4D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> </mml:math> 2 SCFTs and spin chains
Elli Pomoni
Abstract
Abstract This is the writeup of the lectures given at the Winter School ‘YRISW 2018’ to appear in a special issue of J. Phys. A: Math. Theor. In the first part of these lecture notes we review some important facts about 4D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> SCFTs. We begin with basic textbook material, the supersymmetry algebra and its massless representations and the construction of Lagrangians using superspace. Then we turn to more modern topics, the study of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> SCA and its representation theory. Our intention is to understand how much we can learn from representation theory alone, even about the dynamics of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> SCFTs. In the second part of the notes we use these tools to construct spin chains for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> SCFTs, the spectral problem of which computes anomalous dimensions of local operators. We discuss their novel features comparing them with their counterparts in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:math> SYM and search for possible integrability structures that emerge.