Higher gauge theory -- differential versus integral formulation

The term higher gauge theory refers to the generalization of gauge theory to a theory of connections at two levels, essentially given by 1- and 2-forms. So far, there have been two approaches to this subject. The differential picture uses non-Abelian 1- and 2-forms in order to generalize the connection 1-form of a conventional gauge theory to the next level. The integral picture makes use of curves and surfaces labeled with elements of non-Abelian groups and generalizes the formulation of gauge theory in terms of parallel transports. We recall how to circumvent the classic no-go theorems in order to define non-Abelian surface ordered products in the integral picture. We then derive the differential picture from the integral formulation under the assumption that the curve and surface labels depend smoothly on the position of the curves and surfaces. We show that some aspects of the no-go theorems are still present in the differential (but not in the integral) picture. This implies a substantial structural difference between non-perturbative and perturbative approaches to higher gauge theory. We finally demonstrate that higher gauge theory provides a geometrical explanation for the extended topological symmetry of BF-theory in both pictures.Comment: 26 pages, LaTeX with XYPic diagrams; v2: typos corrected and presentation improve

Non-Abelian Wilson Surfaces

A definition of non-abelian genus zero open Wilson surfaces is proposed. The ambiguity in surface-ordering is compensated by the gauge transformations.Comment: JHEP Latex, 10 pages, 6 figures; v2, refs and comments added in sec.

Fluctuation theorems for excess and housekeeping heats for underdamped systems

We present a simple derivation of the integral fluctuation theorems for excess housekeeping heat for an underdamped Langevin system, without using the concept of dual dynamics. In conformity with the earlier results, we find that the fluctuation theorem for housekeeping heat holds when the steady state distributions are symmetric in velocity, whereas there is no such requirement for the excess heat. We first prove the integral fluctuation theorem for the excess heat, and then show that it naturally leads to the integral fluctuation theorem for housekeeping heat. We also derive the modified detailed fluctuation theorems for the excess and housekeeping heats.Comment: 10 pages. Section 3 contains further generalization

Output Costs, Currency Crises, and Interest Rate Defense of a Peg

Central banks typically raise short-term interest rates to defend currency pegs. Higher interest rates, however, often lead to a credit crunch and an output contraction. We model this trade-off in an optimizing, first-generation model in which the crisis may be delayed but is ultimately inevitable. We show that higher interest rates may delay the crisis, but raising interest rates beyond a certain point may actually bring forward the crisis due to the large negative output effect. The optimal interest rate defense involves setting high interest rates (relative to the no defense case) both before and at the moment of the crisis. Furthermore, while the crisis could be delayed even further, it is not optimal to do so.

Living with the Fear of Floating: An Optimal Policy Perspective

As documented in recent studies, developing countries (classified by the IMF as floaters or managed floaters) are extremely reluctant to allow for large nominal exchange rate fluctuations. This 'fear of floating' is reflected in the fact that, in spite of being subject to larger shocks, developing countries exhibit lower exchange rate variability and higher reserve variability than developed countries. Moreover, there is a positive correlation between changes in the exchange rate and interest rates and a negative correlation between both changes in reserves and the exchange rate and changes in interest rates and reserves. We build a simple model that rationalizes these key features as the outcome of an optimal policy response to monetary shocks. The model incorporates three key frictions: an output cost of nominal exchange rate fluctuations, an output cost of higher interest rates to defend the currency, and a fixed cost of intervention.