LEADER 03540nam 2200481 450 001 996466739903316 005 20220125114530.0 010 $a981-16-1703-1 024 7 $a10.1007/978-981-16-1703-4 035 $a(CKB)4100000011955235 035 $a(DE-He213)978-981-16-1703-4 035 $a(MiAaPQ)EBC6637095 035 $a(Au-PeEL)EBL6637095 035 $a(OCoLC)1255465377 035 $a(PPN)269153101 035 $a(EXLCZ)994100000011955235 100 $a20220125d2021 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aYang-Baxter deformation of 2D non-linear Sigma models $etowards applications to AdS/CFT /$fKentaroh Yoshida 205 $a1st ed. 2021. 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$dİ2021 215 $a1 online resource (XII, 70 p. 2 illus.) 225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v40 311 $a981-16-1702-3 327 $aIntegrable Non-linear Sigma Models in (1+1)-dimensions -- Yang-Baxter Sigma Models -- Recent Progress on Yang-Baxter Deformation and Generalized Supergravity. 330 $aIn mathematical physics, one of the fascinating issues is the study of integrable systems. In particular, non-perturbative techniques that have been developed have triggered significant insight for real physics. There are basically two notions of integrability: classical integrability and quantum integrability. In this book, the focus is on the former, classical integrability. When the system has a finite number of degrees of freedom, it has been well captured by the Arnold?Liouville theorem. However, when the number of degrees of freedom is infinite, as in classical field theories, the integrable structure is enriched profoundly. In fact, the study of classically integrable field theories has a long history and various kinds of techniques, including the classical inverse scattering method, which have been developed so far. In previously published books, these techniques have been collected and well described and are easy to find in traditional, standard textbooks. One of the intriguing subjects in classically integrable systems is the investigation of deformations preserving integrability. Usually, it is not considered systematic to perform such a deformation, and one must study systems case by case and show the integrability of the deformed systems by constructing the associated Lax pair or action-angle variables. Recently, a new, systematic method to perform integrable deformations of 2D non-linear sigma models was developed. It was invented by C. Klimcik in 2002, and the integrability of the deformed sigma models was shown in 2008. The original work was done for 2D principal chiral models, but it has been generalized in various directions nowadays. In this book, the recent progress on this Yang?Baxter deformation is described in a pedagogical manner, including some simple examples. Applications of Yang?Baxter deformation to string theory are also described briefly. . 410 0$aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v40 606 $aYang-Baxter equation 615 0$aYang-Baxter equation. 676 $a530.143 700 $aYoshida$b Kentaroh$0880302 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466739903316 996 $aYang-Baxter deformation of 2D non-linear Sigma models$92585977 997 $aUNISA