MSc defence: Alexander T. Kristensson – University of Copenhagen

MSc defence: Alexander T. Kristensson

Title: Thermodynamics of Maximally Supersymmetric Yang-Mills Theory at Finite N

Abstract: This thesis investigates the thermodynamics of maximally supersymmetric Yang-Mills theory. On a compact space RxS^3, this theory exhibits a confinement/deconfinement phase transition mimicking that of QCD. The present work focuses on the extension to finite values of N, by explicitly evaluating the partition functions in the smaller subsectors of su(q), sl(2) and su(2|3). The several expressions that we discover at zero coupling are exact to all orders in x=e^(-1/T), and extends the results found in the literature. In the su(2) sector, the zeros of the partition functions in the complex temperature plane appears to condensate in two arcs, pinching the real axis at the temperature of the planar phase transition. This hints at a Lee-Yang type of behaviour. We also identify a restriction of the partition function that exhibits many of the crucial features of the full case. Furthermore, using restricted Schur polynomials, a generating formula for the one-loop correction to the partition function in the su(2) sector is derived and evaluated at small orders of x.