Perturbing topological field theories

Abstract

The abelian Chern-Simons theory is perturbed by introducing local gauge-invariant interaction terms depending on the curvature. The computation of the correlation function γ 1 dx µ A µ γ 2 dy ν A ν for two smooth closed nonintersecting curves γ 1 , γ 2 is reported up to four loops and is shown to be unaffected by radiative corrections. This result ensures the stability of the linking number of γ 1 and γ 2 with respect to the local perturbations which may be added to the Chern-Simons action.

Shut-down control with energy feedback and energy dissipation for MMC-HVDC systems

“…Each arm consists of two parts, that is, N tot series-connected identical SMs and an arm inductor (L 0 ). As shown in Figure 1, each SM is composed of two IGBTs (T1, T2), two free-wheeling diodes (D1, D2), a capacitor (C 0 ), and an internal resistor R d [21,22]. U c and U SM are the voltages of C 0 and the SM, respectively.…”

“…Similar to the chopper resistor in the doubly fed induction generator [20], the SM capacitors could be discharged by switching in the suitably dimensioned parallel resistors, which needs to install additional devices. In addition, the SM capacitors could also be discharged only by the SM internal resistor [21]. However, for the aforementioned shut-down schemes, the biggest drawback is the fact that the total energy stored in the SM capacitors is dissipated (wasted) by the resistors.…”

On the complete Seiberg-Witten map for theories with topological terms

“…In [13] actions as (3.7) were studied. It was then shown that even these non-power-counting interactions cannot change the topological character of the CS theory, at least, perturbatively.…”

“…This equation can be solved for ∧ f ijk as a series in powers of 13) where the upper index r designates the power in . The first term in the order…”

Linking observables in perturbed topological field theories

“…which is zero owing to the fact that the two surfaces Σ and Σ ′ never intersect, so that x − y never vanishes. Moreover, as done in [14], we can adopt a more rigorous treatment by regularizing the n-dimensional delta functions with coinciding arguments through the point splitting procedure already used by Polyakov [9] δ ǫ (z 1 − z 2 ) = 1…”