PT symmetry, pattern formation, and finite-density QCD
Moses A. Schindler, Stella T. Schindler, Michael C. Ogilvie
Abstract
Abstract A longstanding issue in the study of quantum chromodynamics (QCD) is its behavior at nonzero baryon density, which has implications for many areas of physics. The path integral has a complex integrand when the quark chemical potential is nonzero and therefore has a sign problem, but it also has a generalized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">PT</mml:mi> </mml:mrow> </mml:math> symmetry. We review some new approaches to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">PT</mml:mi> </mml:mrow> </mml:math> -symmetric field theories, including both analytical techniques and methods for lattice simulation. We show that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">PT</mml:mi> </mml:mrow> </mml:math> -symmetric field theories with more than one field generally have a much richer phase structure than their Hermitian counterparts, including stable phases with patterning behavior. The case of a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">PT</mml:mi> </mml:mrow> </mml:math> -symmetric extension of a φ 4 model is explained in detail. The relevance of these results to finite density QCD is explained, and we show that a simple model of finite density QCD exhibits a patterned phase in its critical region.