Rigid Supersymmetric Theories in Curved Superspace

We present a uniform treatment of rigid supersymmetric field theories in a curved spacetime $\mathcal{M}$, focusing on four-dimensional theories with four supercharges. Our discussion is significantly simpler than earlier treatments, because we use classical background values of the auxiliary fields in the supergravity multiplet. We demonstrate our procedure using several examples. For $\mathcal{M}=AdS_4$ we reproduce the known results in the literature. A supersymmetric Lagrangian for $\mathcal{M}=\mathbb{S}^4$ exists, but unless the field theory is conformal, it is not reflection positive. We derive the Lagrangian for $\mathcal{M}=\mathbb{S}^3\times \mathbb{R}$ and note that the time direction $\mathbb{R}$ can be rotated to Euclidean signature and be compactified to $\S^1$ only when the theory has a continuous R-symmetry. The partition function on $\mathcal{M}=\mathbb{S}^3\times \S^1$ is independent of the parameters of the flat space theory and depends holomorphically on some complex background gauge fields. We also consider R-invariant $\mathcal{N}=2$ theories on $\mathbb{S}^3$ and clarify a few points about them.Comment: 26 pages, uses harvmac; v2 with added reference

On form factors in N=4 sym

In this paper we study the form factors for the half-BPS operators $\mathcal{O}^{(n)}_I$ and the $\mathcal{N}=4$ stress tensor supermultiplet current $W^{AB}$ up to the second order of perturbation theory and for the Konishi operator $\mathcal{K}$ at first order of perturbation theory in $\mathcal{N}=4$ SYM theory at weak coupling. For all the objects we observe the exponentiation of the IR divergences with two anomalous dimensions: the cusp anomalous dimension and the collinear anomalous dimension. For the IR finite parts we obtain a similar situation as for the gluon scattering amplitudes, namely, apart from the case of $W^{AB}$ and $\mathcal{K}$ the finite part has some remainder function which we calculate up to the second order. It involves the generalized Goncharov polylogarithms of several variables. All the answers are expressed through the integrals related to the dual conformal invariant ones which might be a signal of integrable structure standing behind the form factors.Comment: 35 pages, 7 figures, LATEX2

Minimal distances between SCFTs

My work is supported by DOE grant DE-FG02-96ER40959