Local and Nonlocal Thermal Field Theory

Abstract: Firstly, nonlocal field theories will be motivated, primarily in the gravity sector. We discuss how nonlocal theories of gravity can circumvent typical problems of finitely-many higher derivative theories and can, among other things, be either ghostfree and (potentially) renormalizable and yield a non-singular Newtonian potential. Afterwards we motivate finite temperature field theory, also known as thermal field theory, and study the thermodynamic behavior of both a local and a nonlocal scalar field theory. We compute (primarily leading-order) thermal corrections to the partition function for in low- and high- temperature expansions and calculate the thermal mass which is acquired through continuous interactions with the heat bath. We prove that the nonlocality does not contribute to the partition function of the free nonlocal theory. The presence of the nonlocality can only be noticed through interactions and we conclude that the partition function of the local and the nonlocal scalar theory are fundamentally different when interactions are included. We explain from both a mathematical and physical point of view why the nonlocality can only be noticed at the level of interactions and conclude that this cannot be generalized to arbitrary nonlocal modifications -- only those which do not introduce new poles in the propagator. We study whether our results can be reconciled with the stringy thermal duality and the conjectured Hagedorn phase and conclude that the former is violated, while Hagedorn behavior emerges in the high temperature expansion of the nonlocal scalar theory. We will interpret all these results.