LEADER 04753nam 22006495 450 001 996466826003316 005 20200705150151.0 010 $a3-030-05085-8 024 7 $a10.1007/978-3-030-05085-6 035 $a(CKB)4100000007610958 035 $a(DE-He213)978-3-030-05085-6 035 $a(MiAaPQ)EBC5919210 035 $z(PPN)258846585 035 $a(PPN)23500135X 035 $a(EXLCZ)994100000007610958 100 $a20190211d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 13$aAn Introduction to Two-Dimensional Quantum Field Theory with (0,2) Supersymmetry$b[electronic resource] /$fby Ilarion V. Melnikov 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (XV, 482 p. 90 illus.) 225 1 $aLecture Notes in Physics,$x0075-8450 ;$v951 311 $a3-030-05083-1 327 $aPreface -- (0,2) Fundamentals.-Conformalities -- Landau-Ginzburg theories -- Heterotic Non-linear Sigma Models -- Gauged Linear Sigma Models. 330 $aThis book introduces two-dimensional supersymmetric field theories with emphasis on both linear and non-linear sigma models. Complex differential geometry, in connection with supersymmetry, has played a key role in most developments of the last thirty years in quantum field theory and string theory. Both structures introduce a great deal of rigidity compared to the more general categories of non-supersymmetric theories and real differential geometry, allowing for many general conceptual results and detailed quantitative predictions. Two-dimensional (0,2) supersymmetric quantum field theories provide a natural arena for the fruitful interplay between geometry and quantum field theory. These theories play an important role in string theory and provide generalizations, still to be explored fully, of rich structures such as mirror symmetry. They also have applications to non-perturbative four-dimensional physics, for instance as descriptions of surface defects or low energy dynamics of solitonic strings in four-dimensional supersymmetric theories. The purpose of these lecture notes is to acquaint the reader with these fascinating theories, assuming a background in conformal theory, quantum field theory and differential geometry at the beginning graduate level. In order to investigate the profound relations between structures from complex geometry and field theory the text begins with a thorough examination of the basic structures of (0,2) quantum field theory and conformal field theory. Next, a simple class of Lagrangian theories, the (0,2) Landau-Ginzburg models, are discussed, together with the resulting renormalization group flows, dynamics, and symmetries. After a thorough introduction and examination of (0,2) non-linear sigma models, the text introduces linear sigma models that, in particular, provide a unified treatment of non-linear sigma models and Landau-Ginzburg theories. Many exercises, along with discussions of relevant mathematical notions and important open problems in the field, are included in the text. 410 0$aLecture Notes in Physics,$x0075-8450 ;$v951 606 $aQuantum field theory 606 $aString theory 606 $aMathematical physics 606 $aPhysics 606 $aElementary particles (Physics) 606 $aQuantum Field Theories, String Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P19048 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aElementary Particles, Quantum Field Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P23029 615 0$aQuantum field theory. 615 0$aString theory. 615 0$aMathematical physics. 615 0$aPhysics. 615 0$aElementary particles (Physics). 615 14$aQuantum Field Theories, String Theory. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aMathematical Methods in Physics. 615 24$aElementary Particles, Quantum Field Theory. 676 $a539.725 700 $aMelnikov$b Ilarion V$4aut$4http://id.loc.gov/vocabulary/relators/aut$01059933 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466826003316 996 $aAn Introduction to Two-Dimensional Quantum Field Theory with (0,2) Supersymmetry$92509717 997 $aUNISA