between scattering in  an asymptotically flat spacetime and a conformal field theory on the celestial sphere at null infinity. The main objects of study are the so-called celestial amplitudes, which recast the scattering matrix into a basis of boost (rather than energy) eigenstates. They transform like conformal correlators living on such a sphere. The theory built upon these correlators is what we call celestial conformal field theory (CCFT). Furugori and collaborators propose this rectified dictionary for massless scalars</div>\n<img \n    src=\"https://images.hive.blog/DQmRRrX5L97o85dsb93CWqq25zXfEGS6j91FVk3sVpjx3po/image\"/>\n<div class=\"text-justify\">The key difference from the standard one is that they claimed that the operators corresponding to the incoming particles are the shadow-transformed operators</div>\n<img src=\"https://images.hive.blog/DQmbpZE6D4d31dQydhhAMLS979bcJZMdB3oQRR3AqrhENGY/image\"/>\n<div class=\"text-justify\">We thus have a map between scattering amplitudes in the asymptotically Minkowski background and correlators on the celestial sphere. These correlators are sometimes called celestial correlators. The authors verified that, using this dictionary, the two-point correlators of (non-shadow) operators take the conventional form in CFT, namely the power law.</div>\t\t\n<br>\t\n<div class=\"text-justify\">Next, they considered the celestial dictionary for massive scalars, which is the same as the naive one, up to suitable factors, and show that it is smoothly connected to the one for massless scalars – that is to say, we get the celestial dictionary for massless scalars if we take the massless limit of the one for massive scalars. Another stunning aspect is that crossing symmetry for scattering amplitudes, which relates amplitudes involving an incoming positive energy particle to ones involving an outgoing negative energy particle, has a quite natural interpretation in the CCFT. The dictionary can be rewritten treating all outgoing particles on an equal footing regardless of whether they have positive or negative energy. Then, by comparison, a relation between operators for particles with outgoing negative energy and operators for particles with incoming positive energy can be established.</div>\t\n<center>\n<img src=\"https://images.hive.blog/DQmYLauiSC1qEpsmN7DTd94HvZjACjNixnpEvjWCrhbUCT3/image\"/>\n</center>\n<div class=\"text-justify\">In addition, they went on the validity of their dictionary using the OPE and thus ensuring the consistency of it. The three-point correlator can be schematically written as</div>\n<img src=\"https://images.hive.blog/DQmR7UPTevLe7dQeFuyPRPskuhz8uftaF6nEWKbXxPUaTUL/image\"/>\n<div class=\"text-justify\">This corroborates that the three-point correlator is consistent with the two-point function power-law behavior. They subsequently considered the concrete example of a tree level scattering amplitude for two incoming massless particles and one outgoing massive particle and verified that the corresponding celestial three-point correlator behavior does not give rise to any inconsistency. In the case of the four-point correlator, they also commented that the OPE gives the expected result</div>\n<img src=\"https://images.hive.blog/DQmaBKTegJVDpzKRiaDdQcFxxwJiYLUcBQmpPrvpKKMYejG/image\"/>\n<div class=\"text-justify\">Note that it's been almost seven years from the naive celestial dictionary. I believe that this new dictionary will prompt a significant reassessment of some features of CCFT, including OPEs and the conformal block decomposition.</div>\n\n***\n<center><sup>Originally posted on [Celestial Brane Amplitudes](http://brane.dblog.org/a-new-celestial-dictionary-y-leads-to-a-power-law-form-for-two-point-correlators). Hive blog powered by [ENGRAVE](https://dblog.org).</sup></center>",
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