Once more on the Witten index of 3d supersymmetric YM-CS theory

The problem of counting the vacuum states in the supersymmetric 3d Yang-Mills-Chern-Simons theory is reconsidered. We resolve the controversy between its original calculation by Witten at large volumes and the calculation based on the evaluation of the effective Lagrangian in the small volume limit. We show that the latter calculation suffers from uncertainties associated with the singularities in the moduli space of classical vacua where the Born-Oppenheimer approximation breaks down. We also show that these singularities can be accurately treated in the Hamiltonian Born-Oppenheimer method, where one has to match carefully the effective wave functions on the Abelian valley and the wave functions of reduced non-Abelian QM theory near the singularities. This gives the same result as original Witten's calculation.Comment: 27 page

Analytic philosophy for biomedical research: the imperative of applying yesterday's timeless messages to today's impasses

The mantra that "the best way to predict the future is to invent it" (attributed to the computer scientist Alan Kay) exemplifies some of the expectations from the technical and innovative sides of biomedical research at present. However, for technical advancements to make real impacts both on patient health and genuine scientific understanding, quite a number of lingering challenges facing the entire spectrum from protein biology all the way to randomized controlled trials should start to be overcome. The proposal in this chapter is that philosophy is essential in this process. By reviewing select examples from the history of science and philosophy, disciplines which were indistinguishable until the mid-nineteenth century, I argue that progress toward the many impasses in biomedicine can be achieved by emphasizing theoretical work (in the true sense of the word 'theory') as a vital foundation for experimental biology. Furthermore, a philosophical biology program that could provide a framework for theoretical investigations is outlined

Two loop virtual corrections to b→(d,s)ℓ+ℓ−b\rightarrow (d,s)\ell ^+\ell ^- b → ( d , s ) ℓ + ℓ - and c→uℓ+ℓ−c\rightarrow u\ell ^+\ell ^- c → u ℓ + ℓ - for arbitrary momentum transfer

Abstract Non-factorizable two loop corrections to heavy to light flavor changing neutral current transitions due to matrix elements of current–current operators are calculated analytically for arbitrary momentum transfer. This extends previous work on $$b\rightarrow (d,s)\ell ^+\ell ^-$$ b → ( d , s ) ℓ + ℓ - transitions. New results for $$c\rightarrow u\ell ^+\ell ^-$$ c → u ℓ + ℓ - transitions are presented. Recent work on polylogarithms is used for the master integrals. For $$b\rightarrow s\ell ^+\ell ^-$$ b → s ℓ + ℓ - transitions, the corrections are most significant for the imaginary parts of the effective Wilson coefficients in the large hadronic recoil range. Analytical results and ready-to-use fitted results for a specific set of parameters are provided