A teoria das cordas éuma estrutura tea³rica da física que descreve objetos fibrosos vibrantes e unidimensionais chamados
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Zua7D3g9poo08jHes/CMxCGOoEOEvlrRDSMYpkAVWgDWJA0xNDv6/iWLqwPDUfiEPMGBbYqe5s9SpUqVEmTNA/cg2D4r5a/sH/YQQSQSQQdC5cvoxjHqwHW3Lw5ZWoKvV3Xyamyeonye0GKDMUoSy1yw0jFi20ZZVAsDrDyOYEDi3DU0X0/cIS/MscQcnJH6sLOpUqVGXTcYo3B8Nyj3AJ6Zfuwgggggggg6Fy5cuXGPVcQ9PFg+0eW7MQpHcjuDqPBf4RZgzNKACFw1n8PvDzpgcJNEXoGRHEDRsv0Su8qH7bA7kBh3Oew/FQh5ubs+bt/10V0YvQY+3eENaBegRz2yvdhBBBBBBBBB0Lly/CzDOj3OD/bEAFGA08wwA7y/wCmkYQgjZIOJpQIvg5gR0Id+8S1YTtoH2v3miKMqgUF7A44IAANvB+bK1o+37g+XcvoKrGkzDvtrsbMWMDzO5O5FIyqFEFB2PCq98Wr2iwpt1r5l1rLlwgggggggggZfhpUAtcARSgC/ldvbTzKlSpOII+P0faDiY59Q23Pv0dCusD2P9+0uoZiq2auXtcwKMV4SGtaPWXv2fUS4eO+ly+lylAnz2jJU+4PS7k787k7nlfbP6hp4aiEpBO8FbZ3CPySzVnah8MtEDYKpfoLsPtLIvgUy4KEkkEEEDBl9ay9n3vsP37eeURBG4w0FbW/L67QhQwGwdCmEg7MP+mh9dntpcEAACgNvG2LHAbmj+T2h5Ny5cuXLlo7WOSGrw/boMqiDsVnd1/3fyqlSsFcUX5S1stbtosHGaAfJL5Aem/DEcJytPmWPWEkkkED01wGuITBRe8+e4ziKW4ym11lxcLS5cIBhx5fqI4c5Q/5T46iODK7Rk+8EGkpOHw3L6XLlxZcehcub6jowQycD0lcxyGHv+p60w6rusrza6IJTkmu5ym/mWr7hnwy+RdhB+SGqoNy+yJF5sxB6I3KwLb2DT7wK89n9uz3WClrJvTPn1GzLhDEu1eXsRyLimPG7A33ESazJ2fHUCsDpjA7PnPv4Lly+hh6FugtUFeCU+cxYq+ZTIzxj8TKdpX7mZV/0fhAwZV5v+UElWgKPpKlSjJ4FkbVZs2+0s1bYoYCp+2bfeVcoqLAYPzAbBOzBuX1uX5CGAV66uwTUVcOHBEB2YoWtbwikZ8DQcHQJnFai3K9PjTyMYn9Cf0+3RZfUZZJIXZWUNM1lAhg2uoXB1vbhD9wo1c5eAgCOAgDQJUrpX1WoiF6Bc54HuZqEQe3qmZq8AyqB5NX2Zgw3qH2mohxW/iCFiMuX4lqXh3A03mB9ol9YaLoXfmIiUqugR2F+6q/GH2g2WZPGWGQjszWZdLubRalHmfxKekN5P7SqqO9n2mO6dYJ65ZQrxy0+xUrLgvNV+WF0Q4CpUr+Csy0H2av4+8Cw4JldOlkJo5GNIhpPJUqgCbXfeUwfd+hlcWXun2lRcXZowGwTs9Fx2rjG637ZQz1YoyyzVgpcjKUbJ4h6BM82vuU2f17S5cMupLwEw7m6r+iWYn2ofeJVXej/TFlZaZ/vCCMqZU2+JUBTYVKlSv4eiUpGHK1+vvMx6QZip6VkBDsJtkN2j7E4cvjXKEItdK0DCx1ikgPMdWNW4bi/wART8k5kUq59oc6K8xe9dU/MyN72Mu4l3UQr9oBhllovES8zTeuCrSu7F2TfE0sSliaUFVbzk+5/Fqh0QPYlwgiUx9eylsF2leIbaEWVVwDUQEC4ZHO/rpczJf3X4/uMXBqX2LFcMwS3aW7TswzaCJaS0xmUCg1kZSPQ/IuX/E20VYr3mFBZBDqCuCHEJoQAyrCqtAas2DOTXtevPULQpQd1p/ftEatLXljaXBlT3xF11vS7EoIqJ34oaTtLT1C9mz8/wATcqui4pspUD1mMiuD0fQfSjUggGIyuJSv8Fp3fqVLlw7kvw3Rn40+ZZZcuXKA8ZlgPQen2JjmhKCXusMseUMSmB7GH+JTEKGRAjtllTLYMEWYs9OEG2doily/Y5FL7zK4dkT4IktM5UJeKXs6/EGCLmbW6KlTKFX1YuoXDiT/AMRiynZWBJ/v/ZG4tZpaJiYQsW09+k9dFEoJ3orZVE1pRWgV7qY+5D+GvtFhjeHcfiJ0UREu9de9yuYdYNwZoxZ6QVYyJDa6Wy8xDhMUKIehNUTL4vz5INX5/HjrA9B7l/eZy6p2ZRFRO9L2C2YTYsJ5Si9rzD7PdwZfRcvwX9ZcHsVqUEXX0bYL+WJBx2X21llVbXdmWK2VJmVIbIKZrg1QWTMVy7XXpZe+MaVVLx3/AH7QYaGXp48KLpFHGv2uPMuqYYYJQSx1mqVEpGX3Hhi9t9wmMWcf3StBuQVKcZ5QP1KIWbCoASHcGXL+svtFOpMF078CN0Nth6BCCCMiokp0dGU7zMQZCZCMuKKwc7Rs5jCxYsfD4u5d39eOplIWvcmqmVfaWBKCUk78SpuVClauehgmiMPQZa27yqjJfDdp95gCt0tR6lN2giQIt233gIQdEZcv6e9gR7Dy/qIJa5BVhAQggi5CWSzw2QcZhtCzVEsrALV1xESraxYsWLBis5cq0TRTMXl3fnycZUoNtf8AsvEuGrmNC/WKDXBl656BALu+09HSyyywwwwzah+GHxpFqdo63qwV7DunrxL+l1z+jnt84iLXae3Y9sQIECBLCPR2QabGLF5JUUL5hcbx+7eOFtW5cWLFizTMfc9Pg/XlCNy/ISsMIax8UfWGWSWKKXHMPmIqyiyjQCak03bq6PcmPSZFXH0QqMssvQZYYYFHPDr2eZWoJm2Oaf1L7fSIcrse4f8AsCBAhLj0CvwGRywt0xhXSIu89YTV7nTwE1E9SLAQBU0BrCNLD5X+rpfkUGYY+cwbjlIr2hLMDwmRDDlV4iRnNx18wsZggFL3xL3PQoYqP5jD196Mwk5+8WlzsR9tIpqRlhhh6DDNXWDCMDOCsHPc7fSMv4UO9whLixYwvgIBlgcy6sISpUdQD6k/WiKRAByWaYlKX5aTUF3Ny24W1LEuO5EZ/wCEf3CiqbmVdIf+wn/oINA5zQv7wGoIrooYYxMOVx6RYAXoEJcvG6NfxDAThVpb7yhxnBABRiBweQYRl5/6Ce+0UGKCEpIc1dBjAwqYCBDS3GHKbFFNo9sYegw5q3aOVr/cLFkv6K8BqLXJf66XFixhZfVCDLA5lqwMQh4alSpUqV0V2lSoHQbMX3IxK8ToFbzOfdMoCDUYMUUVWMQDWaZgHAZcBSGitsIWse1RawxtGka7R6CaOF/j6NweDHyZr30jhR21lxYsWX1QAtgC3K1gxCEOleCvHUCBExGbdp6P/Tx1N/VgfL7wYoopU2RAFxNkXKsPEXB/MHYXALKgZoj2xFNIxtHshS+9/wAv0dYjrnln3z9/MWLFi9Q0Blgi3KghA82pXQgQYl4nIM8mfIIW8DLDEG/hmKKKKVOI4ZlagBcaohKFBc1AcVNMJVdEY2iP3YXf0dShofcdkj3CdHB29+0WL1BVBbDIs/hKIECHnBAgQIMTZwNfR1/MLAkvxguquw3+yZSIiajBiiilER6wgDEsFRmpHtWMVbA8zFtDaRS/TeUANpX0gSPmDycMIfhnyH7m/QFUFsM0X+EqgQISulda6VK8IQIECBBiH5hi8r1rPkVN1pif7pigwYoMQ0jLWaNsJluSUuIjlmjbGhNDB6/TtsbRhB+2X3NIOK7ZAejDNGX2mCBAgQ6V5RKhAgh0BiGXict6Byfl8kjyyICqhb37DBgwYMGURTeUasIwRGNIAtqBMjVMvLv9QCwto4CMmW42e57cdAIECBKgSutSutdQgQIdAdAYhlgYCDuP9PlIQ5V35e6ZQEDSOEgwYMGD0Kt4hvBEwIB0lRdjn6gXp7RwEQIrg0e57cSoggQIECB0qVKlSpUqV0CBAgdQOgMQzju56YfnyqiW+tA07P3BgwYMGDFUo3lcDoF+ZtABRglfTIUAtV0ImSLti3PpxKoIIECBAlSpUqVKlSpUqBAgQPAAQ4TEwxHGQRg6EEe5flCgCOEd4gZL1DuO0HNVBgwYMGKGLjS0Z7T+4HgtA0Pp1CAWq6EbsrP+NJVBBBCCAgdFSpUqVKlSpUCBCDwCycMwMEGspW917P8AXmFlXa0z9+Im4OjL0YMGDAzPs3BaAKRsHq3hEgKAKAlfTBwFarVEoiNkf5iHAcMJ2ZdpOBDkfEIPAFSpUqVKldAgeIDycMxQ6way1K4A9cP4PMqKlXCFjLZG27fZD/nP6h6n6GD4KnabdUr6izSJJxnH4nbg8EBgRjXBHrUqW4idpUqVAgQPEFZOGYpqQZlrtKfxZ+P4qvYcjgZGMEQDv4QIdGPhIdKHUGLZSWckrsvvMNEg4IfBOTimKakOY5F4Fp7ywE3/AImpsX6D/VkUaSk1HqAgdGPiJfgIMvoMQwib9frEpQ+jFfoTUM8XCJNaHLBhl4uUjXJj9fxVRE/Pa7jvESJSajDB1Y+Eh1OhCX0OqxiYaSHF2R+k9zWX1vZh1nOz/CX/AH/FVKl4Zvm3ripYajA6sfoLl9Fi6d3Qow5IDyyA7/8AC/xuLKJg6kZlmw6P9dHo+E8q5cuLFi8E1x8aB6Tj63//2Q==)
Exemplo de uma seção transversal dasuperfÍcie K3 no espaço 3, semelhante a um modelo da Utah State University e da University of Missouri-St. Os matema¡ticos de Louis costumavam examinar dualidades das cordas entre a teoria F e a teoria hetera³tica em oitoDimensões . Crédito: USU
Simplificando, a teoria das cordas éum manãtodo proposto para explicar tudo. Na verdade, não hánada simples nisso. A teoria das cordas éuma estrutura tea³rica da física que descreve objetos fibrosos vibrantes e unidimensionais chamados "cordas", que se propagam atravanãs do espaço e interagem entre si. Pea§a por pea§a, mentes enanãrgicas estãodescobrindo e decifrando cordas fundamentais do universo fasico usando modelos matema¡ticos. Entre esses intranãpidos exploradores estãoos matema¡ticos da Universidade do Estado de Utah, Thomas Hill, e seu mentor, Andreas Malmendier.
