A solvable quantum field theory with asymptotic freedom in (3+1) dimensions
Paul Romatschke
Abstract
Recently, Ai, Bender and Sarkar gave a prescription on how to obtain [Formula: see text]-symmetric field theory results from an analytic continuation of Hermitian field theories. We perform this analytic continuation for the massless (critical) [Formula: see text] model with quartic interaction in (3+1) dimensions. In the large-[Formula: see text] limit, this theory is exactly solvable, and has negative [Formula: see text]-function in the ultraviolet, and a stable bound state in the infrared. The coupling diverges at a scale [Formula: see text], but can be continued into the far infrared. At finite temperature, the theory exhibits two phases separated by a second-order phase transition near [Formula: see text].
Topics & Concepts
PhysicsAnalytic continuationAsymptotic freedomQuartic functionMathematical physicsQuantum field theoryBeta function (physics)Field theory (psychology)ContinuationQuantum mechanicsField (mathematics)Massless particleHermitian matrixThermal quantum field theoryQuantum gravityQuantumPure mathematicsMathematical analysisGauge theoryMathematicsComputer scienceProgramming languageBlack Holes and Theoretical PhysicsQuantum Chromodynamics and Particle InteractionsAdvanced Operator Algebra Research