Com o colega Adrian Clingher, da University of Missouri-St. Louis, a equipe publicou descobertas sobre dois ramos da teoria das cordas no artigo, "A dualidade entre a teoria F e a corda hetera³tica em D = 8 com duas linhas de Wilson", na edição online de 7 de agosto de 2020 de Letters in Mathematical Physics . O trabalho dos pesquisadores da USU éapoiado por uma bolsa da Simons Foundation.
"Na³s estudamos uma familia especial desuperfÍcies K3 -superfÍcies complexas compactas e conectadas de dimensão 2 - que são ferramentas geomanãtricas importantes para a compreensão de simetrias de teorias físicas", disse Hill, que se formou no Programa de Honras da USU com bacharelado em matemática em 2018 e completou um mestrado em matemática na primavera passada. "Neste caso, esta¡vamos examinando a dualidade das cordas entre a teoria F e a teoria hetera³tica das cordas em oitoDimensões ."
Hill diz que a equipe provou que assuperfÍcies K3 investigadas admitem quatro maneiras exclusivas de fatiar assuperfÍcies como fibrações elapticas Jacobianas, formações de fibras em forma de toro. Os pesquisadores construaram equações explacitas para cada uma dessas fibrações.
"Uma parte importante desta pesquisa envolve a identificação de certos blocos de construção geomanãtrica, chamados de 'divisores", dentro de cadasuperfÍcie K3 ", diz ele." Usando esses divisores, informações geomanãtricas cruciais são então codificadas em um gra¡fico abstrato. "
Usando um gra¡fico abstrato, os pesquisadores da Utah State University identificam
divisores dentro de cadasuperfÍcie K3 para examinar simetrias variadas. As
diferentes fibrações elapticas Jacobianas correspondem a cores especaficas de
um subconjunto conectado dos nosdo gra¡fico. As simetrias do gra¡fico e as
possaveis cores dos nossão cruciais para a compreensão das
simetrias das teorias físicas subjacentes. Crédito: Malmendier / Hill, USU
Este processo, diz Hill, permite aos pesquisadores investigar simetrias de teorias físicas subjacentes demonstradas pelo gra¡fico.
"Vocaª pode pensar nesta familia desuperfÍcies como um pedaço de pa£o e cada fibração como uma 'fatia' desse pa£o", diz Malmendier, professor associado do Departamento de Matema¡tica e Estatastica da USU. "Ao examinar a sequaªncia de fatias, podemos visualizar e entender melhor o pa£o inteiro."
O empreendimento descrito no artigo, diz ele, representa horas de trabalho a¡rduo de "papel e la¡pis" para provar teoremas de cada uma das quatro fibrações, seguido por empurrar cada teorema atravanãs de fa³rmulas alganãbricas difaceis.
"Para a última parte deste processo, usamos o software Maple e o pacote especializado de geometria diferencial desenvolvido na USU, que simplificou nossos esforços computacionais", disse Malmendier.